TSTP Solution File: PUZ028-5 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ028-5 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:10:57 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : PUZ028-5 : TPTP v8.1.0. Released v2.0.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 18:14:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(familiar_type, type, (
% 0.12/0.40 familiar: ( $i * $i ) > $o)).
% 0.12/0.40 tff(five_type, type, (
% 0.12/0.40 five: $i)).
% 0.12/0.40 tff(two_type, type, (
% 0.12/0.40 two: $i)).
% 0.12/0.40 tff(not_familiar_type, type, (
% 0.12/0.40 not_familiar: ( $i * $i ) > $o)).
% 0.12/0.40 tff(six_type, type, (
% 0.12/0.40 six: $i)).
% 0.12/0.40 tff(four_type, type, (
% 0.12/0.40 four: $i)).
% 0.12/0.40 tff(one_type, type, (
% 0.12/0.40 one: $i)).
% 0.12/0.40 tff(three_type, type, (
% 0.12/0.40 three: $i)).
% 0.12/0.40 tff(after_type, type, (
% 0.12/0.40 after: ( $i * $i ) > $o)).
% 0.12/0.40 tff(person_type, type, (
% 0.12/0.40 person: $i > $o)).
% 0.12/0.40 tff(1,assumption,(not_familiar(four, six)), introduced(assumption)).
% 0.12/0.40 tff(2,assumption,(familiar(one, six)), introduced(assumption)).
% 0.12/0.40 tff(3,assumption,(not_familiar(three, six)), introduced(assumption)).
% 0.12/0.40 tff(4,assumption,(not_familiar(one, six)), introduced(assumption)).
% 0.12/0.40 tff(5,assumption,(not_familiar(one, four)), introduced(assumption)).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[X3: $i, X2: $i, X1: $i] : refl(((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2))) <=> ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[X3: $i, X2: $i, X1: $i] : rewrite((((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X1, X3))) <=> ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : (((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X1, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 tff(11,axiom,(![X3: $i, X2: $i, X1: $i] : (((~not_familiar(X1, X2)) | (~not_familiar(X2, X3))) | (~not_familiar(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','three_not_familiar')).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.40 tff(14,plain,(
% 0.12/0.40 ![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (((~not_familiar(one, six)) | (~not_familiar(four, six)) | (~not_familiar(one, four))) <=> ((~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(four, six)) | (~not_familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(four, six)) | (~not_familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(four, six)) | (~not_familiar(one, four)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, four)) | (~not_familiar(four, six)) | (~not_familiar(one, six))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[21, 15, 1, 5, 4])).
% 0.19/0.40 tff(23,plain,((~not_familiar(four, six)) | (~not_familiar(one, four)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (~not_familiar(one, four)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[23, 1, 4])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small)) <=> ![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small)) <=> ![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[Small: $i, Medium: $i, Large: $i] : trans(monotonicity(rewrite((after(Large, Small) | (~after(Large, Medium))) <=> ((~after(Large, Medium)) | after(Large, Small))), (((after(Large, Small) | (~after(Large, Medium))) | (~after(Medium, Small))) <=> (((~after(Large, Medium)) | after(Large, Small)) | (~after(Medium, Small))))), rewrite((((~after(Large, Medium)) | after(Large, Small)) | (~after(Medium, Small))) <=> ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))), (((after(Large, Small) | (~after(Large, Medium))) | (~after(Medium, Small))) <=> ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((after(Large, Small) | (~after(Large, Medium))) | (~after(Medium, Small))) <=> ![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,axiom,(![Small: $i, Medium: $i, Large: $i] : ((after(Large, Small) | (~after(Large, Medium))) | (~after(Medium, Small)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity_of_order')).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.40 tff(32,plain,(
% 0.19/0.40 ![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(skolemize,[status(sab)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (after(two, three) <=> after(two, three)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,axiom,(after(two, three)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','order2')).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (after(two, three)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (after(one, two) <=> after(one, two)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(38,axiom,(after(one, two)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','order1')).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (after(one, two)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(two, three)) | (~after(one, two)) | after(one, three))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(two, three)) | (~after(one, two)) | after(one, three))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(two, three)) | (~after(one, two)) | after(one, three))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(two, three)) | (~after(one, two)) | after(one, three)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (after(one, three)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 39, 36, 33])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (after(three, four) <=> after(three, four)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,axiom,(after(three, four)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','order3')).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (after(three, four)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, four)) | (~after(one, three)) | after(one, four))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(three, four)) | (~after(one, three)) | after(one, four))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, four)) | (~after(one, three)) | after(one, four))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(three, four)) | (~after(one, three)) | after(one, four)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (after(one, four)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 46, 33, 43])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl(((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) <=> ![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) <=> ((~person(X)) | not_familiar(X, Y) | familiar(X, Y))), ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) <=> (((~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~person(Y))))), rewrite((((~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~person(Y))) <=> ((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))), ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) <=> ((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)))), (((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~after(X, Y))) <=> (((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~after(X, Y))))), rewrite((((~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y)) | (~after(X, Y))) <=> ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))), (((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~after(X, Y))) <=> ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~after(X, Y))) <=> ![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.41 tff(56,axiom,(![Y: $i, X: $i] : ((((familiar(X, Y) | not_familiar(X, Y)) | (~person(X))) | (~person(Y))) | (~after(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','familiar_or_not')).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.41 tff(59,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (person(four) <=> person(four)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,axiom,(person(four)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person4')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (person(four)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (person(one) <=> person(one)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,axiom,(person(one)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person1')).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (person(one)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~after(one, four)) | (~person(four)) | (~person(one)) | not_familiar(one, four) | familiar(one, four)) <=> ((~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, four)) | (~person(four)) | (~person(one)) | not_familiar(one, four) | familiar(one, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, four)) | (~person(four)) | (~person(one)) | not_familiar(one, four) | familiar(one, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four))),
% 0.19/0.41 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, four)) | (~person(four)) | (~person(one)) | not_familiar(one, four) | familiar(one, four))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(four)) | (~after(one, four)) | not_familiar(one, four) | familiar(one, four)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (not_familiar(one, four) | familiar(one, four)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 66, 63, 60, 50])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (familiar(one, four)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 24])).
% 0.19/0.41 tff(75,assumption,(not_familiar(one, three)), introduced(assumption)).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(three, six)) | (~not_familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, six)) | (~not_familiar(three, six)) | (~not_familiar(one, three)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(three, six)) | (~not_familiar(one, three)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, six)) | (~not_familiar(three, six)) | (~not_familiar(one, three))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 15, 75, 3, 4])).
% 0.19/0.41 tff(80,plain,((~not_familiar(three, six)) | (~not_familiar(one, three)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (~not_familiar(one, three)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 3, 4])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (person(three) <=> person(three)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(83,axiom,(person(three)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person3')).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (person(three)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((~after(one, three)) | (~person(three)) | (~person(one)) | not_familiar(one, three) | familiar(one, three)) <=> ((~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, three)) | (~person(three)) | (~person(one)) | not_familiar(one, three) | familiar(one, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, three)) | (~person(three)) | (~person(one)) | not_familiar(one, three) | familiar(one, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three))),
% 0.19/0.41 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, three)) | (~person(three)) | (~person(one)) | not_familiar(one, three) | familiar(one, three))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(three)) | (~after(one, three)) | not_familiar(one, three) | familiar(one, three)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (not_familiar(one, three) | familiar(one, three)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 66, 84, 60, 43])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (familiar(one, three)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 81])).
% 0.19/0.41 tff(93,assumption,(not_familiar(three, four)), introduced(assumption)).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~not_familiar(three, six)) | (~not_familiar(four, six)) | (~not_familiar(three, four))) <=> ((~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(four, six)) | (~not_familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(four, six)) | (~not_familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(four, six)) | (~not_familiar(three, four)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, six)) | (~not_familiar(three, four)) | (~not_familiar(three, six))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 15, 93, 1, 3])).
% 0.19/0.41 tff(101,plain,((~not_familiar(three, six)) | (~not_familiar(three, four)) | (~not_familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (~not_familiar(three, four)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 1, 3])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~after(three, four)) | (~person(four)) | (~person(three)) | not_familiar(three, four) | familiar(three, four)) <=> ((~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, four)) | (~person(four)) | (~person(three)) | not_familiar(three, four) | familiar(three, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, four)) | (~person(four)) | (~person(three)) | not_familiar(three, four) | familiar(three, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four))),
% 0.19/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, four)) | (~person(four)) | (~person(three)) | not_familiar(three, four) | familiar(three, four))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(three, four)) | (~person(three)) | (~person(four)) | not_familiar(three, four) | familiar(three, four)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (not_familiar(three, four) | familiar(three, four)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 84, 63, 46, 60])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (familiar(three, four)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 102])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[X3: $i, X2: $i, X1: $i] : refl(((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2))) <=> ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (^[X3: $i, X2: $i, X1: $i] : rewrite((((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X1, X3))) <=> ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : (((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X1, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.41 tff(116,axiom,(![X3: $i, X2: $i, X1: $i] : (((~familiar(X1, X2)) | (~familiar(X2, X3))) | (~familiar(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','three_familiar')).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.19/0.42 tff(119,plain,(
% 0.19/0.42 ![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[118])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(three, four)) | (~familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(three, four)) | (~familiar(one, three)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(three, four)) | (~familiar(one, three)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(three, four)) | (~familiar(one, three))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[123, 120, 110, 92, 74])).
% 0.19/0.42 tff(125,plain,((~not_familiar(four, six)) | (~not_familiar(three, six)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (~not_familiar(one, six)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 3, 1])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (after(five, six) <=> after(five, six)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(128,axiom,(after(five, six)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','order5')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (after(five, six)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (after(four, five) <=> after(four, five)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(131,axiom,(after(four, five)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','order4')).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (after(four, five)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(five, six)) | (~after(four, five)) | after(four, six))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(five, six)) | (~after(four, five)) | after(four, six))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(five, six)) | (~after(four, five)) | after(four, six))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(five, six)) | (~after(four, five)) | after(four, six)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (after(four, six)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 132, 129, 33])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, six)) | (~after(one, four)) | after(one, six))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, six)) | (~after(one, four)) | after(one, six))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, six)) | (~after(one, four)) | after(one, six))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, six)) | (~after(one, four)) | after(one, six)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (after(one, six)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 33, 136, 50])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (person(six) <=> person(six)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(142,axiom,(person(six)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person6')).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (person(six)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~after(one, six)) | (~person(six)) | (~person(one)) | not_familiar(one, six) | familiar(one, six)) <=> ((~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, six)) | (~person(six)) | (~person(one)) | not_familiar(one, six) | familiar(one, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, six)) | (~person(six)) | (~person(one)) | not_familiar(one, six) | familiar(one, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six))),
% 0.19/0.42 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, six)) | (~person(six)) | (~person(one)) | not_familiar(one, six) | familiar(one, six))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(six)) | (~after(one, six)) | not_familiar(one, six) | familiar(one, six)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (not_familiar(one, six) | familiar(one, six)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[149, 66, 143, 60, 140])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (familiar(one, six)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[150, 126])).
% 0.19/0.42 tff(152,assumption,(not_familiar(two, six)), introduced(assumption)).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(four, six)) | (~not_familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(four, six)) | (~not_familiar(two, four)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(four, six)) | (~not_familiar(two, four)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(four, six)) | (~not_familiar(two, four))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (~not_familiar(two, four)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 15, 1, 152])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, four)) | (~after(two, three)) | after(two, four))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(three, four)) | (~after(two, three)) | after(two, four))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, four)) | (~after(two, three)) | after(two, four))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(three, four)) | (~after(two, three)) | after(two, four)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (after(two, four)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[159, 36, 46, 33])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (person(two) <=> person(two)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(162,axiom,(person(two)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person2')).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (person(two)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (((~after(two, four)) | (~person(four)) | (~person(two)) | not_familiar(two, four) | familiar(two, four)) <=> ((~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, four)) | (~person(four)) | (~person(two)) | not_familiar(two, four) | familiar(two, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, four)) | (~person(four)) | (~person(two)) | not_familiar(two, four) | familiar(two, four))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four))),
% 0.19/0.42 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, four)) | (~person(four)) | (~person(two)) | not_familiar(two, four) | familiar(two, four))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(four)) | (~after(two, four)) | not_familiar(two, four) | familiar(two, four)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (not_familiar(two, four) | familiar(two, four)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[169, 163, 63, 60, 160])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (familiar(two, four)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[170, 156])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (~not_familiar(three, four)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 3, 1])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (familiar(three, four)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 172])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(three, six)) | (~not_familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(three, six)) | (~not_familiar(two, three)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(three, six)) | (~not_familiar(two, three)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(three, six)) | (~not_familiar(two, three))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (~not_familiar(two, three)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[176, 15, 152, 3])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (((~after(two, three)) | (~person(three)) | (~person(two)) | not_familiar(two, three) | familiar(two, three)) <=> ((~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, three)) | (~person(three)) | (~person(two)) | not_familiar(two, three) | familiar(two, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[179])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, three)) | (~person(three)) | (~person(two)) | not_familiar(two, three) | familiar(two, three))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three))),
% 0.19/0.43 inference(transitivity,[status(thm)],[180, 178])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, three)) | (~person(three)) | (~person(two)) | not_familiar(two, three) | familiar(two, three))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(two, three)) | (~person(two)) | (~person(three)) | not_familiar(two, three) | familiar(two, three)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (not_familiar(two, three) | familiar(two, three)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[183, 163, 84, 36, 60])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (familiar(two, three)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[184, 177])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (((~familiar(two, four)) | (~familiar(three, four)) | (~familiar(two, three))) <=> ((~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, four)) | (~familiar(three, four)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, four)) | (~familiar(three, four)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, four)) | (~familiar(three, four)) | (~familiar(two, three)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(two, four)) | (~familiar(two, three))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 120, 185, 173, 171])).
% 0.19/0.43 tff(193,plain,((~not_familiar(two, six)) | (~not_familiar(three, six)) | (~not_familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (~not_familiar(two, six)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 3, 1])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, six)) | (~after(two, four)) | after(two, six))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, six)) | (~after(two, four)) | after(two, six))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, six)) | (~after(two, four)) | after(two, six))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, six)) | (~after(two, four)) | after(two, six)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (after(two, six)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[197, 33, 160, 136])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (((~after(two, six)) | (~person(six)) | (~person(two)) | not_familiar(two, six) | familiar(two, six)) <=> ((~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, six)) | (~person(six)) | (~person(two)) | not_familiar(two, six) | familiar(two, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, six)) | (~person(six)) | (~person(two)) | not_familiar(two, six) | familiar(two, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six))),
% 0.19/0.43 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, six)) | (~person(six)) | (~person(two)) | not_familiar(two, six) | familiar(two, six))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(six)) | (~after(two, six)) | not_familiar(two, six) | familiar(two, six)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 (not_familiar(two, six) | familiar(two, six)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[204, 163, 143, 60, 198])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (familiar(two, six)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[205, 194])).
% 0.19/0.43 tff(207,assumption,(familiar(two, six)), introduced(assumption)).
% 0.19/0.43 tff(208,assumption,(familiar(five, six)), introduced(assumption)).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (((~familiar(two, six)) | (~familiar(five, six)) | (~familiar(two, five))) <=> ((~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(five, six)) | (~familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[210])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(five, six)) | (~familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[211, 209])).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(five, six)) | (~familiar(two, five)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(two, six)) | (~familiar(two, five))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 (~familiar(two, five)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[214, 120, 208, 207])).
% 0.19/0.44 tff(216,plain,
% 0.19/0.44 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, five)) | (~after(two, four)) | after(two, five))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, five)) | (~after(two, four)) | after(two, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, five)) | (~after(two, four)) | after(two, five))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, five)) | (~after(two, four)) | after(two, five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.44 tff(219,plain,
% 0.19/0.44 (after(two, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[218, 132, 33, 160])).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 (person(five) <=> person(five)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(221,axiom,(person(five)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','person5')).
% 0.19/0.44 tff(222,plain,
% 0.19/0.44 (person(five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (((~after(two, five)) | (~person(five)) | (~person(two)) | not_familiar(two, five) | familiar(two, five)) <=> ((~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, five)) | (~person(five)) | (~person(two)) | not_familiar(two, five) | familiar(two, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, five)) | (~person(five)) | (~person(two)) | not_familiar(two, five) | familiar(two, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five))),
% 0.19/0.44 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.44 tff(227,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(two, five)) | (~person(five)) | (~person(two)) | not_familiar(two, five) | familiar(two, five))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(228,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(two)) | (~person(five)) | (~after(two, five)) | not_familiar(two, five) | familiar(two, five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.44 tff(229,plain,
% 0.19/0.44 (not_familiar(two, five) | familiar(two, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[228, 163, 222, 60, 219])).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 (not_familiar(two, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[229, 215])).
% 0.19/0.44 tff(231,assumption,(familiar(one, five)), introduced(assumption)).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 (((~familiar(one, six)) | (~familiar(five, six)) | (~familiar(one, five))) <=> ((~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(five, six)) | (~familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(five, six)) | (~familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[234, 232])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(five, six)) | (~familiar(one, five)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(one, six)) | (~familiar(one, five))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[237, 120, 208, 231, 2])).
% 0.19/0.44 tff(239,plain,((~familiar(one, six)) | (~familiar(five, six)) | (~familiar(one, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(240,plain,
% 0.19/0.44 (~familiar(one, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[239, 2, 208])).
% 0.19/0.44 tff(241,plain,
% 0.19/0.44 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, five)) | (~after(three, four)) | after(three, five))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, five)) | (~after(three, four)) | after(three, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(242,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(four, five)) | (~after(three, four)) | after(three, five))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(243,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(four, five)) | (~after(three, four)) | after(three, five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.44 tff(244,plain,
% 0.19/0.44 (after(three, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[243, 46, 132, 33])).
% 0.19/0.44 tff(245,plain,
% 0.19/0.44 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(one, three)) | (~after(three, five)) | after(one, five))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(one, three)) | (~after(three, five)) | after(one, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(246,plain,
% 0.19/0.44 (((~after(three, five)) | (~after(one, three)) | after(one, five)) <=> ((~after(one, three)) | (~after(three, five)) | after(one, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, five)) | (~after(one, three)) | after(one, five))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(one, three)) | (~after(three, five)) | after(one, five)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[246])).
% 0.19/0.44 tff(248,plain,
% 0.19/0.44 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, five)) | (~after(one, three)) | after(one, five))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(one, three)) | (~after(three, five)) | after(one, five))),
% 0.19/0.44 inference(transitivity,[status(thm)],[247, 245])).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(three, five)) | (~after(one, three)) | after(one, five))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(250,plain,
% 0.19/0.44 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(one, three)) | (~after(three, five)) | after(one, five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.44 tff(251,plain,
% 0.19/0.44 (after(one, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[250, 33, 43, 244])).
% 0.19/0.44 tff(252,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(253,plain,
% 0.19/0.44 (((~after(one, five)) | (~person(five)) | (~person(one)) | not_familiar(one, five) | familiar(one, five)) <=> ((~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(254,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, five)) | (~person(five)) | (~person(one)) | not_familiar(one, five) | familiar(one, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[253])).
% 0.19/0.44 tff(255,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, five)) | (~person(five)) | (~person(one)) | not_familiar(one, five) | familiar(one, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five))),
% 0.19/0.44 inference(transitivity,[status(thm)],[254, 252])).
% 0.19/0.44 tff(256,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, five)) | (~person(five)) | (~person(one)) | not_familiar(one, five) | familiar(one, five))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(257,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(one)) | (~person(five)) | (~after(one, five)) | not_familiar(one, five) | familiar(one, five)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.19/0.44 tff(258,plain,
% 0.19/0.44 (not_familiar(one, five) | familiar(one, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[257, 66, 222, 60, 251])).
% 0.19/0.44 tff(259,plain,
% 0.19/0.44 (not_familiar(one, five)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[258, 240])).
% 0.19/0.44 tff(260,assumption,(not_familiar(two, five)), introduced(assumption)).
% 0.19/0.44 tff(261,assumption,(not_familiar(one, five)), introduced(assumption)).
% 0.19/0.44 tff(262,assumption,(not_familiar(one, two)), introduced(assumption)).
% 0.19/0.45 tff(263,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(264,plain,
% 0.19/0.45 (((~not_familiar(one, five)) | (~not_familiar(two, five)) | (~not_familiar(one, two))) <=> ((~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(265,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(two, five)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[264])).
% 0.19/0.45 tff(266,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(two, five)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[265, 263])).
% 0.19/0.45 tff(267,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(two, five)) | (~not_familiar(one, two)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(268,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, five)) | (~not_familiar(two, five))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.45 tff(269,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[268, 15, 262, 261, 260])).
% 0.19/0.45 tff(270,plain,((~not_familiar(two, five)) | (~not_familiar(one, two)) | (~not_familiar(one, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(271,plain,
% 0.19/0.45 (~not_familiar(one, two)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[270, 259, 230])).
% 0.19/0.45 tff(272,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, two)) | (~person(two)) | (~person(one)) | not_familiar(one, two) | familiar(one, two))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(one, two)) | (~person(two)) | (~person(one)) | not_familiar(one, two) | familiar(one, two))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(273,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(one, two)) | (~person(two)) | (~person(one)) | not_familiar(one, two) | familiar(one, two))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(274,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(one, two)) | (~person(two)) | (~person(one)) | not_familiar(one, two) | familiar(one, two)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.45 tff(275,plain,
% 0.19/0.45 (not_familiar(one, two) | familiar(one, two)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[274, 66, 163, 39, 60])).
% 0.19/0.45 tff(276,plain,
% 0.19/0.45 (familiar(one, two)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[275, 271])).
% 0.19/0.45 tff(277,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(278,plain,
% 0.19/0.45 (((~familiar(one, six)) | (~familiar(two, six)) | (~familiar(one, two))) <=> ((~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(279,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(two, six)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.45 tff(280,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(two, six)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[279, 277])).
% 0.19/0.45 tff(281,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(two, six)) | (~familiar(one, two)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(282,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(one, six)) | (~familiar(one, two))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.45 tff(283,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[282, 120, 276, 207, 2])).
% 0.19/0.45 tff(284,plain,((~familiar(one, six)) | (~familiar(two, six)) | (~familiar(five, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(285,plain,
% 0.19/0.45 (~familiar(five, six)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[284, 206, 151])).
% 0.19/0.45 tff(286,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(287,plain,
% 0.19/0.45 (((~after(five, six)) | (~person(six)) | (~person(five)) | not_familiar(five, six) | familiar(five, six)) <=> ((~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(288,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(five, six)) | (~person(six)) | (~person(five)) | not_familiar(five, six) | familiar(five, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[287])).
% 0.19/0.45 tff(289,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(five, six)) | (~person(six)) | (~person(five)) | not_familiar(five, six) | familiar(five, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six))),
% 0.19/0.45 inference(transitivity,[status(thm)],[288, 286])).
% 0.19/0.45 tff(290,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(five, six)) | (~person(six)) | (~person(five)) | not_familiar(five, six) | familiar(five, six))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(291,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(five, six)) | (~person(five)) | (~person(six)) | not_familiar(five, six) | familiar(five, six)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.19/0.45 tff(292,plain,
% 0.19/0.45 (not_familiar(five, six) | familiar(five, six)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[291, 222, 143, 129, 60])).
% 0.19/0.45 tff(293,plain,
% 0.19/0.45 (not_familiar(five, six)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[292, 285])).
% 0.19/0.45 tff(294,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(295,plain,
% 0.19/0.45 (((~not_familiar(three, six)) | (~not_familiar(five, six)) | (~not_familiar(three, five))) <=> ((~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(296,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(five, six)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[295])).
% 0.19/0.45 tff(297,plain,
% 0.19/0.45 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(five, six)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[296, 294])).
% 0.19/0.45 tff(298,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, six)) | (~not_familiar(five, six)) | (~not_familiar(three, five)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(299,plain,
% 0.19/0.45 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(three, six)) | (~not_familiar(three, five))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.45 tff(300,plain,
% 0.19/0.45 (~not_familiar(three, five)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[299, 15, 293, 3])).
% 0.19/0.45 tff(301,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(302,plain,
% 0.19/0.45 (((~after(three, five)) | (~person(five)) | (~person(three)) | not_familiar(three, five) | familiar(three, five)) <=> ((~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(303,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, five)) | (~person(five)) | (~person(three)) | not_familiar(three, five) | familiar(three, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[302])).
% 0.19/0.46 tff(304,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, five)) | (~person(five)) | (~person(three)) | not_familiar(three, five) | familiar(three, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five))),
% 0.19/0.46 inference(transitivity,[status(thm)],[303, 301])).
% 0.19/0.46 tff(305,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, five)) | (~person(five)) | (~person(three)) | not_familiar(three, five) | familiar(three, five))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(306,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(five)) | (~after(three, five)) | not_familiar(three, five) | familiar(three, five)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.19/0.46 tff(307,plain,
% 0.19/0.46 (not_familiar(three, five) | familiar(three, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[306, 84, 222, 60, 244])).
% 0.19/0.46 tff(308,plain,
% 0.19/0.46 (familiar(three, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[307, 300])).
% 0.19/0.46 tff(309,assumption,(not_familiar(four, five)), introduced(assumption)).
% 0.19/0.46 tff(310,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(311,plain,
% 0.19/0.46 (((~not_familiar(one, six)) | (~not_familiar(two, six)) | (~not_familiar(one, two))) <=> ((~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(312,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(two, six)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[311])).
% 0.19/0.46 tff(313,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(two, six)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[312, 310])).
% 0.19/0.46 tff(314,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(two, six)) | (~not_familiar(one, two)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(315,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, six)) | (~not_familiar(one, two)) | (~not_familiar(one, six))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.19/0.46 tff(316,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[315, 15, 262, 152, 4])).
% 0.19/0.46 tff(317,plain,((~not_familiar(one, six)) | (~not_familiar(one, two)) | (~not_familiar(two, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(318,plain,
% 0.19/0.46 (~not_familiar(one, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[317, 262, 152])).
% 0.19/0.46 tff(319,plain,
% 0.19/0.46 (familiar(one, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[150, 318])).
% 0.19/0.46 tff(320,plain,
% 0.19/0.46 (~familiar(one, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[239, 319, 208])).
% 0.19/0.46 tff(321,plain,
% 0.19/0.46 (not_familiar(one, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[258, 320])).
% 0.19/0.46 tff(322,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(323,plain,
% 0.19/0.46 (((~not_familiar(one, five)) | (~not_familiar(four, five)) | (~not_familiar(one, four))) <=> ((~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(324,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(four, five)) | (~not_familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[323])).
% 0.19/0.46 tff(325,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(four, five)) | (~not_familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[324, 322])).
% 0.19/0.46 tff(326,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(four, five)) | (~not_familiar(one, four)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(327,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(one, five)) | (~not_familiar(one, four))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.19/0.46 tff(328,plain,
% 0.19/0.46 (~not_familiar(one, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[327, 15, 309, 321])).
% 0.19/0.46 tff(329,plain,
% 0.19/0.46 (familiar(one, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 328])).
% 0.19/0.46 tff(330,assumption,(familiar(one, four)), introduced(assumption)).
% 0.19/0.46 tff(331,assumption,(familiar(four, six)), introduced(assumption)).
% 0.19/0.46 tff(332,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(333,plain,
% 0.19/0.46 (((~familiar(one, six)) | (~familiar(four, six)) | (~familiar(one, four))) <=> ((~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(334,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(four, six)) | (~familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[333])).
% 0.19/0.46 tff(335,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(four, six)) | (~familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[334, 332])).
% 0.19/0.46 tff(336,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(four, six)) | (~familiar(one, four)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(337,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, six)) | (~familiar(one, six))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.19/0.46 tff(338,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[337, 120, 331, 330, 2])).
% 0.19/0.46 tff(339,plain,((~familiar(four, six)) | (~familiar(one, four)) | (~familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(340,plain,
% 0.19/0.46 (~familiar(four, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[339, 329, 319])).
% 0.19/0.46 tff(341,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(342,plain,
% 0.19/0.46 (((~after(four, six)) | (~person(six)) | (~person(four)) | not_familiar(four, six) | familiar(four, six)) <=> ((~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(343,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, six)) | (~person(six)) | (~person(four)) | not_familiar(four, six) | familiar(four, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[342])).
% 0.19/0.46 tff(344,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, six)) | (~person(six)) | (~person(four)) | not_familiar(four, six) | familiar(four, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six))),
% 0.19/0.46 inference(transitivity,[status(thm)],[343, 341])).
% 0.19/0.46 tff(345,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, six)) | (~person(six)) | (~person(four)) | not_familiar(four, six) | familiar(four, six))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(346,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(four)) | (~person(six)) | (~after(four, six)) | not_familiar(four, six) | familiar(four, six)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.19/0.46 tff(347,plain,
% 0.19/0.46 (not_familiar(four, six) | familiar(four, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[346, 63, 143, 60, 136])).
% 0.19/0.46 tff(348,plain,
% 0.19/0.46 (not_familiar(four, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[347, 340])).
% 0.19/0.46 tff(349,plain,
% 0.19/0.46 (~not_familiar(two, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[155, 15, 348, 152])).
% 0.19/0.46 tff(350,plain,
% 0.19/0.46 (familiar(two, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[170, 349])).
% 0.19/0.46 tff(351,assumption,(familiar(three, four)), introduced(assumption)).
% 0.19/0.46 tff(352,plain,
% 0.19/0.46 (~familiar(one, three)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[123, 120, 351, 330])).
% 0.19/0.46 tff(353,plain,
% 0.19/0.46 (not_familiar(one, three)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[91, 352])).
% 0.19/0.46 tff(354,assumption,(familiar(two, four)), introduced(assumption)).
% 0.19/0.46 tff(355,plain,
% 0.19/0.46 (~familiar(two, three)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[191, 120, 351, 354])).
% 0.19/0.46 tff(356,plain,
% 0.19/0.46 (not_familiar(two, three)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[184, 355])).
% 0.19/0.46 tff(357,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(358,plain,
% 0.19/0.46 (((~not_familiar(one, three)) | (~not_familiar(two, three)) | (~not_familiar(one, two))) <=> ((~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(359,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, three)) | (~not_familiar(two, three)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[358])).
% 0.19/0.46 tff(360,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, three)) | (~not_familiar(two, three)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[359, 357])).
% 0.19/0.46 tff(361,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, three)) | (~not_familiar(two, three)) | (~not_familiar(one, two)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(362,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, three)) | (~not_familiar(two, three))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.19/0.46 tff(363,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[362, 15, 262, 356, 353])).
% 0.19/0.46 tff(364,plain,((~familiar(three, four)) | (~not_familiar(one, two)) | (~familiar(one, four)) | (~familiar(two, four))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(365,plain,
% 0.19/0.46 (~familiar(three, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[364, 262, 329, 350])).
% 0.19/0.46 tff(366,plain,
% 0.19/0.46 (not_familiar(three, four)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[109, 365])).
% 0.19/0.46 tff(367,plain,
% 0.19/0.46 (~not_familiar(three, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[101, 366, 348])).
% 0.19/0.46 tff(368,plain,
% 0.19/0.46 (((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(five, six)) | (~after(three, five)) | after(three, six))) <=> ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(five, six)) | (~after(three, five)) | after(three, six))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(369,plain,
% 0.19/0.46 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | ((~after(five, six)) | (~after(three, five)) | after(three, six))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(370,plain,
% 0.19/0.46 ((~![Small: $i, Medium: $i, Large: $i] : ((~after(Medium, Small)) | (~after(Large, Medium)) | after(Large, Small))) | (~after(five, six)) | (~after(three, five)) | after(three, six)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.19/0.46 tff(371,plain,
% 0.19/0.46 (after(three, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[370, 129, 33, 244])).
% 0.19/0.46 tff(372,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(373,plain,
% 0.19/0.46 (((~after(three, six)) | (~person(six)) | (~person(three)) | not_familiar(three, six) | familiar(three, six)) <=> ((~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(374,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, six)) | (~person(six)) | (~person(three)) | not_familiar(three, six) | familiar(three, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[373])).
% 0.19/0.46 tff(375,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, six)) | (~person(six)) | (~person(three)) | not_familiar(three, six) | familiar(three, six))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six))),
% 0.19/0.46 inference(transitivity,[status(thm)],[374, 372])).
% 0.19/0.46 tff(376,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(three, six)) | (~person(six)) | (~person(three)) | not_familiar(three, six) | familiar(three, six))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(377,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~person(three)) | (~person(six)) | (~after(three, six)) | not_familiar(three, six) | familiar(three, six)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.19/0.46 tff(378,plain,
% 0.19/0.46 (not_familiar(three, six) | familiar(three, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[377, 84, 143, 60, 371])).
% 0.19/0.46 tff(379,plain,
% 0.19/0.46 (familiar(three, six)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[378, 367])).
% 0.19/0.46 tff(380,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(381,plain,
% 0.19/0.46 (((~familiar(three, six)) | (~familiar(five, six)) | (~familiar(three, five))) <=> ((~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(382,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(five, six)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[381])).
% 0.19/0.46 tff(383,plain,
% 0.19/0.46 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(five, six)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[382, 380])).
% 0.19/0.46 tff(384,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(five, six)) | (~familiar(three, five)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(385,plain,
% 0.19/0.46 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(three, six)) | (~familiar(three, five))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.19/0.46 tff(386,plain,
% 0.19/0.46 (~familiar(three, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[385, 120, 208, 379])).
% 0.19/0.46 tff(387,plain,
% 0.19/0.46 (not_familiar(three, five)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[307, 386])).
% 0.19/0.46 tff(388,assumption,(familiar(three, six)), introduced(assumption)).
% 0.19/0.46 tff(389,assumption,(familiar(one, three)), introduced(assumption)).
% 0.19/0.47 tff(390,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(391,plain,
% 0.19/0.47 (((~familiar(one, six)) | (~familiar(three, six)) | (~familiar(one, three))) <=> ((~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(392,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(three, six)) | (~familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[391])).
% 0.19/0.47 tff(393,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(three, six)) | (~familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[392, 390])).
% 0.19/0.47 tff(394,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, six)) | (~familiar(three, six)) | (~familiar(one, three)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(395,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, six)) | (~familiar(three, six))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.19/0.47 tff(396,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[395, 120, 389, 388, 2])).
% 0.19/0.47 tff(397,plain,((~familiar(three, six)) | (~familiar(one, three)) | (~familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(398,plain,
% 0.19/0.47 (~familiar(one, three)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[397, 379, 319])).
% 0.19/0.47 tff(399,plain,
% 0.19/0.47 (not_familiar(one, three)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[91, 398])).
% 0.19/0.47 tff(400,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(401,plain,
% 0.19/0.47 (((~not_familiar(one, five)) | (~not_familiar(three, five)) | (~not_familiar(one, three))) <=> ((~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(402,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(three, five)) | (~not_familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[401])).
% 0.19/0.47 tff(403,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(three, five)) | (~not_familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[402, 400])).
% 0.19/0.47 tff(404,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, five)) | (~not_familiar(three, five)) | (~not_familiar(one, three)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(405,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, five)) | (~not_familiar(one, three)) | (~not_familiar(three, five))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.19/0.47 tff(406,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[405, 15, 399, 387, 321])).
% 0.19/0.47 tff(407,plain,((~not_familiar(one, two)) | (~familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(four, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(408,plain,
% 0.19/0.47 (~not_familiar(one, two)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[407, 152, 208, 309])).
% 0.19/0.47 tff(409,plain,
% 0.19/0.47 (familiar(one, two)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[275, 408])).
% 0.19/0.47 tff(410,assumption,(familiar(one, two)), introduced(assumption)).
% 0.19/0.47 tff(411,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(412,plain,
% 0.19/0.47 (((~familiar(one, three)) | (~familiar(two, three)) | (~familiar(one, two))) <=> ((~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(413,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(two, three)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[412])).
% 0.19/0.47 tff(414,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(two, three)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[413, 411])).
% 0.19/0.47 tff(415,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(two, three)) | (~familiar(one, two)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(416,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, two)) | (~familiar(two, three))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.19/0.47 tff(417,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[416, 120, 410, 185, 92])).
% 0.19/0.47 tff(418,plain,((~not_familiar(three, six)) | (~familiar(one, two)) | (~not_familiar(two, six)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(419,plain,
% 0.19/0.47 (~not_familiar(three, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[418, 4, 152, 409])).
% 0.19/0.47 tff(420,plain,
% 0.19/0.47 (familiar(three, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[378, 419])).
% 0.19/0.47 tff(421,plain,
% 0.19/0.47 (~familiar(three, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[385, 120, 208, 388])).
% 0.19/0.47 tff(422,plain,
% 0.19/0.47 (not_familiar(three, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[307, 421])).
% 0.19/0.47 tff(423,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(424,plain,
% 0.19/0.47 (((~familiar(three, six)) | (~familiar(four, six)) | (~familiar(three, four))) <=> ((~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(425,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(four, six)) | (~familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[424])).
% 0.19/0.47 tff(426,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(four, six)) | (~familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[425, 423])).
% 0.19/0.47 tff(427,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, six)) | (~familiar(four, six)) | (~familiar(three, four)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(428,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, six)) | (~familiar(three, six))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.19/0.47 tff(429,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[428, 120, 351, 331, 388])).
% 0.19/0.47 tff(430,plain,((~familiar(three, six)) | (~familiar(three, four)) | (~familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(431,plain,
% 0.19/0.47 (~familiar(three, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[430, 388, 331])).
% 0.19/0.47 tff(432,plain,
% 0.19/0.47 (not_familiar(three, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[109, 431])).
% 0.19/0.47 tff(433,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(434,plain,
% 0.19/0.47 (((~not_familiar(three, five)) | (~not_familiar(four, five)) | (~not_familiar(three, four))) <=> ((~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(435,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, five)) | (~not_familiar(four, five)) | (~not_familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[434])).
% 0.19/0.47 tff(436,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, five)) | (~not_familiar(four, five)) | (~not_familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[435, 433])).
% 0.19/0.47 tff(437,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(three, five)) | (~not_familiar(four, five)) | (~not_familiar(three, four)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(438,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(three, four)) | (~not_familiar(three, five))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.19/0.47 tff(439,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[438, 15, 432, 309, 422])).
% 0.19/0.47 tff(440,plain,((~familiar(three, six)) | (~not_familiar(four, five)) | (~familiar(five, six)) | (~familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(441,plain,
% 0.19/0.47 (~familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[440, 420, 208, 309])).
% 0.19/0.47 tff(442,plain,
% 0.19/0.47 (not_familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[347, 441])).
% 0.19/0.47 tff(443,plain,
% 0.19/0.47 (~not_familiar(one, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[23, 442, 4])).
% 0.19/0.47 tff(444,plain,
% 0.19/0.47 (familiar(one, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[73, 443])).
% 0.19/0.47 tff(445,plain,
% 0.19/0.47 (~not_familiar(two, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 15, 442, 152])).
% 0.19/0.47 tff(446,plain,
% 0.19/0.47 (familiar(two, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[170, 445])).
% 0.19/0.47 tff(447,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(two, four)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(two, four)) | (~familiar(one, two)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(448,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(two, four)) | (~familiar(one, two)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(449,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(two, four)) | (~familiar(one, two))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.19/0.47 tff(450,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[449, 120, 409, 446, 444])).
% 0.19/0.47 tff(451,plain,((~not_familiar(one, six)) | (~not_familiar(two, six)) | (~familiar(five, six)) | (~not_familiar(four, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(452,plain,
% 0.19/0.47 (~not_familiar(one, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[451, 152, 208, 309])).
% 0.19/0.47 tff(453,plain,
% 0.19/0.47 (familiar(one, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 452])).
% 0.19/0.47 tff(454,plain,
% 0.19/0.47 (~familiar(one, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[239, 453, 208])).
% 0.19/0.47 tff(455,plain,
% 0.19/0.47 (not_familiar(one, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[258, 454])).
% 0.19/0.47 tff(456,plain,
% 0.19/0.47 (~not_familiar(one, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[327, 15, 309, 455])).
% 0.19/0.47 tff(457,plain,
% 0.19/0.47 (familiar(one, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[73, 456])).
% 0.19/0.47 tff(458,plain,
% 0.19/0.47 (~familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[339, 457, 453])).
% 0.19/0.47 tff(459,plain,
% 0.19/0.47 (not_familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[347, 458])).
% 0.19/0.47 tff(460,plain,
% 0.19/0.47 (~not_familiar(two, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 15, 459, 152])).
% 0.19/0.47 tff(461,plain,
% 0.19/0.47 (familiar(two, four)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[170, 460])).
% 0.19/0.47 tff(462,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[449, 120, 409, 461, 457])).
% 0.19/0.47 tff(463,plain,((~not_familiar(two, six)) | (~not_familiar(four, five)) | (~familiar(five, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(464,plain,
% 0.19/0.47 (~not_familiar(two, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[463, 208, 309])).
% 0.19/0.47 tff(465,plain,
% 0.19/0.47 (familiar(two, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[205, 464])).
% 0.19/0.47 tff(466,plain,
% 0.19/0.47 (~familiar(one, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[284, 465, 208])).
% 0.19/0.47 tff(467,plain,
% 0.19/0.47 (not_familiar(one, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 466])).
% 0.19/0.47 tff(468,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(469,plain,
% 0.19/0.47 (((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(two, three))) <=> ((~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(470,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[469])).
% 0.19/0.47 tff(471,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[470, 468])).
% 0.19/0.47 tff(472,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(two, three)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(473,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(two, three)) | (~familiar(three, six))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.19/0.47 tff(474,plain,
% 0.19/0.47 (~familiar(two, three)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[473, 120, 207, 388])).
% 0.19/0.47 tff(475,plain,
% 0.19/0.47 (not_familiar(two, three)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[184, 474])).
% 0.19/0.47 tff(476,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(477,plain,
% 0.19/0.47 (((~not_familiar(two, five)) | (~not_familiar(three, five)) | (~not_familiar(two, three))) <=> ((~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(478,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(three, five)) | (~not_familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[477])).
% 0.19/0.47 tff(479,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(three, five)) | (~not_familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[478, 476])).
% 0.19/0.47 tff(480,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(three, five)) | (~not_familiar(two, three)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(481,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, five)) | (~not_familiar(two, three)) | (~not_familiar(three, five))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.19/0.47 tff(482,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[481, 15, 475, 422, 230])).
% 0.19/0.47 tff(483,plain,((~familiar(three, six)) | (~familiar(five, six)) | (~familiar(two, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(484,plain,
% 0.19/0.47 (~familiar(three, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[483, 208, 465])).
% 0.19/0.47 tff(485,plain,
% 0.19/0.47 (not_familiar(three, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[378, 484])).
% 0.19/0.47 tff(486,plain,
% 0.19/0.47 (~not_familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 485, 467])).
% 0.19/0.47 tff(487,plain,
% 0.19/0.47 (familiar(four, six)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[347, 486])).
% 0.19/0.47 tff(488,plain,
% 0.19/0.47 (~familiar(two, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[214, 120, 208, 465])).
% 0.19/0.47 tff(489,plain,
% 0.19/0.47 (not_familiar(two, five)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[229, 488])).
% 0.19/0.47 tff(490,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(491,plain,
% 0.19/0.47 (((~not_familiar(two, five)) | (~not_familiar(four, five)) | (~not_familiar(two, four))) <=> ((~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(492,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(four, five)) | (~not_familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[491])).
% 0.19/0.47 tff(493,plain,
% 0.19/0.47 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(four, five)) | (~not_familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[492, 490])).
% 0.19/0.47 tff(494,plain,
% 0.19/0.47 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, five)) | (~not_familiar(four, five)) | (~not_familiar(two, four)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(495,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(two, four)) | (~not_familiar(two, five))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.19/0.48 tff(496,plain,
% 0.19/0.48 (~not_familiar(two, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[495, 15, 309, 489])).
% 0.19/0.48 tff(497,plain,
% 0.19/0.48 (familiar(two, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[170, 496])).
% 0.19/0.48 tff(498,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(four, six)) | (~familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(four, six)) | (~familiar(two, four)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(499,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, six)) | (~familiar(four, six)) | (~familiar(two, four)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(500,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, six)) | (~familiar(four, six)) | (~familiar(two, four))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.19/0.48 tff(501,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[500, 120, 497, 487, 465])).
% 0.19/0.48 tff(502,plain,((~familiar(five, six)) | (~not_familiar(four, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(503,plain,
% 0.19/0.48 (~familiar(five, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[502, 309])).
% 0.19/0.48 tff(504,plain,
% 0.19/0.48 (not_familiar(five, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[292, 503])).
% 0.19/0.48 tff(505,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(506,plain,
% 0.19/0.48 (((~not_familiar(four, six)) | (~not_familiar(five, six)) | (~not_familiar(four, five))) <=> ((~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(507,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, six)) | (~not_familiar(five, six)) | (~not_familiar(four, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[506])).
% 0.19/0.48 tff(508,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, six)) | (~not_familiar(five, six)) | (~not_familiar(four, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[507, 505])).
% 0.19/0.48 tff(509,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(four, six)) | (~not_familiar(five, six)) | (~not_familiar(four, five)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(510,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(four, five)) | (~not_familiar(five, six)) | (~not_familiar(four, six))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.19/0.48 tff(511,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[510, 15, 309, 504, 1])).
% 0.19/0.48 tff(512,plain,((~not_familiar(four, six)) | (~not_familiar(four, five))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(513,plain,
% 0.19/0.48 (~not_familiar(four, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[512, 309])).
% 0.19/0.48 tff(514,plain,
% 0.19/0.48 (familiar(four, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[347, 513])).
% 0.19/0.48 tff(515,plain,
% 0.19/0.48 (~familiar(one, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[339, 331, 2])).
% 0.19/0.48 tff(516,plain,
% 0.19/0.48 (not_familiar(one, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[73, 515])).
% 0.19/0.48 tff(517,plain,
% 0.19/0.48 (~familiar(two, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[500, 120, 331, 207])).
% 0.19/0.48 tff(518,plain,
% 0.19/0.48 (not_familiar(two, four)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[170, 517])).
% 0.19/0.48 tff(519,plain,
% 0.19/0.48 (~familiar(one, two)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[282, 120, 207, 2])).
% 0.19/0.48 tff(520,plain,
% 0.19/0.48 (not_familiar(one, two)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[275, 519])).
% 0.19/0.48 tff(521,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(522,plain,
% 0.19/0.48 (((~not_familiar(one, four)) | (~not_familiar(two, four)) | (~not_familiar(one, two))) <=> ((~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(523,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(two, four)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[522])).
% 0.19/0.48 tff(524,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(two, four)) | (~not_familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[523, 521])).
% 0.19/0.48 tff(525,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(two, four)) | (~not_familiar(one, two)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(526,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, two)) | (~not_familiar(one, four)) | (~not_familiar(two, four))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.19/0.48 tff(527,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[526, 15, 520, 518, 516])).
% 0.19/0.48 tff(528,plain,((~familiar(two, six)) | (~familiar(four, six)) | (~familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(529,plain,
% 0.19/0.48 (~familiar(two, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[528, 331, 2])).
% 0.19/0.48 tff(530,plain,
% 0.19/0.48 (not_familiar(two, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[205, 529])).
% 0.19/0.48 tff(531,assumption,(not_familiar(five, six)), introduced(assumption)).
% 0.19/0.48 tff(532,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(533,plain,
% 0.19/0.48 (((~not_familiar(two, six)) | (~not_familiar(five, six)) | (~not_familiar(two, five))) <=> ((~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(534,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(five, six)) | (~not_familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[533])).
% 0.19/0.48 tff(535,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(five, six)) | (~not_familiar(two, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[534, 532])).
% 0.19/0.48 tff(536,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, six)) | (~not_familiar(five, six)) | (~not_familiar(two, five)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(537,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(two, six)) | (~not_familiar(two, five))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.19/0.48 tff(538,plain,
% 0.19/0.48 (~not_familiar(two, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[537, 15, 531, 530])).
% 0.19/0.48 tff(539,plain,
% 0.19/0.48 (familiar(two, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[229, 538])).
% 0.19/0.48 tff(540,plain,
% 0.19/0.48 (~familiar(one, three)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[397, 388, 2])).
% 0.19/0.48 tff(541,plain,
% 0.19/0.48 (not_familiar(one, three)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[91, 540])).
% 0.19/0.48 tff(542,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(three, four)) | (~not_familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, four)) | (~not_familiar(three, four)) | (~not_familiar(one, three)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(543,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, four)) | (~not_familiar(three, four)) | (~not_familiar(one, three)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(544,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(one, four)) | (~not_familiar(three, four)) | (~not_familiar(one, three))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.19/0.48 tff(545,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[544, 15, 432, 541, 516])).
% 0.19/0.48 tff(546,plain,((~familiar(three, six)) | (~familiar(one, six)) | (~familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(547,plain,
% 0.19/0.48 (~familiar(three, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[546, 331, 2])).
% 0.19/0.48 tff(548,plain,
% 0.19/0.48 (not_familiar(three, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[378, 547])).
% 0.19/0.48 tff(549,plain,
% 0.19/0.48 (~not_familiar(three, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[299, 15, 531, 548])).
% 0.19/0.48 tff(550,plain,
% 0.19/0.48 (familiar(three, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[307, 549])).
% 0.19/0.48 tff(551,plain,
% 0.19/0.48 (~not_familiar(two, three)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[176, 15, 530, 548])).
% 0.19/0.48 tff(552,plain,
% 0.19/0.48 (familiar(two, three)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[184, 551])).
% 0.19/0.48 tff(553,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(554,plain,
% 0.19/0.48 (((~familiar(two, five)) | (~familiar(three, five)) | (~familiar(two, three))) <=> ((~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(555,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(three, five)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[554])).
% 0.19/0.48 tff(556,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(three, five)) | (~familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[555, 553])).
% 0.19/0.48 tff(557,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(three, five)) | (~familiar(two, three)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(558,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(two, three)) | (~familiar(three, five))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.19/0.48 tff(559,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[558, 120, 552, 550, 539])).
% 0.19/0.48 tff(560,plain,((~familiar(four, six)) | (~not_familiar(five, six)) | (~familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(561,plain,
% 0.19/0.48 (~familiar(one, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[560, 514, 504])).
% 0.19/0.48 tff(562,plain,
% 0.19/0.48 (not_familiar(one, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[150, 561])).
% 0.19/0.48 tff(563,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(564,plain,
% 0.19/0.48 (((~not_familiar(one, six)) | (~not_familiar(five, six)) | (~not_familiar(one, five))) <=> ((~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(565,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(five, six)) | (~not_familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[564])).
% 0.19/0.48 tff(566,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(five, six)) | (~not_familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[565, 563])).
% 0.19/0.48 tff(567,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(one, six)) | (~not_familiar(five, six)) | (~not_familiar(one, five)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(568,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.19/0.48 tff(569,plain,
% 0.19/0.48 (~not_familiar(one, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[568, 15, 531, 4])).
% 0.19/0.48 tff(570,plain,
% 0.19/0.48 (familiar(one, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[258, 569])).
% 0.19/0.48 tff(571,plain,
% 0.19/0.48 (~not_familiar(three, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[299, 15, 531, 3])).
% 0.19/0.48 tff(572,plain,
% 0.19/0.48 (familiar(three, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[307, 571])).
% 0.19/0.48 tff(573,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(574,plain,
% 0.19/0.48 (((~familiar(one, five)) | (~familiar(three, five)) | (~familiar(one, three))) <=> ((~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(575,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(three, five)) | (~familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[574])).
% 0.19/0.48 tff(576,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(three, five)) | (~familiar(one, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[575, 573])).
% 0.19/0.48 tff(577,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(three, five)) | (~familiar(one, three)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(578,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, three)) | (~familiar(one, five)) | (~familiar(three, five))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.19/0.48 tff(579,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[578, 120, 92, 572, 570])).
% 0.19/0.48 tff(580,plain,((~not_familiar(three, six)) | (~not_familiar(five, six)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(581,plain,
% 0.19/0.48 (~not_familiar(three, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[580, 504, 562])).
% 0.19/0.48 tff(582,plain,
% 0.19/0.48 (familiar(three, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[378, 581])).
% 0.19/0.48 tff(583,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, four)) | (~not_familiar(three, four)) | (~not_familiar(two, three)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, four)) | (~not_familiar(three, four)) | (~not_familiar(two, three)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(584,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | ((~not_familiar(two, four)) | (~not_familiar(three, four)) | (~not_familiar(two, three)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(585,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~not_familiar(X1, X3)) | (~not_familiar(X2, X3)) | (~not_familiar(X1, X2)))) | (~not_familiar(two, four)) | (~not_familiar(three, four)) | (~not_familiar(two, three))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.19/0.48 tff(586,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[585, 15, 475, 432, 518])).
% 0.19/0.48 tff(587,plain,((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(588,plain,
% 0.19/0.48 (~familiar(two, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[587, 582, 514])).
% 0.19/0.48 tff(589,plain,
% 0.19/0.48 (not_familiar(two, six)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[205, 588])).
% 0.19/0.48 tff(590,plain,
% 0.19/0.48 (~not_familiar(two, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[537, 15, 504, 589])).
% 0.19/0.48 tff(591,plain,
% 0.19/0.48 (familiar(two, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[229, 590])).
% 0.19/0.48 tff(592,plain,
% 0.19/0.48 (~not_familiar(one, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[568, 15, 504, 562])).
% 0.19/0.48 tff(593,plain,
% 0.19/0.48 (familiar(one, five)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[258, 592])).
% 0.19/0.48 tff(594,plain,
% 0.19/0.48 (~not_familiar(one, two)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[317, 589, 562])).
% 0.19/0.48 tff(595,plain,
% 0.19/0.48 (familiar(one, two)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[275, 594])).
% 0.19/0.48 tff(596,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(597,plain,
% 0.19/0.48 (((~familiar(one, five)) | (~familiar(two, five)) | (~familiar(one, two))) <=> ((~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(598,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(two, five)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[597])).
% 0.19/0.48 tff(599,plain,
% 0.19/0.48 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(two, five)) | (~familiar(one, two)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[598, 596])).
% 0.19/0.48 tff(600,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(two, five)) | (~familiar(one, two)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(601,plain,
% 0.19/0.48 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(one, five)) | (~familiar(one, two))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.19/0.48 tff(602,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[601, 120, 595, 593, 591])).
% 0.19/0.48 tff(603,plain,(~not_familiar(four, five)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(604,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(605,plain,
% 0.19/0.49 (((~after(four, five)) | (~person(five)) | (~person(four)) | not_familiar(four, five) | familiar(four, five)) <=> ((~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(606,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, five)) | (~person(five)) | (~person(four)) | not_familiar(four, five) | familiar(four, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[605])).
% 0.19/0.49 tff(607,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, five)) | (~person(five)) | (~person(four)) | not_familiar(four, five) | familiar(four, five))) <=> ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five))),
% 0.19/0.49 inference(transitivity,[status(thm)],[606, 604])).
% 0.19/0.49 tff(608,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | ((~after(four, five)) | (~person(five)) | (~person(four)) | not_familiar(four, five) | familiar(four, five))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(609,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~after(X, Y)) | (~person(Y)) | (~person(X)) | not_familiar(X, Y) | familiar(X, Y))) | (~after(four, five)) | (~person(four)) | (~person(five)) | not_familiar(four, five) | familiar(four, five)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.19/0.49 tff(610,plain,
% 0.19/0.49 (not_familiar(four, five) | familiar(four, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[609, 63, 222, 132, 60])).
% 0.19/0.49 tff(611,plain,
% 0.19/0.49 (familiar(four, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[610, 603])).
% 0.19/0.49 tff(612,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(613,plain,
% 0.19/0.49 (((~familiar(three, five)) | (~familiar(four, five)) | (~familiar(three, four))) <=> ((~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(614,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, five)) | (~familiar(four, five)) | (~familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[613])).
% 0.19/0.49 tff(615,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, five)) | (~familiar(four, five)) | (~familiar(three, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[614, 612])).
% 0.19/0.49 tff(616,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(three, five)) | (~familiar(four, five)) | (~familiar(three, four)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(617,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(three, four)) | (~familiar(four, five)) | (~familiar(three, five))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.19/0.49 tff(618,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[617, 120, 173, 611, 308])).
% 0.19/0.49 tff(619,plain,((~not_familiar(three, six)) | (~not_familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(620,plain,
% 0.19/0.49 (~not_familiar(three, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[619, 1])).
% 0.19/0.49 tff(621,plain,
% 0.19/0.49 (familiar(three, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[378, 620])).
% 0.19/0.49 tff(622,plain,
% 0.19/0.49 (~familiar(one, three)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[397, 2, 388])).
% 0.19/0.49 tff(623,plain,
% 0.19/0.49 (not_familiar(one, three)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 622])).
% 0.19/0.49 tff(624,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[362, 15, 520, 475, 623])).
% 0.19/0.49 tff(625,plain,((~familiar(two, six)) | (~familiar(three, six)) | (~familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(626,plain,
% 0.19/0.49 (~familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[625, 2, 621])).
% 0.19/0.49 tff(627,plain,
% 0.19/0.49 (not_familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[205, 626])).
% 0.19/0.49 tff(628,plain,
% 0.19/0.49 (~not_familiar(two, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[155, 15, 1, 627])).
% 0.19/0.49 tff(629,plain,
% 0.19/0.49 (familiar(two, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[170, 628])).
% 0.19/0.49 tff(630,assumption,(familiar(two, five)), introduced(assumption)).
% 0.19/0.49 tff(631,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(four, five)) | (~familiar(two, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(four, five)) | (~familiar(two, four)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(632,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(two, five)) | (~familiar(four, five)) | (~familiar(two, four)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(633,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(two, five)) | (~familiar(four, five)) | (~familiar(two, four))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.19/0.49 tff(634,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[633, 120, 611, 354, 630])).
% 0.19/0.49 tff(635,plain,((~familiar(two, five)) | (~familiar(two, four))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(636,plain,
% 0.19/0.49 (~familiar(two, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[635, 629])).
% 0.19/0.49 tff(637,plain,
% 0.19/0.49 (not_familiar(two, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[229, 636])).
% 0.19/0.49 tff(638,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[537, 15, 531, 260, 152])).
% 0.19/0.49 tff(639,plain,((~not_familiar(five, six)) | (~not_familiar(two, five)) | (~not_familiar(two, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(640,plain,
% 0.19/0.49 (~not_familiar(five, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[639, 637, 627])).
% 0.19/0.49 tff(641,plain,
% 0.19/0.49 (familiar(five, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[292, 640])).
% 0.19/0.49 tff(642,plain,
% 0.19/0.49 (~familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[239, 641, 2])).
% 0.19/0.49 tff(643,plain,
% 0.19/0.49 (not_familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[258, 642])).
% 0.19/0.49 tff(644,plain,
% 0.19/0.49 (~familiar(three, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[385, 120, 641, 621])).
% 0.19/0.49 tff(645,plain,
% 0.19/0.49 (not_familiar(three, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[307, 644])).
% 0.19/0.49 tff(646,plain,
% 0.19/0.49 (~familiar(one, three)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[397, 2, 621])).
% 0.19/0.49 tff(647,plain,
% 0.19/0.49 (not_familiar(one, three)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 646])).
% 0.19/0.49 tff(648,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[405, 15, 647, 645, 643])).
% 0.19/0.49 tff(649,plain,((~familiar(one, six)) | (~not_familiar(four, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(650,plain,
% 0.19/0.49 (~familiar(one, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[649, 1])).
% 0.19/0.49 tff(651,plain,
% 0.19/0.49 (not_familiar(one, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[150, 650])).
% 0.19/0.49 tff(652,plain,
% 0.19/0.49 (~not_familiar(one, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[23, 651, 1])).
% 0.19/0.49 tff(653,plain,
% 0.19/0.49 (familiar(one, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[73, 652])).
% 0.19/0.49 tff(654,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(655,plain,
% 0.19/0.49 (((~familiar(one, five)) | (~familiar(four, five)) | (~familiar(one, four))) <=> ((~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(656,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(four, five)) | (~familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[655])).
% 0.19/0.49 tff(657,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(four, five)) | (~familiar(one, four)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[656, 654])).
% 0.19/0.49 tff(658,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(one, five)) | (~familiar(four, five)) | (~familiar(one, four)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(659,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(one, four)) | (~familiar(four, five)) | (~familiar(one, five))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.19/0.49 tff(660,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[659, 120, 611, 330, 231])).
% 0.19/0.49 tff(661,plain,((~familiar(one, five)) | (~familiar(one, four))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(662,plain,
% 0.19/0.49 (~familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[661, 653])).
% 0.19/0.49 tff(663,plain,
% 0.19/0.49 (not_familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[258, 662])).
% 0.19/0.49 tff(664,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[568, 15, 531, 261, 4])).
% 0.19/0.49 tff(665,plain,((~not_familiar(five, six)) | (~not_familiar(one, five)) | (~not_familiar(one, six))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(666,plain,
% 0.19/0.49 (~not_familiar(five, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[665, 663, 651])).
% 0.19/0.49 tff(667,plain,
% 0.19/0.49 (familiar(five, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[292, 666])).
% 0.19/0.49 tff(668,plain,
% 0.19/0.49 (~familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[483, 667, 621])).
% 0.19/0.49 tff(669,plain,
% 0.19/0.49 (not_familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[205, 668])).
% 0.19/0.49 tff(670,plain,
% 0.19/0.49 (~not_familiar(two, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[155, 15, 1, 669])).
% 0.19/0.49 tff(671,plain,
% 0.19/0.49 (familiar(two, four)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[170, 670])).
% 0.19/0.49 tff(672,plain,
% 0.19/0.49 (~not_familiar(one, two)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[317, 669, 651])).
% 0.19/0.49 tff(673,plain,
% 0.19/0.49 (familiar(one, two)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 672])).
% 0.19/0.49 tff(674,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[449, 120, 673, 671, 653])).
% 0.19/0.49 tff(675,plain,(~not_familiar(four, six)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(676,plain,
% 0.19/0.49 (familiar(four, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[347, 675])).
% 0.19/0.49 tff(677,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(678,plain,
% 0.19/0.49 (((~familiar(four, six)) | (~familiar(five, six)) | (~familiar(four, five))) <=> ((~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(679,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(four, six)) | (~familiar(five, six)) | (~familiar(four, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[678])).
% 0.19/0.49 tff(680,plain,
% 0.19/0.49 (((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(four, six)) | (~familiar(five, six)) | (~familiar(four, five)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[679, 677])).
% 0.19/0.49 tff(681,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | ((~familiar(four, six)) | (~familiar(five, six)) | (~familiar(four, five)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(682,plain,
% 0.19/0.49 ((~![X3: $i, X2: $i, X1: $i] : ((~familiar(X1, X3)) | (~familiar(X2, X3)) | (~familiar(X1, X2)))) | (~familiar(five, six)) | (~familiar(four, six)) | (~familiar(four, five))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.19/0.49 tff(683,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[682, 120, 611, 208, 676])).
% 0.19/0.49 tff(684,plain,(~familiar(five, six)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(685,plain,
% 0.19/0.49 (not_familiar(five, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[292, 684])).
% 0.19/0.49 tff(686,plain,
% 0.19/0.49 ((~not_familiar(five, six)) | (~familiar(one, six))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[560, 676])).
% 0.19/0.49 tff(687,plain,
% 0.19/0.49 (~familiar(one, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[686, 685])).
% 0.19/0.49 tff(688,plain,
% 0.19/0.49 (not_familiar(one, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[150, 687])).
% 0.19/0.49 tff(689,plain,
% 0.19/0.49 (~not_familiar(three, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[580, 688, 685])).
% 0.19/0.49 tff(690,plain,
% 0.19/0.49 (familiar(three, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[378, 689])).
% 0.19/0.49 tff(691,plain,
% 0.19/0.49 ((~familiar(two, six)) | (~familiar(three, six))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[587, 676])).
% 0.19/0.49 tff(692,plain,
% 0.19/0.49 (~familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[691, 690])).
% 0.19/0.49 tff(693,plain,
% 0.19/0.49 (not_familiar(two, six)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[205, 692])).
% 0.19/0.49 tff(694,plain,
% 0.19/0.49 (~not_familiar(two, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[639, 693, 685])).
% 0.19/0.49 tff(695,plain,
% 0.19/0.49 (familiar(two, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[229, 694])).
% 0.19/0.49 tff(696,plain,
% 0.19/0.49 (~not_familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[665, 688, 685])).
% 0.19/0.49 tff(697,plain,
% 0.19/0.49 (familiar(one, five)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[258, 696])).
% 0.19/0.49 tff(698,plain,
% 0.19/0.49 (~not_familiar(one, two)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[317, 693, 688])).
% 0.19/0.49 tff(699,plain,
% 0.19/0.49 (familiar(one, two)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 698])).
% 0.19/0.49 tff(700,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[601, 120, 699, 697, 695])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------