TSTP Solution File: NUM021-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM021-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 13:02:41 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM021-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 06:27:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(less_type, type, (
% 0.20/0.39 less: ( $i * $i ) > $o)).
% 0.20/0.39 tff(a_type, type, (
% 0.20/0.39 a: $i)).
% 0.20/0.39 tff(c_type, type, (
% 0.20/0.39 c: $i)).
% 0.20/0.39 tff(equalish_type, type, (
% 0.20/0.39 equalish: ( $i * $i ) > $o)).
% 0.20/0.39 tff(add_type, type, (
% 0.20/0.39 add: ( $i * $i ) > $i)).
% 0.20/0.39 tff(b_type, type, (
% 0.20/0.39 b: $i)).
% 0.20/0.39 tff(successor_type, type, (
% 0.20/0.39 successor: $i > $i)).
% 0.20/0.39 tff(predecessor_of_1st_minus_2nd_type, type, (
% 0.20/0.39 predecessor_of_1st_minus_2nd: ( $i * $i ) > $i)).
% 0.20/0.39 tff(divides_type, type, (
% 0.20/0.39 divides: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,assumption,(equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((~less(b, a)) <=> (~less(b, a))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,axiom,(~less(b, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_greater_equal_a')).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (~less(b, a)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (^[B: $i, A: $i, C: $i] : refl(((~equalish(add(successor(A), B), C)) | less(B, C)) <=> ((~equalish(add(successor(A), B), C)) | less(B, C)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(8,axiom,(![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))), file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax','smaller_number')).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,(
% 0.20/0.39 ![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))),
% 0.20/0.39 inference(skolemize,[status(sab)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (((~![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))) | ((~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)) | less(b, a))) <=> ((~![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))) | (~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)) | less(b, a))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((~![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))) | ((~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)) | less(b, a))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((~![B: $i, A: $i, C: $i] : ((~equalish(add(successor(A), B), C)) | less(B, C))) | (~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)) | less(b, a)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[14, 11, 4, 1])).
% 0.20/0.39 tff(16,plain,(~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(17,assumption,(equalish(c, a)), introduced(assumption)).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (less(b, c) <=> less(b, c)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(19,axiom,(less(b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_less_than_c')).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (less(b, c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (^[B: $i, A: $i] : refl(((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)) <=> ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)) <=> ![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B)) <=> ![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,axiom,(![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))), file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax','less_lemma')).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,(
% 0.20/0.40 ![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))),
% 0.20/0.40 inference(skolemize,[status(sab)],[25])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))) | ((~less(b, c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c))) <=> ((~![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))) | (~less(b, c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))) | ((~less(b, c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~less(A, B)) | equalish(add(successor(predecessor_of_1st_minus_2nd(B, A)), A), B))) | (~less(b, c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (^[Z: $i, Y: $i, X: $i] : rewrite((((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z)) <=> ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.40 tff(36,axiom,(![Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~equalish(Y, Z))) | equalish(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.40 tff(39,plain,(
% 0.20/0.40 ![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a) | (~equalish(c, a)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | (~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a) | (~equalish(c, a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | ((~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a) | (~equalish(c, a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![Z: $i, Y: $i, X: $i] : ((~equalish(X, Y)) | equalish(X, Z) | (~equalish(Y, Z)))) | (~equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), c)) | equalish(add(successor(predecessor_of_1st_minus_2nd(c, b)), b), a) | (~equalish(c, a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 40, 31, 17, 16])).
% 0.20/0.40 tff(45,plain,(~equalish(c, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (divides(c, a) <=> divides(c, a)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(47,axiom,(divides(c, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','impossible_c_divides_a')).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (divides(c, a)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (^[B: $i, A: $i] : refl((equalish(A, B) | less(A, B) | (~divides(A, B))) <=> (equalish(A, B) | less(A, B) | (~divides(A, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B))) <=> ![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B))) <=> ![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (^[B: $i, A: $i] : rewrite((((~divides(A, B)) | less(A, B)) | equalish(A, B)) <=> (equalish(A, B) | less(A, B) | (~divides(A, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![B: $i, A: $i] : (((~divides(A, B)) | less(A, B)) | equalish(A, B)) <=> ![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.40 tff(54,axiom,(![B: $i, A: $i] : (((~divides(A, B)) | less(A, B)) | equalish(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/NUM001-2.ax','divides_only_less_or_equal')).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.40 tff(57,plain,(
% 0.20/0.40 ![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))) | (equalish(c, a) | less(c, a) | (~divides(c, a)))) <=> ((~![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))) | equalish(c, a) | less(c, a) | (~divides(c, a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))) | (equalish(c, a) | less(c, a) | (~divides(c, a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : (equalish(A, B) | less(A, B) | (~divides(A, B)))) | equalish(c, a) | less(c, a) | (~divides(c, a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (equalish(c, a) | less(c, a)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (less(c, a)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 45])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B))) <=> ![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B))) <=> ![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~less(A, B)) | (~less(C, A))) <=> ((~less(C, A)) | (~less(A, B)))), ((((~less(A, B)) | (~less(C, A))) | less(C, B)) <=> (((~less(C, A)) | (~less(A, B))) | less(C, B)))), rewrite((((~less(C, A)) | (~less(A, B))) | less(C, B)) <=> (less(C, B) | (~less(C, A)) | (~less(A, B)))), ((((~less(A, B)) | (~less(C, A))) | less(C, B)) <=> (less(C, B) | (~less(C, A)) | (~less(A, B)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (((~less(A, B)) | (~less(C, A))) | less(C, B)) <=> ![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.40 tff(68,axiom,(![B: $i, A: $i, C: $i] : (((~less(A, B)) | (~less(C, A))) | less(C, B))), file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax','transitivity_of_less')).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.40 tff(71,plain,(
% 0.20/0.40 ![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))) | (less(b, a) | (~less(b, c)) | (~less(c, a)))) <=> ((~![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))) | less(b, a) | (~less(b, c)) | (~less(c, a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((~![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))) | (less(b, a) | (~less(b, c)) | (~less(c, a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~![B: $i, A: $i, C: $i] : (less(C, B) | (~less(C, A)) | (~less(A, B)))) | less(b, a) | (~less(b, c)) | (~less(c, a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[75, 72, 20, 4, 63])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------