TSTP Solution File: PUZ030-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ030-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ030-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 18:22:03 EDT 2022
% 0.13/0.33 % 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(oneof_type, type, (
% 0.13/0.39 oneof: $i > $o)).
% 0.13/0.39 tff(mill_type, type, (
% 0.13/0.39 mill: $i)).
% 0.13/0.39 tff(mustard_type, type, (
% 0.13/0.39 mustard: $i > $o)).
% 0.13/0.39 tff(dix_type, type, (
% 0.13/0.39 dix: $i)).
% 0.13/0.39 tff(neither_type, type, (
% 0.13/0.39 neither: $i > $o)).
% 0.13/0.39 tff(barry_type, type, (
% 0.13/0.39 barry: $i)).
% 0.13/0.39 tff(both_type, type, (
% 0.13/0.39 both: $i > $o)).
% 0.13/0.39 tff(salt_type, type, (
% 0.13/0.39 salt: $i > $o)).
% 0.13/0.39 tff(lang_type, type, (
% 0.13/0.39 lang: $i)).
% 0.13/0.39 tff(cole_type, type, (
% 0.13/0.39 cole: $i)).
% 0.13/0.39 tff(1,assumption,(~oneof(mill)), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(~mustard(mill)), introduced(assumption)).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[X: $i] : refl(((~both(X)) | mustard(X)) <=> ((~both(X)) | mustard(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X: $i] : ((~both(X)) | mustard(X)) <=> ![X: $i] : ((~both(X)) | mustard(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![X: $i] : ((~both(X)) | mustard(X)) <=> ![X: $i] : ((~both(X)) | mustard(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(![X: $i] : ((~both(X)) | mustard(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','both2')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![X: $i] : ((~both(X)) | mustard(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ![X: $i] : ((~both(X)) | mustard(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![X: $i] : ((~both(X)) | mustard(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(mill)) | mustard(mill))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(mill)) | mustard(mill))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(mill)) | mustard(mill))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(mill)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~both(mill)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[12, 9, 2])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[X: $i] : refl((both(X) | oneof(X) | neither(X)) <=> (both(X) | oneof(X) | neither(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![X: $i] : (both(X) | oneof(X) | neither(X)) <=> ![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $i] : (both(X) | oneof(X) | neither(X)) <=> ![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (^[X: $i] : rewrite(((both(X) | neither(X)) | oneof(X)) <=> (both(X) | oneof(X) | neither(X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i] : ((both(X) | neither(X)) | oneof(X)) <=> ![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.39 tff(19,axiom,(![X: $i] : ((both(X) | neither(X)) | oneof(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','one_condition_holds1')).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.39 tff(22,plain,(
% 0.13/0.39 ![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i] : (both(X) | oneof(X) | neither(X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(mill) | neither(mill) | oneof(mill))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | both(mill) | neither(mill) | oneof(mill))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((both(mill) | oneof(mill) | neither(mill)) <=> (both(mill) | neither(mill) | oneof(mill))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(mill) | oneof(mill) | neither(mill))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(mill) | neither(mill) | oneof(mill)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(mill) | oneof(mill) | neither(mill))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | both(mill) | neither(mill) | oneof(mill))),
% 0.13/0.39 inference(transitivity,[status(thm)],[26, 24])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(mill) | oneof(mill) | neither(mill))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | both(mill) | neither(mill) | oneof(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (both(mill) | neither(mill)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 23, 1])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (neither(mill)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[30, 13])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[X: $i] : refl(((~neither(X)) | (~salt(X))) <=> ((~neither(X)) | (~salt(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $i] : ((~neither(X)) | (~salt(X))) <=> ![X: $i] : ((~neither(X)) | (~salt(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $i] : ((~neither(X)) | (~salt(X))) <=> ![X: $i] : ((~neither(X)) | (~salt(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,axiom,(![X: $i] : ((~neither(X)) | (~salt(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','neither2')).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![X: $i] : ((~neither(X)) | (~salt(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,(
% 0.13/0.39 ![X: $i] : ((~neither(X)) | (~salt(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![X: $i] : ((~neither(X)) | (~salt(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(mill)) | (~salt(mill)))) <=> ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(mill)) | (~salt(mill)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(mill)) | (~salt(mill)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(mill)) | (~salt(mill))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (~salt(mill)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((salt(mill) | (~both(barry))) <=> (salt(mill) | (~both(barry)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (((~both(barry)) | salt(mill)) <=> (salt(mill) | (~both(barry)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(45,axiom,((~both(barry)) | salt(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule9_2')).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (salt(mill) | (~both(barry))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (salt(mill) | (~both(barry))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (~both(barry)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[47, 42])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (((~neither(mill)) | mustard(lang)) <=> ((~neither(mill)) | mustard(lang))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(50,axiom,((~neither(mill)) | mustard(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule8_3')).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[55, 49])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~neither(mill)) | mustard(lang)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (mustard(lang)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[58, 31])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (((~both(lang)) | mustard(mill)) <=> ((~both(lang)) | mustard(mill))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(61,axiom,((~both(lang)) | mustard(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule9_3')).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[66, 60])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 ((~both(lang)) | mustard(mill)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (~both(lang)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[69, 2])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 (^[X: $i] : refl((both(X) | (~mustard(X)) | (~salt(X))) <=> (both(X) | (~mustard(X)) | (~salt(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (![X: $i] : (both(X) | (~mustard(X)) | (~salt(X))) <=> ![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (![X: $i] : (both(X) | (~mustard(X)) | (~salt(X))) <=> ![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~salt(X)) | (~mustard(X))) <=> ((~mustard(X)) | (~salt(X)))), ((((~salt(X)) | (~mustard(X))) | both(X)) <=> (((~mustard(X)) | (~salt(X))) | both(X)))), rewrite((((~mustard(X)) | (~salt(X))) | both(X)) <=> (both(X) | (~mustard(X)) | (~salt(X)))), ((((~salt(X)) | (~mustard(X))) | both(X)) <=> (both(X) | (~mustard(X)) | (~salt(X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (![X: $i] : (((~salt(X)) | (~mustard(X))) | both(X)) <=> ![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.13/0.39 tff(76,axiom,(![X: $i] : (((~salt(X)) | (~mustard(X))) | both(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','both3')).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 (![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.13/0.39 tff(79,plain,(
% 0.13/0.39 ![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[78])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | (both(lang) | (~mustard(lang)) | (~salt(lang)))) <=> ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | both(lang) | (~mustard(lang)) | (~salt(lang)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | (both(lang) | (~mustard(lang)) | (~salt(lang)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(83,plain,
% 0.13/0.39 ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | both(lang) | (~mustard(lang)) | (~salt(lang))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.39 tff(84,plain,
% 0.13/0.39 ((~mustard(lang)) | (~salt(lang))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[83, 80, 70])).
% 0.13/0.39 tff(85,plain,
% 0.13/0.39 (~salt(lang)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[84, 59])).
% 0.13/0.39 tff(86,plain,
% 0.13/0.39 (((~oneof(barry)) | salt(lang)) <=> ((~oneof(barry)) | salt(lang))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(87,axiom,((~oneof(barry)) | salt(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule7_2')).
% 0.13/0.39 tff(88,plain,
% 0.13/0.39 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[91, 86])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[92, 86])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 ((~oneof(barry)) | salt(lang)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[94, 86])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 (~oneof(barry)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[95, 85])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(barry) | neither(barry) | both(barry))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(barry) | neither(barry) | both(barry))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 ((both(barry) | oneof(barry) | neither(barry)) <=> (oneof(barry) | neither(barry) | both(barry))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(99,plain,
% 0.13/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(barry) | oneof(barry) | neither(barry))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(barry) | neither(barry) | both(barry)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(barry) | oneof(barry) | neither(barry))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(barry) | neither(barry) | both(barry))),
% 0.13/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.13/0.40 tff(101,plain,
% 0.13/0.40 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(barry) | oneof(barry) | neither(barry))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(102,plain,
% 0.13/0.40 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(barry) | neither(barry) | both(barry)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.13/0.40 tff(103,plain,
% 0.13/0.40 (neither(barry) | both(barry)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[102, 23, 96])).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (neither(barry)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[103, 48])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (^[X: $i] : refl(((~mustard(X)) | (~neither(X))) <=> ((~mustard(X)) | (~neither(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (![X: $i] : ((~mustard(X)) | (~neither(X))) <=> ![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 (![X: $i] : ((~mustard(X)) | (~neither(X))) <=> ![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (^[X: $i] : rewrite(((~neither(X)) | (~mustard(X))) <=> ((~mustard(X)) | (~neither(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 (![X: $i] : ((~neither(X)) | (~mustard(X))) <=> ![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.13/0.40 tff(110,axiom,(![X: $i] : ((~neither(X)) | (~mustard(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','neither3')).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 (![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.13/0.40 tff(112,plain,
% 0.13/0.40 (![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.13/0.40 tff(113,plain,(
% 0.13/0.40 ![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[112])).
% 0.13/0.40 tff(114,plain,
% 0.13/0.40 (![X: $i] : ((~mustard(X)) | (~neither(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 (((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(lang)) | (~neither(lang)))) <=> ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(lang)) | (~neither(lang)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(lang)) | (~neither(lang)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(lang)) | (~neither(lang))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (~neither(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 114, 59])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(lang) | both(lang) | neither(lang))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(lang) | both(lang) | neither(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 ((both(lang) | oneof(lang) | neither(lang)) <=> (oneof(lang) | both(lang) | neither(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(lang) | oneof(lang) | neither(lang))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(lang) | both(lang) | neither(lang)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[120])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(lang) | oneof(lang) | neither(lang))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(lang) | both(lang) | neither(lang))),
% 0.19/0.40 inference(transitivity,[status(thm)],[121, 119])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(lang) | oneof(lang) | neither(lang))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(lang) | both(lang) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (oneof(lang) | neither(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 23, 70])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (oneof(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[125, 118])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((salt(barry) | (~oneof(lang))) <=> (salt(barry) | (~oneof(lang)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (((~oneof(lang)) | salt(barry)) <=> (salt(barry) | (~oneof(lang)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(129,axiom,((~oneof(lang)) | salt(barry)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule1_3')).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (salt(barry) | (~oneof(lang))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (salt(barry) | (~oneof(lang))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (salt(barry)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 126])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(barry)) | (~salt(barry)))) <=> ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(barry)) | (~salt(barry)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(barry)) | (~salt(barry)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(barry)) | (~salt(barry))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[135, 38, 132, 104])).
% 0.19/0.40 tff(137,plain,(mustard(mill) | oneof(mill)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (mustard(mill)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[137, 1])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(mill)) | (~neither(mill)))) <=> ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(mill)) | (~neither(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(mill)) | (~neither(mill)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(mill)) | (~neither(mill))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (~neither(mill)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[141, 114, 138])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (both(mill)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 142])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 ((mustard(barry) | (~both(mill))) <=> (mustard(barry) | (~both(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (((~both(mill)) | mustard(barry)) <=> (mustard(barry) | (~both(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(146,axiom,((~both(mill)) | mustard(barry)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule2_3')).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 (mustard(barry) | (~both(mill))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 (mustard(barry) | (~both(mill))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 (mustard(barry)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[148, 143])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 (((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(barry)) | (~neither(barry)))) <=> ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(barry)) | (~neither(barry)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(barry)) | (~neither(barry)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(barry)) | (~neither(barry))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 (~neither(barry)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[152, 114, 149])).
% 0.19/0.40 tff(154,assumption,(mustard(mill)), introduced(assumption)).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 (~neither(mill)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[141, 114, 154])).
% 0.19/0.40 tff(156,assumption,(~salt(barry)), introduced(assumption)).
% 0.19/0.40 tff(157,plain,
% 0.19/0.40 ((salt(barry) | (~oneof(cole))) <=> (salt(barry) | (~oneof(cole)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 (((~oneof(cole)) | salt(barry)) <=> (salt(barry) | (~oneof(cole)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(159,axiom,((~oneof(cole)) | salt(barry)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule1_2')).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (salt(barry) | (~oneof(cole))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 (salt(barry) | (~oneof(cole))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[160, 157])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 (~oneof(cole)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[161, 156])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.40 ((oneof(cole) | oneof(dix) | (~mustard(mill))) <=> (oneof(cole) | oneof(dix) | (~mustard(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(164,plain,
% 0.19/0.40 (((oneof(cole) | (~mustard(mill))) | oneof(dix)) <=> (oneof(cole) | oneof(dix) | (~mustard(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(165,plain,
% 0.19/0.40 (((~mustard(mill)) | oneof(cole)) <=> (oneof(cole) | (~mustard(mill)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(166,plain,
% 0.19/0.40 ((((~mustard(mill)) | oneof(cole)) | oneof(dix)) <=> ((oneof(cole) | (~mustard(mill))) | oneof(dix))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 ((((~mustard(mill)) | oneof(cole)) | oneof(dix)) <=> (oneof(cole) | oneof(dix) | (~mustard(mill)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.40 tff(168,axiom,(((~mustard(mill)) | oneof(cole)) | oneof(dix)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule10_1')).
% 0.19/0.40 tff(169,plain,
% 0.19/0.40 (oneof(cole) | oneof(dix) | (~mustard(mill))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.40 tff(170,plain,
% 0.19/0.40 (oneof(cole) | oneof(dix) | (~mustard(mill))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.19/0.40 tff(171,plain,
% 0.19/0.40 (oneof(dix)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[170, 162, 154])).
% 0.19/0.40 tff(172,plain,
% 0.19/0.40 ((salt(lang) | (~oneof(dix))) <=> (salt(lang) | (~oneof(dix)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(173,plain,
% 0.19/0.40 (((~oneof(dix)) | salt(lang)) <=> (salt(lang) | (~oneof(dix)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(174,axiom,((~oneof(dix)) | salt(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule7_3')).
% 0.19/0.40 tff(175,plain,
% 0.19/0.40 (salt(lang) | (~oneof(dix))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.40 tff(176,plain,
% 0.19/0.40 (salt(lang) | (~oneof(dix))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.19/0.40 tff(177,plain,
% 0.19/0.40 (salt(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[176, 171])).
% 0.19/0.40 tff(178,plain,
% 0.19/0.40 (((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(lang)) | (~salt(lang)))) <=> ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(lang)) | (~salt(lang)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(179,plain,
% 0.19/0.40 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(lang)) | (~salt(lang)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(180,plain,
% 0.19/0.40 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(lang)) | (~salt(lang))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.40 tff(181,plain,
% 0.19/0.40 (~neither(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[180, 38, 177])).
% 0.19/0.40 tff(182,plain,
% 0.19/0.40 (~oneof(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 156])).
% 0.19/0.40 tff(183,plain,
% 0.19/0.40 (both(lang) | neither(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 23, 182])).
% 0.19/0.40 tff(184,plain,
% 0.19/0.40 (both(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[183, 181])).
% 0.19/0.40 tff(185,plain,
% 0.19/0.40 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(lang)) | mustard(lang))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(lang)) | mustard(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(186,plain,
% 0.19/0.40 ((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(lang)) | mustard(lang))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(187,plain,
% 0.19/0.40 ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(lang)) | mustard(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.40 tff(188,plain,
% 0.19/0.40 (mustard(lang)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[187, 9, 184])).
% 0.19/0.40 tff(189,assumption,(~neither(barry)), introduced(assumption)).
% 0.19/0.40 tff(190,plain,
% 0.19/0.40 ((neither(mill) | (~mustard(dix)) | neither(lang)) <=> (neither(mill) | (~mustard(dix)) | neither(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(191,plain,
% 0.19/0.40 ((((~mustard(dix)) | neither(lang)) | neither(mill)) <=> (neither(mill) | (~mustard(dix)) | neither(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(192,plain,
% 0.19/0.40 (((~mustard(dix)) | neither(lang)) <=> ((~mustard(dix)) | neither(lang))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(193,plain,
% 0.19/0.40 ((((~mustard(dix)) | neither(lang)) | neither(mill)) <=> (((~mustard(dix)) | neither(lang)) | neither(mill))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.40 tff(194,plain,
% 0.19/0.40 ((((~mustard(dix)) | neither(lang)) | neither(mill)) <=> (neither(mill) | (~mustard(dix)) | neither(lang))),
% 0.19/0.40 inference(transitivity,[status(thm)],[193, 191])).
% 0.19/0.40 tff(195,axiom,(((~mustard(dix)) | neither(lang)) | neither(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule6_1')).
% 0.19/0.40 tff(196,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.40 tff(197,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[196, 190])).
% 0.19/0.40 tff(198,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.19/0.40 tff(199,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[198, 190])).
% 0.19/0.40 tff(200,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[199, 190])).
% 0.19/0.40 tff(201,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[200, 190])).
% 0.19/0.40 tff(202,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[201, 190])).
% 0.19/0.40 tff(203,plain,
% 0.19/0.40 (neither(mill) | (~mustard(dix)) | neither(lang)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[202, 190])).
% 0.19/0.40 tff(204,plain,
% 0.19/0.40 (~mustard(dix)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[203, 181, 155])).
% 0.19/0.40 tff(205,plain,
% 0.19/0.40 (^[X: $i] : refl((salt(X) | mustard(X) | (~oneof(X))) <=> (salt(X) | mustard(X) | (~oneof(X))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(206,plain,
% 0.19/0.40 (![X: $i] : (salt(X) | mustard(X) | (~oneof(X))) <=> ![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.40 tff(207,plain,
% 0.19/0.40 (![X: $i] : (salt(X) | mustard(X) | (~oneof(X))) <=> ![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite(((~oneof(X)) | salt(X)) <=> (salt(X) | (~oneof(X)))), ((((~oneof(X)) | salt(X)) | mustard(X)) <=> ((salt(X) | (~oneof(X))) | mustard(X)))), rewrite(((salt(X) | (~oneof(X))) | mustard(X)) <=> (salt(X) | mustard(X) | (~oneof(X)))), ((((~oneof(X)) | salt(X)) | mustard(X)) <=> (salt(X) | mustard(X) | (~oneof(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 (![X: $i] : (((~oneof(X)) | salt(X)) | mustard(X)) <=> ![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.41 tff(210,axiom,(![X: $i] : (((~oneof(X)) | salt(X)) | mustard(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','oneof1')).
% 0.19/0.41 tff(211,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.19/0.41 tff(213,plain,(
% 0.19/0.41 ![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[212])).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 (((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | (salt(dix) | mustard(dix) | (~oneof(dix)))) <=> ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | salt(dix) | mustard(dix) | (~oneof(dix)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | (salt(dix) | mustard(dix) | (~oneof(dix)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(217,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | salt(dix) | mustard(dix) | (~oneof(dix))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.41 tff(218,plain,
% 0.19/0.41 (salt(dix) | mustard(dix)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[217, 214, 171])).
% 0.19/0.41 tff(219,plain,
% 0.19/0.41 (salt(dix)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[218, 204])).
% 0.19/0.41 tff(220,plain,
% 0.19/0.41 (((~salt(dix)) | neither(barry) | both(cole)) <=> ((~salt(dix)) | neither(barry) | both(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(221,plain,
% 0.19/0.41 ((((~salt(dix)) | neither(barry)) | both(cole)) <=> ((~salt(dix)) | neither(barry) | both(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(222,plain,
% 0.19/0.41 (((~salt(dix)) | neither(barry)) <=> ((~salt(dix)) | neither(barry))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(223,plain,
% 0.19/0.41 ((((~salt(dix)) | neither(barry)) | both(cole)) <=> (((~salt(dix)) | neither(barry)) | both(cole))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.41 tff(224,plain,
% 0.19/0.41 ((((~salt(dix)) | neither(barry)) | both(cole)) <=> ((~salt(dix)) | neither(barry) | both(cole))),
% 0.19/0.41 inference(transitivity,[status(thm)],[223, 221])).
% 0.19/0.41 tff(225,axiom,(((~salt(dix)) | neither(barry)) | both(cole)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule5_1')).
% 0.19/0.41 tff(226,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.41 tff(227,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[226, 220])).
% 0.19/0.41 tff(228,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.19/0.41 tff(229,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[228, 220])).
% 0.19/0.41 tff(230,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[229, 220])).
% 0.19/0.41 tff(231,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[230, 220])).
% 0.19/0.41 tff(232,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[231, 220])).
% 0.19/0.41 tff(233,plain,
% 0.19/0.41 ((~salt(dix)) | neither(barry) | both(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[232, 220])).
% 0.19/0.41 tff(234,plain,
% 0.19/0.41 (both(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[233, 219, 189])).
% 0.19/0.41 tff(235,plain,
% 0.19/0.41 (^[X: $i] : refl(((~both(X)) | (~neither(X))) <=> ((~both(X)) | (~neither(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(236,plain,
% 0.19/0.41 (![X: $i] : ((~both(X)) | (~neither(X))) <=> ![X: $i] : ((~both(X)) | (~neither(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[235])).
% 0.19/0.41 tff(237,plain,
% 0.19/0.41 (![X: $i] : ((~both(X)) | (~neither(X))) <=> ![X: $i] : ((~both(X)) | (~neither(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(238,axiom,(![X: $i] : ((~both(X)) | (~neither(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','neither1')).
% 0.19/0.41 tff(239,plain,
% 0.19/0.41 (![X: $i] : ((~both(X)) | (~neither(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.41 tff(240,plain,(
% 0.19/0.41 ![X: $i] : ((~both(X)) | (~neither(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[239])).
% 0.19/0.41 tff(241,plain,
% 0.19/0.41 (![X: $i] : ((~both(X)) | (~neither(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.19/0.41 tff(242,plain,
% 0.19/0.41 (((~![X: $i] : ((~both(X)) | (~neither(X)))) | ((~both(cole)) | (~neither(cole)))) <=> ((~![X: $i] : ((~both(X)) | (~neither(X)))) | (~both(cole)) | (~neither(cole)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(243,plain,
% 0.19/0.41 ((~![X: $i] : ((~both(X)) | (~neither(X)))) | ((~both(cole)) | (~neither(cole)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(244,plain,
% 0.19/0.41 ((~![X: $i] : ((~both(X)) | (~neither(X)))) | (~both(cole)) | (~neither(cole))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.19/0.41 tff(245,plain,
% 0.19/0.41 (~neither(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[244, 241, 234])).
% 0.19/0.41 tff(246,plain,
% 0.19/0.41 ((neither(mill) | (~mustard(lang)) | neither(cole)) <=> (neither(mill) | (~mustard(lang)) | neither(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(247,plain,
% 0.19/0.41 ((((~mustard(lang)) | neither(cole)) | neither(mill)) <=> (neither(mill) | (~mustard(lang)) | neither(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(248,plain,
% 0.19/0.41 (((~mustard(lang)) | neither(cole)) <=> ((~mustard(lang)) | neither(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(249,plain,
% 0.19/0.41 ((((~mustard(lang)) | neither(cole)) | neither(mill)) <=> (((~mustard(lang)) | neither(cole)) | neither(mill))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[248])).
% 0.19/0.41 tff(250,plain,
% 0.19/0.41 ((((~mustard(lang)) | neither(cole)) | neither(mill)) <=> (neither(mill) | (~mustard(lang)) | neither(cole))),
% 0.19/0.41 inference(transitivity,[status(thm)],[249, 247])).
% 0.19/0.41 tff(251,axiom,(((~mustard(lang)) | neither(cole)) | neither(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule8_1')).
% 0.19/0.41 tff(252,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.19/0.41 tff(253,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[252, 246])).
% 0.19/0.41 tff(254,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.19/0.41 tff(255,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[254, 246])).
% 0.19/0.41 tff(256,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[255, 246])).
% 0.19/0.41 tff(257,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.19/0.41 tff(258,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[257, 246])).
% 0.19/0.41 tff(259,plain,
% 0.19/0.41 (neither(mill) | (~mustard(lang)) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[258, 246])).
% 0.19/0.41 tff(260,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[259, 245, 188, 155])).
% 0.19/0.41 tff(261,plain,(salt(barry) | neither(barry) | (~mustard(mill))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(262,plain,
% 0.19/0.41 (salt(barry)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[261, 153, 138])).
% 0.19/0.41 tff(263,plain,
% 0.19/0.41 (^[X: $i] : refl(((~mustard(X)) | (~salt(X)) | (~oneof(X))) <=> ((~mustard(X)) | (~salt(X)) | (~oneof(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(264,plain,
% 0.19/0.41 (![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X))) <=> ![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[263])).
% 0.19/0.41 tff(265,plain,
% 0.19/0.41 (![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X))) <=> ![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(266,plain,
% 0.19/0.41 (^[X: $i] : rewrite((((~oneof(X)) | (~salt(X))) | (~mustard(X))) <=> ((~mustard(X)) | (~salt(X)) | (~oneof(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(267,plain,
% 0.19/0.41 (![X: $i] : (((~oneof(X)) | (~salt(X))) | (~mustard(X))) <=> ![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[266])).
% 0.19/0.41 tff(268,axiom,(![X: $i] : (((~oneof(X)) | (~salt(X))) | (~mustard(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','oneof4')).
% 0.19/0.41 tff(269,plain,
% 0.19/0.41 (![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.19/0.41 tff(270,plain,
% 0.19/0.41 (![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.19/0.41 tff(271,plain,(
% 0.19/0.41 ![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[270])).
% 0.19/0.41 tff(272,plain,
% 0.19/0.41 (![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.19/0.41 tff(273,plain,
% 0.19/0.41 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(barry)) | (~mustard(barry)) | (~oneof(barry)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(barry)) | (~mustard(barry)) | (~oneof(barry)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(274,plain,
% 0.19/0.41 (((~mustard(barry)) | (~salt(barry)) | (~oneof(barry))) <=> ((~salt(barry)) | (~mustard(barry)) | (~oneof(barry)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(275,plain,
% 0.19/0.41 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(barry)) | (~salt(barry)) | (~oneof(barry)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(barry)) | (~mustard(barry)) | (~oneof(barry))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[274])).
% 0.19/0.41 tff(276,plain,
% 0.19/0.41 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(barry)) | (~salt(barry)) | (~oneof(barry)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(barry)) | (~mustard(barry)) | (~oneof(barry)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[275, 273])).
% 0.19/0.41 tff(277,plain,
% 0.19/0.41 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(barry)) | (~salt(barry)) | (~oneof(barry)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(278,plain,
% 0.19/0.41 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(barry)) | (~mustard(barry)) | (~oneof(barry))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.19/0.41 tff(279,plain,
% 0.19/0.41 ((~salt(barry)) | (~oneof(barry))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[278, 272, 149])).
% 0.19/0.41 tff(280,plain,
% 0.19/0.41 (~oneof(barry)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[279, 262])).
% 0.19/0.41 tff(281,plain,
% 0.19/0.41 (((~salt(cole)) | oneof(barry) | neither(mill)) <=> ((~salt(cole)) | oneof(barry) | neither(mill))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(282,plain,
% 0.19/0.41 ((((~salt(cole)) | oneof(barry)) | neither(mill)) <=> ((~salt(cole)) | oneof(barry) | neither(mill))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(283,plain,
% 0.19/0.41 (((~salt(cole)) | oneof(barry)) <=> ((~salt(cole)) | oneof(barry))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(284,plain,
% 0.19/0.41 ((((~salt(cole)) | oneof(barry)) | neither(mill)) <=> (((~salt(cole)) | oneof(barry)) | neither(mill))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[283])).
% 0.19/0.41 tff(285,plain,
% 0.19/0.41 ((((~salt(cole)) | oneof(barry)) | neither(mill)) <=> ((~salt(cole)) | oneof(barry) | neither(mill))),
% 0.19/0.41 inference(transitivity,[status(thm)],[284, 282])).
% 0.19/0.41 tff(286,axiom,(((~salt(cole)) | oneof(barry)) | neither(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule3_1')).
% 0.19/0.41 tff(287,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.19/0.41 tff(288,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[287, 281])).
% 0.19/0.41 tff(289,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.19/0.41 tff(290,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[289, 281])).
% 0.19/0.41 tff(291,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[290, 281])).
% 0.19/0.41 tff(292,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[291, 281])).
% 0.19/0.41 tff(293,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[292, 281])).
% 0.19/0.41 tff(294,plain,
% 0.19/0.41 ((~salt(cole)) | oneof(barry) | neither(mill)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[293, 281])).
% 0.19/0.41 tff(295,plain,
% 0.19/0.41 (~salt(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[294, 280, 142])).
% 0.19/0.41 tff(296,plain,
% 0.19/0.41 (^[X: $i] : refl((salt(X) | (~both(X))) <=> (salt(X) | (~both(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(297,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | (~both(X))) <=> ![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[296])).
% 0.19/0.41 tff(298,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | (~both(X))) <=> ![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(299,plain,
% 0.19/0.41 (^[X: $i] : rewrite(((~both(X)) | salt(X)) <=> (salt(X) | (~both(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(300,plain,
% 0.19/0.41 (![X: $i] : ((~both(X)) | salt(X)) <=> ![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[299])).
% 0.19/0.41 tff(301,axiom,(![X: $i] : ((~both(X)) | salt(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','both1')).
% 0.19/0.41 tff(302,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.19/0.41 tff(303,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.19/0.41 tff(304,plain,(
% 0.19/0.41 ![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[303])).
% 0.19/0.41 tff(305,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | (~both(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.19/0.41 tff(306,plain,
% 0.19/0.41 (((~![X: $i] : (salt(X) | (~both(X)))) | (salt(cole) | (~both(cole)))) <=> ((~![X: $i] : (salt(X) | (~both(X)))) | salt(cole) | (~both(cole)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(307,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | (~both(X)))) | (salt(cole) | (~both(cole)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(308,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | (~both(X)))) | salt(cole) | (~both(cole))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.19/0.41 tff(309,plain,
% 0.19/0.41 (~both(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[308, 305, 295])).
% 0.19/0.41 tff(310,plain,
% 0.19/0.41 (~salt(dix)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[233, 309, 153])).
% 0.19/0.41 tff(311,plain,
% 0.19/0.41 (((~![X: $i] : (salt(X) | (~both(X)))) | (salt(dix) | (~both(dix)))) <=> ((~![X: $i] : (salt(X) | (~both(X)))) | salt(dix) | (~both(dix)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(312,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | (~both(X)))) | (salt(dix) | (~both(dix)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(313,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | (~both(X)))) | salt(dix) | (~both(dix))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.19/0.41 tff(314,plain,
% 0.19/0.41 (~both(dix)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[313, 305, 310])).
% 0.19/0.41 tff(315,assumption,(~mustard(lang)), introduced(assumption)).
% 0.19/0.41 tff(316,assumption,(~both(dix)), introduced(assumption)).
% 0.19/0.41 tff(317,plain,
% 0.19/0.41 ((mustard(lang) | (~neither(cole))) <=> (mustard(lang) | (~neither(cole)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(318,plain,
% 0.19/0.41 (((~neither(cole)) | mustard(lang)) <=> (mustard(lang) | (~neither(cole)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(319,axiom,((~neither(cole)) | mustard(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule8_2')).
% 0.19/0.41 tff(320,plain,
% 0.19/0.41 (mustard(lang) | (~neither(cole))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.19/0.41 tff(321,plain,
% 0.19/0.41 (mustard(lang) | (~neither(cole))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[320, 317])).
% 0.19/0.41 tff(322,plain,
% 0.19/0.41 (~neither(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[321, 315])).
% 0.19/0.41 tff(323,assumption,(~salt(cole)), introduced(assumption)).
% 0.19/0.41 tff(324,plain,
% 0.19/0.41 (^[X: $i] : refl((salt(X) | mustard(X) | neither(X)) <=> (salt(X) | mustard(X) | neither(X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(325,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | neither(X)) <=> ![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[324])).
% 0.19/0.41 tff(326,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | neither(X)) <=> ![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(327,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite((salt(X) | mustard(X)) <=> (salt(X) | mustard(X))), (((salt(X) | mustard(X)) | neither(X)) <=> ((salt(X) | mustard(X)) | neither(X)))), rewrite(((salt(X) | mustard(X)) | neither(X)) <=> (salt(X) | mustard(X) | neither(X))), (((salt(X) | mustard(X)) | neither(X)) <=> (salt(X) | mustard(X) | neither(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(328,plain,
% 0.19/0.41 (![X: $i] : ((salt(X) | mustard(X)) | neither(X)) <=> ![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[327])).
% 0.19/0.41 tff(329,axiom,(![X: $i] : ((salt(X) | mustard(X)) | neither(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','neither4')).
% 0.19/0.41 tff(330,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.41 tff(331,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[330, 326])).
% 0.19/0.41 tff(332,plain,(
% 0.19/0.41 ![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[331])).
% 0.19/0.41 tff(333,plain,
% 0.19/0.41 (![X: $i] : (salt(X) | mustard(X) | neither(X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[332, 325])).
% 0.19/0.41 tff(334,plain,
% 0.19/0.41 (((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (salt(cole) | mustard(cole) | neither(cole))) <=> ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | salt(cole) | mustard(cole) | neither(cole))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(335,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (salt(cole) | mustard(cole) | neither(cole))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(336,plain,
% 0.19/0.41 ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | salt(cole) | mustard(cole) | neither(cole)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.41 tff(337,plain,
% 0.19/0.41 (mustard(cole) | neither(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[336, 333, 323])).
% 0.19/0.41 tff(338,plain,
% 0.19/0.41 (mustard(cole)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[337, 322])).
% 0.19/0.41 tff(339,plain,
% 0.19/0.41 (((~mustard(cole)) | both(dix) | both(lang)) <=> ((~mustard(cole)) | both(dix) | both(lang))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(340,plain,
% 0.19/0.41 ((((~mustard(cole)) | both(dix)) | both(lang)) <=> ((~mustard(cole)) | both(dix) | both(lang))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(341,plain,
% 0.19/0.41 (((~mustard(cole)) | both(dix)) <=> ((~mustard(cole)) | both(dix))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(342,plain,
% 0.19/0.41 ((((~mustard(cole)) | both(dix)) | both(lang)) <=> (((~mustard(cole)) | both(dix)) | both(lang))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[341])).
% 0.19/0.41 tff(343,plain,
% 0.19/0.41 ((((~mustard(cole)) | both(dix)) | both(lang)) <=> ((~mustard(cole)) | both(dix) | both(lang))),
% 0.19/0.41 inference(transitivity,[status(thm)],[342, 340])).
% 0.19/0.41 tff(344,axiom,(((~mustard(cole)) | both(dix)) | both(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule4_1')).
% 0.19/0.41 tff(345,plain,
% 0.19/0.41 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.19/0.41 tff(346,plain,
% 0.19/0.41 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[345, 339])).
% 0.19/0.41 tff(347,plain,
% 0.19/0.41 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[346, 339])).
% 0.19/0.41 tff(348,plain,
% 0.19/0.41 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[347, 339])).
% 0.19/0.41 tff(349,plain,
% 0.19/0.41 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[348, 339])).
% 0.19/0.42 tff(350,plain,
% 0.19/0.42 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[349, 339])).
% 0.19/0.42 tff(351,plain,
% 0.19/0.42 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[350, 339])).
% 0.19/0.42 tff(352,plain,
% 0.19/0.42 ((~mustard(cole)) | both(dix) | both(lang)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[351, 339])).
% 0.19/0.42 tff(353,plain,
% 0.19/0.42 (both(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[352, 338, 316])).
% 0.19/0.42 tff(354,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[187, 9, 353, 315])).
% 0.19/0.42 tff(355,plain,(mustard(lang) | both(dix) | salt(cole)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(356,plain,
% 0.19/0.42 (mustard(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[355, 314, 295])).
% 0.19/0.42 tff(357,plain,
% 0.19/0.42 (~neither(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[117, 114, 356])).
% 0.19/0.42 tff(358,plain,
% 0.19/0.42 (~mustard(dix)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[203, 357, 142])).
% 0.19/0.42 tff(359,plain,
% 0.19/0.42 (neither(cole)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[259, 356, 142])).
% 0.19/0.42 tff(360,plain,
% 0.19/0.42 (^[X: $i] : refl(((~oneof(X)) | (~neither(X))) <=> ((~oneof(X)) | (~neither(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(361,plain,
% 0.19/0.42 (![X: $i] : ((~oneof(X)) | (~neither(X))) <=> ![X: $i] : ((~oneof(X)) | (~neither(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[360])).
% 0.19/0.42 tff(362,plain,
% 0.19/0.42 (![X: $i] : ((~oneof(X)) | (~neither(X))) <=> ![X: $i] : ((~oneof(X)) | (~neither(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(363,axiom,(![X: $i] : ((~oneof(X)) | (~neither(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','oneof3')).
% 0.19/0.42 tff(364,plain,
% 0.19/0.42 (![X: $i] : ((~oneof(X)) | (~neither(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.42 tff(365,plain,(
% 0.19/0.42 ![X: $i] : ((~oneof(X)) | (~neither(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[364])).
% 0.19/0.42 tff(366,plain,
% 0.19/0.42 (![X: $i] : ((~oneof(X)) | (~neither(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[365, 361])).
% 0.19/0.42 tff(367,plain,
% 0.19/0.42 (((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~oneof(cole)) | (~neither(cole)))) <=> ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | (~oneof(cole)) | (~neither(cole)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(368,plain,
% 0.19/0.42 ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~oneof(cole)) | (~neither(cole)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(369,plain,
% 0.19/0.42 ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | (~oneof(cole)) | (~neither(cole))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.19/0.42 tff(370,plain,
% 0.19/0.42 (~oneof(cole)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[369, 366, 359])).
% 0.19/0.42 tff(371,plain,
% 0.19/0.42 (oneof(dix)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[170, 370, 138])).
% 0.19/0.42 tff(372,plain,
% 0.19/0.42 (mustard(dix) | (~oneof(dix))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[217, 214, 310])).
% 0.19/0.42 tff(373,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[372, 371, 358])).
% 0.19/0.42 tff(374,plain,(oneof(mill)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(375,plain,
% 0.19/0.42 (((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~neither(mill)) | (~oneof(mill)))) <=> ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | (~neither(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(376,plain,
% 0.19/0.42 (((~oneof(mill)) | (~neither(mill))) <=> ((~neither(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(377,plain,
% 0.19/0.42 (((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~oneof(mill)) | (~neither(mill)))) <=> ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~neither(mill)) | (~oneof(mill))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[376])).
% 0.19/0.42 tff(378,plain,
% 0.19/0.42 (((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~oneof(mill)) | (~neither(mill)))) <=> ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | (~neither(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[377, 375])).
% 0.19/0.42 tff(379,plain,
% 0.19/0.42 ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | ((~oneof(mill)) | (~neither(mill)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(380,plain,
% 0.19/0.42 ((~![X: $i] : ((~oneof(X)) | (~neither(X)))) | (~neither(mill)) | (~oneof(mill))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.19/0.42 tff(381,plain,
% 0.19/0.42 (~neither(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[380, 366, 374])).
% 0.19/0.42 tff(382,plain,
% 0.19/0.42 (~both(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[187, 9, 315])).
% 0.19/0.42 tff(383,plain,
% 0.19/0.42 (^[X: $i] : refl(((~both(X)) | (~oneof(X))) <=> ((~both(X)) | (~oneof(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(384,plain,
% 0.19/0.42 (![X: $i] : ((~both(X)) | (~oneof(X))) <=> ![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[383])).
% 0.19/0.42 tff(385,plain,
% 0.19/0.42 (![X: $i] : ((~both(X)) | (~oneof(X))) <=> ![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(386,plain,
% 0.19/0.42 (^[X: $i] : rewrite(((~oneof(X)) | (~both(X))) <=> ((~both(X)) | (~oneof(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(387,plain,
% 0.19/0.42 (![X: $i] : ((~oneof(X)) | (~both(X))) <=> ![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[386])).
% 0.19/0.42 tff(388,axiom,(![X: $i] : ((~oneof(X)) | (~both(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','oneof2')).
% 0.19/0.42 tff(389,plain,
% 0.19/0.42 (![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.19/0.42 tff(390,plain,
% 0.19/0.42 (![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.19/0.42 tff(391,plain,(
% 0.19/0.42 ![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[390])).
% 0.19/0.42 tff(392,plain,
% 0.19/0.42 (![X: $i] : ((~both(X)) | (~oneof(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[391, 384])).
% 0.19/0.42 tff(393,plain,
% 0.19/0.42 (((~![X: $i] : ((~both(X)) | (~oneof(X)))) | ((~both(mill)) | (~oneof(mill)))) <=> ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | (~both(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(394,plain,
% 0.19/0.42 ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | ((~both(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(395,plain,
% 0.19/0.42 ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | (~both(mill)) | (~oneof(mill))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.19/0.42 tff(396,plain,
% 0.19/0.42 (~both(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[395, 392, 374])).
% 0.19/0.42 tff(397,plain,
% 0.19/0.42 (((~oneof(cole)) | mustard(mill)) <=> ((~oneof(cole)) | mustard(mill))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(398,axiom,((~oneof(cole)) | mustard(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule10_2')).
% 0.19/0.42 tff(399,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.19/0.42 tff(400,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[399, 397])).
% 0.19/0.42 tff(401,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[400, 397])).
% 0.19/0.42 tff(402,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.19/0.42 tff(403,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[402, 397])).
% 0.19/0.42 tff(404,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[403, 397])).
% 0.19/0.42 tff(405,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.19/0.42 tff(406,plain,
% 0.19/0.42 ((~oneof(cole)) | mustard(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[405, 397])).
% 0.19/0.42 tff(407,plain,
% 0.19/0.42 (~oneof(cole)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[406, 2])).
% 0.19/0.42 tff(408,assumption,(~neither(cole)), introduced(assumption)).
% 0.19/0.42 tff(409,plain,
% 0.19/0.42 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(cole) | both(cole) | neither(cole))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(cole) | both(cole) | neither(cole))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(410,plain,
% 0.19/0.42 ((both(cole) | oneof(cole) | neither(cole)) <=> (oneof(cole) | both(cole) | neither(cole))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(411,plain,
% 0.19/0.42 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(cole) | oneof(cole) | neither(cole))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (oneof(cole) | both(cole) | neither(cole)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[410])).
% 0.19/0.42 tff(412,plain,
% 0.19/0.42 (((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(cole) | oneof(cole) | neither(cole))) <=> ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(cole) | both(cole) | neither(cole))),
% 0.19/0.42 inference(transitivity,[status(thm)],[411, 409])).
% 0.19/0.42 tff(413,plain,
% 0.19/0.42 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | (both(cole) | oneof(cole) | neither(cole))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(414,plain,
% 0.19/0.42 ((~![X: $i] : (both(X) | oneof(X) | neither(X))) | oneof(cole) | both(cole) | neither(cole)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.19/0.42 tff(415,plain,
% 0.19/0.42 (oneof(cole) | both(cole)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[414, 23, 408])).
% 0.19/0.42 tff(416,plain,
% 0.19/0.42 (both(cole)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[415, 407])).
% 0.19/0.42 tff(417,plain,
% 0.19/0.42 ((salt(dix) | (~both(cole))) <=> (salt(dix) | (~both(cole)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(418,plain,
% 0.19/0.42 (((~both(cole)) | salt(dix)) <=> (salt(dix) | (~both(cole)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(419,axiom,((~both(cole)) | salt(dix)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule5_3')).
% 0.19/0.42 tff(420,plain,
% 0.19/0.42 (salt(dix) | (~both(cole))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.19/0.42 tff(421,plain,
% 0.19/0.42 (salt(dix) | (~both(cole))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[420, 417])).
% 0.19/0.42 tff(422,plain,
% 0.19/0.42 (salt(dix)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[421, 416])).
% 0.19/0.42 tff(423,plain,
% 0.19/0.42 (((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(dix)) | (~salt(dix)))) <=> ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(dix)) | (~salt(dix)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(424,plain,
% 0.19/0.42 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | ((~neither(dix)) | (~salt(dix)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(425,plain,
% 0.19/0.42 ((~![X: $i] : ((~neither(X)) | (~salt(X)))) | (~neither(dix)) | (~salt(dix))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.19/0.42 tff(426,plain,
% 0.19/0.42 (~neither(dix)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[425, 38, 422])).
% 0.19/0.42 tff(427,assumption,(~both(lang)), introduced(assumption)).
% 0.19/0.42 tff(428,plain,
% 0.19/0.42 (((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | (salt(mill) | mustard(mill) | (~oneof(mill)))) <=> ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | salt(mill) | mustard(mill) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(429,plain,
% 0.19/0.42 ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | (salt(mill) | mustard(mill) | (~oneof(mill)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(430,plain,
% 0.19/0.42 ((~![X: $i] : (salt(X) | mustard(X) | (~oneof(X)))) | salt(mill) | mustard(mill) | (~oneof(mill))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.19/0.42 tff(431,plain,
% 0.19/0.42 (salt(mill) | mustard(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[430, 214, 374])).
% 0.19/0.42 tff(432,plain,
% 0.19/0.42 (salt(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[431, 2])).
% 0.19/0.42 tff(433,plain,
% 0.19/0.42 ((both(lang) | (~salt(mill)) | both(barry)) <=> (both(lang) | (~salt(mill)) | both(barry))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(434,plain,
% 0.19/0.42 ((((~salt(mill)) | both(barry)) | both(lang)) <=> (both(lang) | (~salt(mill)) | both(barry))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(435,plain,
% 0.19/0.42 (((~salt(mill)) | both(barry)) <=> ((~salt(mill)) | both(barry))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(436,plain,
% 0.19/0.42 ((((~salt(mill)) | both(barry)) | both(lang)) <=> (((~salt(mill)) | both(barry)) | both(lang))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[435])).
% 0.19/0.42 tff(437,plain,
% 0.19/0.42 ((((~salt(mill)) | both(barry)) | both(lang)) <=> (both(lang) | (~salt(mill)) | both(barry))),
% 0.19/0.42 inference(transitivity,[status(thm)],[436, 434])).
% 0.19/0.42 tff(438,axiom,(((~salt(mill)) | both(barry)) | both(lang)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule9_1')).
% 0.19/0.42 tff(439,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.19/0.42 tff(440,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[439, 433])).
% 0.19/0.42 tff(441,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[440, 433])).
% 0.19/0.42 tff(442,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[441, 433])).
% 0.19/0.42 tff(443,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[442, 433])).
% 0.19/0.42 tff(444,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[443, 433])).
% 0.19/0.42 tff(445,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[444, 433])).
% 0.19/0.42 tff(446,plain,
% 0.19/0.42 (both(lang) | (~salt(mill)) | both(barry)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[445, 433])).
% 0.19/0.42 tff(447,plain,
% 0.19/0.42 (both(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[446, 432, 427])).
% 0.19/0.42 tff(448,plain,
% 0.19/0.42 (((~![X: $i] : ((~both(X)) | mustard(X))) | (mustard(barry) | (~both(barry)))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(barry) | (~both(barry)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(449,plain,
% 0.19/0.42 (((~both(barry)) | mustard(barry)) <=> (mustard(barry) | (~both(barry)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(450,plain,
% 0.19/0.42 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(barry)) | mustard(barry))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | (mustard(barry) | (~both(barry))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[449])).
% 0.19/0.42 tff(451,plain,
% 0.19/0.42 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(barry)) | mustard(barry))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(barry) | (~both(barry)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[450, 448])).
% 0.19/0.42 tff(452,plain,
% 0.19/0.42 ((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(barry)) | mustard(barry))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(453,plain,
% 0.19/0.42 ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(barry) | (~both(barry))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.19/0.42 tff(454,plain,
% 0.19/0.42 (mustard(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[453, 9, 447])).
% 0.19/0.42 tff(455,plain,
% 0.19/0.42 (((~mustard(barry)) | neither(dix) | both(mill)) <=> ((~mustard(barry)) | neither(dix) | both(mill))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(456,plain,
% 0.19/0.42 ((((~mustard(barry)) | neither(dix)) | both(mill)) <=> ((~mustard(barry)) | neither(dix) | both(mill))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(457,plain,
% 0.19/0.42 (((~mustard(barry)) | neither(dix)) <=> ((~mustard(barry)) | neither(dix))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(458,plain,
% 0.19/0.42 ((((~mustard(barry)) | neither(dix)) | both(mill)) <=> (((~mustard(barry)) | neither(dix)) | both(mill))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.42 tff(459,plain,
% 0.19/0.42 ((((~mustard(barry)) | neither(dix)) | both(mill)) <=> ((~mustard(barry)) | neither(dix) | both(mill))),
% 0.19/0.42 inference(transitivity,[status(thm)],[458, 456])).
% 0.19/0.42 tff(460,axiom,(((~mustard(barry)) | neither(dix)) | both(mill)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule2_1')).
% 0.19/0.42 tff(461,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.19/0.42 tff(462,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[461, 455])).
% 0.19/0.42 tff(463,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[462, 455])).
% 0.19/0.42 tff(464,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[463, 455])).
% 0.19/0.42 tff(465,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[464, 455])).
% 0.19/0.42 tff(466,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[465, 455])).
% 0.19/0.42 tff(467,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[466, 455])).
% 0.19/0.42 tff(468,plain,
% 0.19/0.42 ((~mustard(barry)) | neither(dix) | both(mill)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[467, 455])).
% 0.19/0.42 tff(469,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[468, 454, 426, 396])).
% 0.19/0.42 tff(470,plain,(mustard(mill) | both(lang) | neither(cole)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(471,plain,
% 0.19/0.42 (mustard(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[470, 382, 322])).
% 0.19/0.42 tff(472,assumption,(~salt(dix)), introduced(assumption)).
% 0.19/0.42 tff(473,plain,
% 0.19/0.42 ((salt(dix) | (~neither(barry))) <=> (salt(dix) | (~neither(barry)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(474,plain,
% 0.19/0.42 (((~neither(barry)) | salt(dix)) <=> (salt(dix) | (~neither(barry)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(475,axiom,((~neither(barry)) | salt(dix)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule5_2')).
% 0.19/0.42 tff(476,plain,
% 0.19/0.42 (salt(dix) | (~neither(barry))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.19/0.42 tff(477,plain,
% 0.19/0.42 (salt(dix) | (~neither(barry))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.19/0.42 tff(478,plain,
% 0.19/0.42 (~neither(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[477, 472])).
% 0.19/0.42 tff(479,plain,
% 0.19/0.42 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(mill)) | (~mustard(mill)) | (~oneof(mill)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(mill)) | (~mustard(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(480,plain,
% 0.19/0.42 (((~mustard(mill)) | (~salt(mill)) | (~oneof(mill))) <=> ((~salt(mill)) | (~mustard(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(481,plain,
% 0.19/0.42 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(mill)) | (~salt(mill)) | (~oneof(mill)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(mill)) | (~mustard(mill)) | (~oneof(mill))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[480])).
% 0.19/0.42 tff(482,plain,
% 0.19/0.42 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(mill)) | (~salt(mill)) | (~oneof(mill)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(mill)) | (~mustard(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[481, 479])).
% 0.19/0.42 tff(483,plain,
% 0.19/0.42 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(mill)) | (~salt(mill)) | (~oneof(mill)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(484,plain,
% 0.19/0.42 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(mill)) | (~mustard(mill)) | (~oneof(mill))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.19/0.42 tff(485,plain,
% 0.19/0.42 ((~salt(mill)) | (~mustard(mill))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[484, 272, 374])).
% 0.19/0.42 tff(486,plain,
% 0.19/0.42 (~salt(mill)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[485, 154])).
% 0.19/0.42 tff(487,plain,
% 0.19/0.42 (~both(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[47, 486])).
% 0.19/0.42 tff(488,plain,
% 0.19/0.42 (oneof(barry) | neither(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 23, 487])).
% 0.19/0.42 tff(489,plain,
% 0.19/0.42 (oneof(barry)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[488, 478])).
% 0.19/0.42 tff(490,plain,
% 0.19/0.42 (salt(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 489])).
% 0.19/0.42 tff(491,plain,
% 0.19/0.42 (~neither(lang)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[180, 38, 490])).
% 0.19/0.43 tff(492,plain,
% 0.19/0.43 (salt(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[261, 478, 154])).
% 0.19/0.43 tff(493,plain,
% 0.19/0.43 (((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | (both(barry) | (~mustard(barry)) | (~salt(barry)))) <=> ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | both(barry) | (~mustard(barry)) | (~salt(barry)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(494,plain,
% 0.19/0.43 ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | (both(barry) | (~mustard(barry)) | (~salt(barry)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(495,plain,
% 0.19/0.43 ((~![X: $i] : (both(X) | (~mustard(X)) | (~salt(X)))) | both(barry) | (~mustard(barry)) | (~salt(barry))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.19/0.43 tff(496,plain,
% 0.19/0.43 ((~mustard(barry)) | (~salt(barry))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[495, 80, 487])).
% 0.19/0.43 tff(497,plain,
% 0.19/0.43 (~mustard(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[496, 492])).
% 0.19/0.43 tff(498,plain,
% 0.19/0.43 ((mustard(barry) | (~neither(dix))) <=> (mustard(barry) | (~neither(dix)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(499,plain,
% 0.19/0.43 (((~neither(dix)) | mustard(barry)) <=> (mustard(barry) | (~neither(dix)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(500,axiom,((~neither(dix)) | mustard(barry)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule2_2')).
% 0.19/0.43 tff(501,plain,
% 0.19/0.43 (mustard(barry) | (~neither(dix))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.19/0.43 tff(502,plain,
% 0.19/0.43 (mustard(barry) | (~neither(dix))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.19/0.43 tff(503,plain,
% 0.19/0.43 (~neither(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[502, 497])).
% 0.19/0.43 tff(504,plain,
% 0.19/0.43 (((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (neither(dix) | salt(dix) | mustard(dix))) <=> ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | neither(dix) | salt(dix) | mustard(dix))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(505,plain,
% 0.19/0.43 ((salt(dix) | mustard(dix) | neither(dix)) <=> (neither(dix) | salt(dix) | mustard(dix))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(506,plain,
% 0.19/0.43 (((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (salt(dix) | mustard(dix) | neither(dix))) <=> ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (neither(dix) | salt(dix) | mustard(dix)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[505])).
% 0.19/0.43 tff(507,plain,
% 0.19/0.43 (((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (salt(dix) | mustard(dix) | neither(dix))) <=> ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | neither(dix) | salt(dix) | mustard(dix))),
% 0.19/0.43 inference(transitivity,[status(thm)],[506, 504])).
% 0.19/0.43 tff(508,plain,
% 0.19/0.43 ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | (salt(dix) | mustard(dix) | neither(dix))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(509,plain,
% 0.19/0.43 ((~![X: $i] : (salt(X) | mustard(X) | neither(X))) | neither(dix) | salt(dix) | mustard(dix)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.19/0.43 tff(510,plain,
% 0.19/0.43 (mustard(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[509, 333, 503, 472])).
% 0.19/0.43 tff(511,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 510, 491, 381])).
% 0.19/0.43 tff(512,plain,(salt(dix) | (~mustard(mill))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(513,plain,
% 0.19/0.43 (salt(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[512, 471])).
% 0.19/0.43 tff(514,assumption,(salt(dix)), introduced(assumption)).
% 0.19/0.43 tff(515,assumption,(~neither(lang)), introduced(assumption)).
% 0.19/0.43 tff(516,plain,
% 0.19/0.43 (oneof(lang) | neither(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 23, 427])).
% 0.19/0.43 tff(517,plain,
% 0.19/0.43 (oneof(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[516, 515])).
% 0.19/0.43 tff(518,plain,
% 0.19/0.43 (salt(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 517])).
% 0.19/0.43 tff(519,plain,
% 0.19/0.43 (~neither(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[135, 38, 518])).
% 0.19/0.43 tff(520,plain,
% 0.19/0.43 (both(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[233, 519, 514])).
% 0.19/0.43 tff(521,plain,
% 0.19/0.43 (~mustard(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 515, 381])).
% 0.19/0.43 tff(522,plain,
% 0.19/0.43 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(dix)) | mustard(dix))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(dix)) | mustard(dix))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(523,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(dix)) | mustard(dix))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(524,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | mustard(X))) | (~both(dix)) | mustard(dix)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.19/0.43 tff(525,plain,
% 0.19/0.43 (~both(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[524, 9, 521])).
% 0.19/0.43 tff(526,plain,
% 0.19/0.43 (~mustard(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[352, 525, 427])).
% 0.19/0.43 tff(527,plain,
% 0.19/0.43 (((~![X: $i] : ((~both(X)) | mustard(X))) | (mustard(cole) | (~both(cole)))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(cole) | (~both(cole)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(528,plain,
% 0.19/0.43 (((~both(cole)) | mustard(cole)) <=> (mustard(cole) | (~both(cole)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(529,plain,
% 0.19/0.43 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(cole)) | mustard(cole))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | (mustard(cole) | (~both(cole))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[528])).
% 0.19/0.43 tff(530,plain,
% 0.19/0.43 (((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(cole)) | mustard(cole))) <=> ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(cole) | (~both(cole)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[529, 527])).
% 0.19/0.43 tff(531,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | mustard(X))) | ((~both(cole)) | mustard(cole))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(532,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | mustard(X))) | mustard(cole) | (~both(cole))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.19/0.43 tff(533,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[532, 9, 526, 520])).
% 0.19/0.43 tff(534,plain,(neither(lang) | both(lang) | (~salt(dix))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(535,plain,
% 0.19/0.43 (neither(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[534, 382, 513])).
% 0.19/0.43 tff(536,plain,
% 0.19/0.43 ((mustard(dix) | (~neither(lang))) <=> (mustard(dix) | (~neither(lang)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(537,plain,
% 0.19/0.43 (((~neither(lang)) | mustard(dix)) <=> (mustard(dix) | (~neither(lang)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(538,axiom,((~neither(lang)) | mustard(dix)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule6_2')).
% 0.19/0.43 tff(539,plain,
% 0.19/0.43 (mustard(dix) | (~neither(lang))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.19/0.43 tff(540,plain,
% 0.19/0.43 (mustard(dix) | (~neither(lang))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.19/0.43 tff(541,plain,
% 0.19/0.43 (mustard(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[540, 535])).
% 0.19/0.43 tff(542,plain,
% 0.19/0.43 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(dix)) | (~mustard(dix)) | (~oneof(dix)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(dix)) | (~mustard(dix)) | (~oneof(dix)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(543,plain,
% 0.19/0.43 (((~mustard(dix)) | (~salt(dix)) | (~oneof(dix))) <=> ((~salt(dix)) | (~mustard(dix)) | (~oneof(dix)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(544,plain,
% 0.19/0.43 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(dix)) | (~salt(dix)) | (~oneof(dix)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~salt(dix)) | (~mustard(dix)) | (~oneof(dix))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[543])).
% 0.19/0.43 tff(545,plain,
% 0.19/0.43 (((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(dix)) | (~salt(dix)) | (~oneof(dix)))) <=> ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(dix)) | (~mustard(dix)) | (~oneof(dix)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[544, 542])).
% 0.19/0.43 tff(546,plain,
% 0.19/0.43 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | ((~mustard(dix)) | (~salt(dix)) | (~oneof(dix)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(547,plain,
% 0.19/0.43 ((~![X: $i] : ((~mustard(X)) | (~salt(X)) | (~oneof(X)))) | (~salt(dix)) | (~mustard(dix)) | (~oneof(dix))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.19/0.43 tff(548,plain,
% 0.19/0.43 ((~mustard(dix)) | (~oneof(dix))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[547, 272, 513])).
% 0.19/0.43 tff(549,plain,
% 0.19/0.43 (~oneof(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[548, 541])).
% 0.19/0.43 tff(550,plain,
% 0.19/0.43 (oneof(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[170, 549, 471])).
% 0.19/0.43 tff(551,plain,
% 0.19/0.43 (((~![X: $i] : ((~both(X)) | (~oneof(X)))) | ((~both(cole)) | (~oneof(cole)))) <=> ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | (~both(cole)) | (~oneof(cole)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(552,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | ((~both(cole)) | (~oneof(cole)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(553,plain,
% 0.19/0.43 ((~![X: $i] : ((~both(X)) | (~oneof(X)))) | (~both(cole)) | (~oneof(cole))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.19/0.43 tff(554,plain,
% 0.19/0.43 (~both(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[553, 392, 550])).
% 0.19/0.43 tff(555,plain,
% 0.19/0.43 (salt(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[161, 550])).
% 0.19/0.43 tff(556,plain,
% 0.19/0.43 (~neither(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[135, 38, 555])).
% 0.19/0.43 tff(557,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[233, 556, 554, 513])).
% 0.19/0.43 tff(558,plain,(mustard(lang)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(559,plain,
% 0.19/0.43 (neither(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[259, 558, 381])).
% 0.19/0.43 tff(560,plain,
% 0.19/0.43 (((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(cole)) | (~neither(cole)))) <=> ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(cole)) | (~neither(cole)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(561,plain,
% 0.19/0.43 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | ((~mustard(cole)) | (~neither(cole)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(562,plain,
% 0.19/0.43 ((~![X: $i] : ((~mustard(X)) | (~neither(X)))) | (~mustard(cole)) | (~neither(cole))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.19/0.43 tff(563,plain,
% 0.19/0.43 (~mustard(cole)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[562, 114, 559])).
% 0.19/0.43 tff(564,plain,
% 0.19/0.43 ((mustard(cole) | (~both(lang))) <=> (mustard(cole) | (~both(lang)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(565,plain,
% 0.19/0.43 (((~both(lang)) | mustard(cole)) <=> (mustard(cole) | (~both(lang)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(566,axiom,((~both(lang)) | mustard(cole)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rule4_3')).
% 0.19/0.43 tff(567,plain,
% 0.19/0.43 (mustard(cole) | (~both(lang))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.19/0.43 tff(568,plain,
% 0.19/0.43 (mustard(cole) | (~both(lang))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[567, 564])).
% 0.19/0.43 tff(569,plain,
% 0.19/0.43 (~both(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[568, 563])).
% 0.19/0.43 tff(570,plain,
% 0.19/0.43 (~neither(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 114, 558])).
% 0.19/0.43 tff(571,plain,
% 0.19/0.43 (~salt(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[534, 569, 570])).
% 0.19/0.43 tff(572,plain,
% 0.19/0.43 (~mustard(mill)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[512, 571])).
% 0.19/0.43 tff(573,plain,
% 0.19/0.43 (salt(mill)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[431, 572])).
% 0.19/0.43 tff(574,plain,
% 0.19/0.43 (both(barry)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[446, 573, 569])).
% 0.19/0.43 tff(575,plain,
% 0.19/0.43 (oneof(lang)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 23, 569, 570])).
% 0.19/0.43 tff(576,plain,
% 0.19/0.43 (~mustard(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 570, 381])).
% 0.19/0.43 tff(577,plain,
% 0.19/0.43 (neither(dix)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[509, 333, 571, 576])).
% 0.19/0.43 tff(578,plain,
% 0.19/0.43 (((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))) <=> ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(579,plain,
% 0.19/0.43 ((((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry))) | (~oneof(mill))) <=> ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(580,plain,
% 0.19/0.43 ((((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~salt(mill)) | (~both(barry))) | (~mustard(lang))) <=> ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(581,plain,
% 0.19/0.43 ((((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~both(barry))) | (~salt(mill))) <=> ((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(582,plain,
% 0.19/0.43 ((((~neither(dix)) | (~neither(cole)) | (~both(barry))) | (~oneof(lang))) <=> ((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~both(barry)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(583,plain,
% 0.19/0.43 ((((~neither(cole)) | (~neither(dix))) | (~both(barry))) <=> ((~neither(dix)) | (~neither(cole)) | (~both(barry)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(584,plain,
% 0.19/0.43 (((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) <=> (((~neither(dix)) | (~neither(cole)) | (~both(barry))) | (~oneof(lang)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[583])).
% 0.19/0.43 tff(585,plain,
% 0.19/0.43 (((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) <=> ((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~both(barry)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[584, 582])).
% 0.19/0.43 tff(586,plain,
% 0.19/0.43 ((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) <=> (((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~both(barry))) | (~salt(mill)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[585])).
% 0.19/0.43 tff(587,plain,
% 0.19/0.43 ((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) <=> ((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[586, 581])).
% 0.19/0.43 tff(588,plain,
% 0.19/0.43 (((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) | (~mustard(lang))) <=> (((~oneof(lang)) | (~neither(dix)) | (~neither(cole)) | (~salt(mill)) | (~both(barry))) | (~mustard(lang)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[587])).
% 0.19/0.43 tff(589,plain,
% 0.19/0.43 (((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) | (~mustard(lang))) <=> ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[588, 580])).
% 0.19/0.43 tff(590,plain,
% 0.19/0.43 ((((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) | (~mustard(lang))) | (~oneof(mill))) <=> (((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry))) | (~oneof(mill)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[589])).
% 0.19/0.43 tff(591,plain,
% 0.19/0.43 ((((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) | (~mustard(lang))) | (~oneof(mill))) <=> ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[590, 579])).
% 0.19/0.44 tff(592,axiom,(((((((~neither(cole)) | (~neither(dix))) | (~both(barry))) | (~oneof(lang))) | (~salt(mill))) | (~mustard(lang))) | (~oneof(mill))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_who_takes_what')).
% 0.19/0.44 tff(593,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.19/0.44 tff(594,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[593, 578])).
% 0.19/0.44 tff(595,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[594, 578])).
% 0.19/0.44 tff(596,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[595, 578])).
% 0.19/0.44 tff(597,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[596, 578])).
% 0.19/0.44 tff(598,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[597, 578])).
% 0.19/0.44 tff(599,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[598, 578])).
% 0.19/0.44 tff(600,plain,
% 0.19/0.44 ((~oneof(lang)) | (~neither(dix)) | (~mustard(lang)) | (~neither(cole)) | (~salt(mill)) | (~both(barry)) | (~oneof(mill))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[599, 578])).
% 0.19/0.44 tff(601,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[600, 577, 575, 558, 559, 573, 574, 374])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------