%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:12:14 AM UTC 2026
% Result : Unsatisfiable 46.70s 7.48s
% Output : Refutation 47.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 10
% Syntax : Number of formulae : 141 ( 141 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 252 ( 252 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : product(identity,X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4,plain,
! [X0] : true = product(inverse(X0),X0,identity),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f6,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f8,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f10,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f12,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X2,X3,X0,X1] : ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
fof(f14,plain,
! [X2,X3,X0,X1] : true = ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
equalish(a,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f16,plain,
true = equalish(a,b),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_substitution) ).
fof(f18,plain,
true != equalish(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(identity,X0,X1),true,equalish(X1,X0),true),true),
inference(superposition,[],[f8,f2]) ).
fof(f22,plain,
! [X0,X1] : true = ifeq(product(inverse(X0),X0,X1),true,ifeq(true,true,equalish(identity,X1),true),true),
inference(superposition,[],[f8,f4]) ).
fof(f24,plain,
! [X0,X1] : true = ifeq(product(inverse(X0),X0,X1),true,equalish(identity,X1),true),
inference(forward_demodulation,[],[f22,f1]) ).
fof(f27,plain,
! [X0,X1] : true = ifeq(product(identity,X0,X1),true,equalish(X1,X0),true),
inference(forward_demodulation,[],[f19,f1]) ).
fof(f28,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(X0,X1,a),true,product(X0,X1,b),true),true),
inference(superposition,[],[f14,f16]) ).
fof(f29,plain,
! [X0,X1] : true = ifeq(equalish(X0,X1),true,ifeq(true,true,product(identity,X0,X1),true),true),
inference(superposition,[],[f14,f2]) ).
fof(f30,plain,
! [X0,X1] : true = ifeq(equalish(identity,X0),true,ifeq(true,true,product(inverse(X1),X1,X0),true),true),
inference(superposition,[],[f14,f4]) ).
fof(f33,plain,
! [X0,X1] : true = ifeq(equalish(identity,X0),true,product(inverse(X1),X1,X0),true),
inference(forward_demodulation,[],[f30,f1]) ).
fof(f34,plain,
! [X0,X1] : true = ifeq(equalish(X0,X1),true,product(identity,X0,X1),true),
inference(forward_demodulation,[],[f29,f1]) ).
fof(f35,plain,
! [X0,X1] : true = ifeq(product(X0,X1,a),true,product(X0,X1,b),true),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f43,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(product(X1,X0,X2),true,ifeq(product(X3,X1,identity),true,product(X3,X2,X0),true),true),true),
inference(superposition,[],[f10,f2]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(product(X3,identity,X0),true,product(X3,X1,X2),true),true),true),
inference(superposition,[],[f10,f2]) ).
fof(f47,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(product(X3,inverse(X1),X0),true,product(X3,identity,X2),true),true),true),
inference(superposition,[],[f10,f4]) ).
fof(f49,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,ifeq(true,true,product(identity,X3,X2),true),true),true),
inference(superposition,[],[f10,f2]) ).
fof(f50,plain,
! [X2,X3,X0,X1] : true = ifeq(product(identity,X0,X1),true,ifeq(product(X2,X0,X3),true,ifeq(true,true,product(inverse(X2),X3,X1),true),true),true),
inference(superposition,[],[f10,f4]) ).
fof(f56,plain,
! [X2,X3,X0,X1] : true = ifeq(product(identity,X0,X1),true,ifeq(product(X2,X0,X3),true,product(inverse(X2),X3,X1),true),true),
inference(forward_demodulation,[],[f50,f1]) ).
fof(f57,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,product(identity,X3,X2),true),true),
inference(forward_demodulation,[],[f49,f1]) ).
fof(f59,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,inverse(X1),X0),true,product(X3,identity,X2),true),true),
inference(forward_demodulation,[],[f47,f1]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,identity,X0),true,product(X3,X1,X2),true),true),
inference(forward_demodulation,[],[f46,f1]) ).
fof(f63,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X1,X0,X2),true,ifeq(product(X3,X1,identity),true,product(X3,X2,X0),true),true),
inference(forward_demodulation,[],[f43,f1]) ).
fof(f64,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(product(X1,X0,X2),true,ifeq(product(X1,identity,X3),true,product(X3,X0,X2),true),true),true),
inference(superposition,[],[f12,f2]) ).
fof(f65,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(product(X1,identity,X2),true,ifeq(product(X1,inverse(X0),X3),true,product(X3,X0,X2),true),true),true),
inference(superposition,[],[f12,f4]) ).
fof(f67,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(product(identity,X0,X3),true,product(X3,X1,X2),true),true),true),
inference(superposition,[],[f12,f2]) ).
fof(f70,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(identity,X2,X3),true,ifeq(true,true,product(X0,X1,X3),true),true),true),
inference(superposition,[],[f12,f2]) ).
fof(f71,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(inverse(X0),X2,X3),true,ifeq(true,true,product(identity,X1,X3),true),true),true),
inference(superposition,[],[f12,f4]) ).
fof(f77,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(inverse(X0),X2,X3),true,product(identity,X1,X3),true),true),
inference(forward_demodulation,[],[f71,f1]) ).
fof(f78,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(identity,X2,X3),true,product(X0,X1,X3),true),true),
inference(forward_demodulation,[],[f70,f1]) ).
fof(f81,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(identity,X0,X3),true,product(X3,X1,X2),true),true),
inference(forward_demodulation,[],[f67,f1]) ).
fof(f83,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X1,identity,X2),true,ifeq(product(X1,inverse(X0),X3),true,product(X3,X0,X2),true),true),
inference(forward_demodulation,[],[f65,f1]) ).
fof(f84,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X1,X0,X2),true,ifeq(product(X1,identity,X3),true,product(X3,X0,X2),true),true),
inference(forward_demodulation,[],[f64,f1]) ).
fof(f85,plain,
true = ifeq(true,true,product(identity,a,b),true),
inference(superposition,[],[f34,f16]) ).
fof(f88,plain,
true = product(identity,a,b),
inference(forward_demodulation,[],[f85,f1]) ).
fof(f137,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(inverse(X0),X0,X1),true,product(identity,X1,identity),true),true),
inference(superposition,[],[f57,f4]) ).
fof(f155,plain,
! [X0,X1] : true = ifeq(product(inverse(X0),X0,X1),true,product(identity,X1,identity),true),
inference(forward_demodulation,[],[f137,f1]) ).
fof(f186,plain,
true = ifeq(true,true,equalish(b,a),true),
inference(superposition,[],[f27,f88]) ).
fof(f193,plain,
true = equalish(b,a),
inference(forward_demodulation,[],[f186,f1]) ).
fof(f198,plain,
true = ifeq(true,true,product(identity,b,a),true),
inference(superposition,[],[f34,f193]) ).
fof(f202,plain,
true = product(identity,b,a),
inference(forward_demodulation,[],[f198,f1]) ).
fof(f239,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(inverse(X0),multiply(X0,X1),X2),true,product(identity,X1,X2),true),true),
inference(superposition,[],[f77,f6]) ).
fof(f252,plain,
! [X2,X0,X1] : true = ifeq(product(inverse(X0),multiply(X0,X1),X2),true,product(identity,X1,X2),true),
inference(forward_demodulation,[],[f239,f1]) ).
fof(f327,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(X2,identity,X0),true,product(X2,X1,multiply(X0,X1)),true),true),
inference(superposition,[],[f60,f6]) ).
fof(f349,plain,
! [X2,X0,X1] : true = ifeq(product(X2,identity,X0),true,product(X2,X1,multiply(X0,X1)),true),
inference(forward_demodulation,[],[f327,f1]) ).
fof(f358,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,X1),true),true),
inference(superposition,[],[f63,f4]) ).
fof(f370,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,product(inverse(X0),X2,X1),true),
inference(forward_demodulation,[],[f358,f1]) ).
fof(f378,plain,
! [X0] : true = ifeq(true,true,product(inverse(inverse(X0)),identity,X0),true),
inference(superposition,[],[f370,f4]) ).
fof(f379,plain,
! [X0,X1] : true = ifeq(true,true,product(inverse(X0),multiply(X0,X1),X1),true),
inference(superposition,[],[f370,f6]) ).
fof(f388,plain,
! [X0,X1] : true = product(inverse(X0),multiply(X0,X1),X1),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f389,plain,
! [X0] : true = product(inverse(inverse(X0)),identity,X0),
inference(forward_demodulation,[],[f378,f1]) ).
fof(f418,plain,
! [X0,X1] : true = ifeq(true,true,product(inverse(inverse(X0)),X1,multiply(X0,X1)),true),
inference(superposition,[],[f370,f388]) ).
fof(f422,plain,
! [X0,X1] : true = product(inverse(inverse(X0)),X1,multiply(X0,X1)),
inference(forward_demodulation,[],[f418,f1]) ).
fof(f445,plain,
! [X0] : true = ifeq(true,true,equalish(identity,multiply(X0,inverse(X0))),true),
inference(superposition,[],[f24,f422]) ).
fof(f499,plain,
! [X0] : true = equalish(identity,multiply(X0,inverse(X0))),
inference(forward_demodulation,[],[f445,f1]) ).
fof(f1068,plain,
! [X2,X0,X1] : true = ifeq(product(multiply(X0,inverse(X1)),X1,X2),true,ifeq(true,true,product(X0,identity,X2),true),true),
inference(superposition,[],[f59,f6]) ).
fof(f1087,plain,
! [X2,X0,X1] : true = ifeq(product(multiply(X0,inverse(X1)),X1,X2),true,product(X0,identity,X2),true),
inference(forward_demodulation,[],[f1068,f1]) ).
fof(f1304,plain,
! [X2,X0,X1] : true = ifeq(product(identity,X0,X1),true,ifeq(true,true,product(inverse(X2),multiply(X2,X0),X1),true),true),
inference(superposition,[],[f56,f6]) ).
fof(f1340,plain,
! [X2,X0,X1] : true = ifeq(product(identity,X0,X1),true,product(inverse(X2),multiply(X2,X0),X1),true),
inference(forward_demodulation,[],[f1304,f1]) ).
fof(f1619,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(identity,multiply(X0,X1),X2),true,product(X0,X1,X2),true),true),
inference(superposition,[],[f78,f6]) ).
fof(f1690,plain,
! [X2,X0,X1] : true = ifeq(product(identity,multiply(X0,X1),X2),true,product(X0,X1,X2),true),
inference(forward_demodulation,[],[f1619,f1]) ).
fof(f1865,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(identity,X0,X2),true,product(X2,X1,multiply(X0,X1)),true),true),
inference(superposition,[],[f81,f6]) ).
fof(f1942,plain,
! [X2,X0,X1] : true = ifeq(product(identity,X0,X2),true,product(X2,X1,multiply(X0,X1)),true),
inference(forward_demodulation,[],[f1865,f1]) ).
fof(f1953,plain,
! [X0] : true = ifeq(true,true,product(a,X0,multiply(b,X0)),true),
inference(superposition,[],[f1942,f202]) ).
fof(f1978,plain,
! [X0] : true = product(a,X0,multiply(b,X0)),
inference(forward_demodulation,[],[f1953,f1]) ).
fof(f2996,plain,
! [X0] : true = ifeq(true,true,product(identity,multiply(X0,inverse(X0)),identity),true),
inference(superposition,[],[f155,f422]) ).
fof(f3015,plain,
! [X0] : true = product(identity,multiply(X0,inverse(X0)),identity),
inference(forward_demodulation,[],[f2996,f1]) ).
fof(f5041,plain,
! [X0,X1] : true = ifeq(true,true,product(inverse(X1),X1,multiply(X0,inverse(X0))),true),
inference(superposition,[],[f33,f499]) ).
fof(f5053,plain,
! [X0,X1] : true = product(inverse(X1),X1,multiply(X0,inverse(X0))),
inference(forward_demodulation,[],[f5041,f1]) ).
fof(f5105,plain,
! [X0,X1] : true = ifeq(true,true,product(inverse(inverse(X0)),multiply(X1,inverse(X1)),X0),true),
inference(superposition,[],[f370,f5053]) ).
fof(f5139,plain,
! [X0,X1] : true = product(inverse(inverse(X0)),multiply(X1,inverse(X1)),X0),
inference(forward_demodulation,[],[f5105,f1]) ).
fof(f5176,plain,
! [X0] : true = ifeq(true,true,product(identity,inverse(inverse(X0)),X0),true),
inference(superposition,[],[f252,f5139]) ).
fof(f5280,plain,
! [X0] : true = product(identity,inverse(inverse(X0)),X0),
inference(forward_demodulation,[],[f5176,f1]) ).
fof(f5351,plain,
true = ifeq(true,true,product(identity,inverse(inverse(a)),b),true),
inference(superposition,[],[f35,f5280]) ).
fof(f5353,plain,
true = product(identity,inverse(inverse(a)),b),
inference(forward_demodulation,[],[f5351,f1]) ).
fof(f5755,plain,
true = ifeq(true,true,equalish(b,inverse(inverse(a))),true),
inference(superposition,[],[f27,f5353]) ).
fof(f5845,plain,
true = equalish(b,inverse(inverse(a))),
inference(forward_demodulation,[],[f5755,f1]) ).
fof(f5856,plain,
true = ifeq(true,true,product(identity,b,inverse(inverse(a))),true),
inference(superposition,[],[f34,f5845]) ).
fof(f5860,plain,
true = product(identity,b,inverse(inverse(a))),
inference(forward_demodulation,[],[f5856,f1]) ).
fof(f5881,plain,
! [X0] : true = ifeq(true,true,product(inverse(X0),multiply(X0,b),inverse(inverse(a))),true),
inference(superposition,[],[f1340,f5860]) ).
fof(f5961,plain,
! [X0] : true = product(inverse(X0),multiply(X0,b),inverse(inverse(a))),
inference(forward_demodulation,[],[f5881,f1]) ).
fof(f7428,plain,
! [X0] : true = ifeq(true,true,product(inverse(inverse(X0)),inverse(inverse(a)),multiply(X0,b)),true),
inference(superposition,[],[f370,f5961]) ).
fof(f7438,plain,
! [X0] : true = product(inverse(inverse(X0)),inverse(inverse(a)),multiply(X0,b)),
inference(forward_demodulation,[],[f7428,f1]) ).
fof(f7476,plain,
true = ifeq(true,true,product(identity,multiply(inverse(a),b),identity),true),
inference(superposition,[],[f155,f7438]) ).
fof(f7567,plain,
true = product(identity,multiply(inverse(a),b),identity),
inference(forward_demodulation,[],[f7476,f1]) ).
fof(f7926,plain,
true = ifeq(true,true,product(inverse(a),b,identity),true),
inference(superposition,[],[f1690,f7567]) ).
fof(f8029,plain,
true = product(inverse(a),b,identity),
inference(forward_demodulation,[],[f7926,f1]) ).
fof(f8039,plain,
! [X0,X1] : true = ifeq(product(b,X0,X1),true,ifeq(true,true,product(inverse(a),X1,X0),true),true),
inference(superposition,[],[f63,f8029]) ).
fof(f8115,plain,
! [X0,X1] : true = ifeq(product(b,X0,X1),true,product(inverse(a),X1,X0),true),
inference(forward_demodulation,[],[f8039,f1]) ).
fof(f9422,plain,
! [X0] : true = ifeq(true,true,product(X0,inverse(X0),identity),true),
inference(superposition,[],[f1690,f3015]) ).
fof(f9528,plain,
! [X0] : true = product(X0,inverse(X0),identity),
inference(forward_demodulation,[],[f9422,f1]) ).
fof(f9548,plain,
true = ifeq(true,true,product(inverse(a),identity,inverse(b)),true),
inference(superposition,[],[f8115,f9528]) ).
fof(f9639,plain,
true = product(inverse(a),identity,inverse(b)),
inference(forward_demodulation,[],[f9548,f1]) ).
fof(f9661,plain,
! [X0] : true = ifeq(true,true,product(inverse(a),X0,multiply(inverse(b),X0)),true),
inference(superposition,[],[f349,f9639]) ).
fof(f9752,plain,
! [X0] : true = product(inverse(a),X0,multiply(inverse(b),X0)),
inference(forward_demodulation,[],[f9661,f1]) ).
fof(f9760,plain,
true = ifeq(true,true,product(identity,multiply(inverse(b),a),identity),true),
inference(superposition,[],[f155,f9752]) ).
fof(f9879,plain,
true = product(identity,multiply(inverse(b),a),identity),
inference(forward_demodulation,[],[f9760,f1]) ).
fof(f11392,plain,
true = ifeq(true,true,product(inverse(b),a,identity),true),
inference(superposition,[],[f1690,f9879]) ).
fof(f11495,plain,
true = product(inverse(b),a,identity),
inference(forward_demodulation,[],[f11392,f1]) ).
fof(f11543,plain,
true = ifeq(true,true,product(inverse(inverse(b)),identity,a),true),
inference(superposition,[],[f370,f11495]) ).
fof(f11553,plain,
true = product(inverse(inverse(b)),identity,a),
inference(forward_demodulation,[],[f11543,f1]) ).
fof(f11589,plain,
! [X0,X1] : true = ifeq(product(inverse(inverse(b)),X0,X1),true,ifeq(true,true,product(a,X0,X1),true),true),
inference(superposition,[],[f84,f11553]) ).
fof(f11679,plain,
! [X0,X1] : true = ifeq(product(inverse(inverse(b)),X0,X1),true,product(a,X0,X1),true),
inference(forward_demodulation,[],[f11589,f1]) ).
fof(f13828,plain,
true = ifeq(true,true,product(a,identity,b),true),
inference(superposition,[],[f11679,f389]) ).
fof(f13928,plain,
true = product(a,identity,b),
inference(forward_demodulation,[],[f13828,f1]) ).
fof(f13964,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(a,inverse(X0),X1),true,product(X1,X0,b),true),true),
inference(superposition,[],[f83,f13928]) ).
fof(f14052,plain,
! [X0,X1] : true = ifeq(product(a,inverse(X0),X1),true,product(X1,X0,b),true),
inference(forward_demodulation,[],[f13964,f1]) ).
fof(f17357,plain,
! [X0] : true = ifeq(true,true,product(multiply(b,inverse(X0)),X0,b),true),
inference(superposition,[],[f14052,f1978]) ).
fof(f17433,plain,
! [X0] : true = product(multiply(b,inverse(X0)),X0,b),
inference(forward_demodulation,[],[f17357,f1]) ).
fof(f17521,plain,
true = ifeq(true,true,product(b,identity,b),true),
inference(superposition,[],[f1087,f17433]) ).
fof(f17622,plain,
true = product(b,identity,b),
inference(forward_demodulation,[],[f17521,f1]) ).
fof(f17646,plain,
! [X0] : true = ifeq(equalish(b,X0),true,ifeq(true,true,product(b,identity,X0),true),true),
inference(superposition,[],[f14,f17622]) ).
fof(f17700,plain,
! [X0] : true = ifeq(equalish(b,X0),true,product(b,identity,X0),true),
inference(forward_demodulation,[],[f17646,f1]) ).
fof(f18783,plain,
true = ifeq(true,true,product(b,identity,inverse(inverse(a))),true),
inference(superposition,[],[f17700,f5845]) ).
fof(f18815,plain,
true = product(b,identity,inverse(inverse(a))),
inference(forward_demodulation,[],[f18783,f1]) ).
fof(f19179,plain,
true = ifeq(true,true,product(inverse(b),inverse(inverse(a)),identity),true),
inference(superposition,[],[f370,f18815]) ).
fof(f19189,plain,
true = product(inverse(b),inverse(inverse(a)),identity),
inference(forward_demodulation,[],[f19179,f1]) ).
fof(f19241,plain,
! [X0,X1] : true = ifeq(product(inverse(inverse(a)),X0,X1),true,ifeq(true,true,product(inverse(b),X1,X0),true),true),
inference(superposition,[],[f63,f19189]) ).
fof(f19316,plain,
! [X0,X1] : true = ifeq(product(inverse(inverse(a)),X0,X1),true,product(inverse(b),X1,X0),true),
inference(forward_demodulation,[],[f19241,f1]) ).
fof(f19846,plain,
! [X0] : true = ifeq(true,true,product(inverse(b),multiply(X0,inverse(X0)),inverse(a)),true),
inference(superposition,[],[f19316,f5053]) ).
fof(f20029,plain,
! [X0] : true = product(inverse(b),multiply(X0,inverse(X0)),inverse(a)),
inference(forward_demodulation,[],[f19846,f1]) ).
fof(f23548,plain,
true = ifeq(true,true,product(identity,inverse(b),inverse(a)),true),
inference(superposition,[],[f252,f20029]) ).
fof(f23640,plain,
true = product(identity,inverse(b),inverse(a)),
inference(forward_demodulation,[],[f23548,f1]) ).
fof(f23649,plain,
true = ifeq(true,true,equalish(inverse(a),inverse(b)),true),
inference(superposition,[],[f27,f23640]) ).
fof(f23741,plain,
true = equalish(inverse(a),inverse(b)),
inference(forward_demodulation,[],[f23649,f1]) ).
fof(f23750,plain,
$false,
inference(forward_subsumption_resolution,[],[f23741,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n009.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 09:16:30 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.70/7.48 % (1760629)Detected a unit-equality problem, will run specialized UEQ schedule.
% 46.70/7.48 % (1760638)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=538771043:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 46.70/7.48 % (1760634)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=41642784:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 46.70/7.48 % (1760639)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=874712040:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 46.70/7.48 % (1760640)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=523396474:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 46.70/7.48 % (1760635)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3596302195:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 46.70/7.48 % (1760636)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3011626157:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 46.70/7.48 % (1760637)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=432049049:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 46.70/7.48 % (1760638)Instruction limit reached!
% 46.70/7.48 % (1760638)------------------------------
% 46.70/7.48 % (1760638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760638)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760638)Termination reason: Instruction limit
% 46.70/7.48 % (1760638)Termination phase: Saturation
% 46.70/7.48 % (1760638)Time elapsed: 0.055 s
% 46.70/7.48 % (1760638)Peak memory usage: 89 MB
% 46.70/7.48 % (1760638)Instructions burned: 183 (million)
% 46.70/7.48 % (1760637)Instruction limit reached!
% 46.70/7.48 % (1760637)------------------------------
% 46.70/7.48 % (1760637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760637)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760637)Termination reason: Instruction limit
% 46.70/7.48 % (1760637)Termination phase: Saturation
% 46.70/7.48 % (1760637)Time elapsed: 0.078 s
% 46.70/7.48 % (1760637)Peak memory usage: 88 MB
% 46.70/7.48 % (1760637)Instructions burned: 138 (million)
% 46.70/7.48 % (1760648)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1474270021:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 46.70/7.48 % (1760639)Instruction limit reached!
% 46.70/7.48 % (1760639)------------------------------
% 46.70/7.48 % (1760639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760639)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760639)Termination reason: Instruction limit
% 46.70/7.48 % (1760639)Termination phase: Saturation
% 46.70/7.48 % (1760639)Time elapsed: 0.161 s
% 46.70/7.48 % (1760639)Peak memory usage: 91 MB
% 46.70/7.48 % (1760639)Instructions burned: 257 (million)
% 46.70/7.48 % (1760649)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1131690828:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 46.70/7.48 % (1760651)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3352234817:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 46.70/7.48 % (1760651)Instruction limit reached!
% 46.70/7.48 % (1760651)------------------------------
% 46.70/7.48 % (1760651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760651)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760651)Termination reason: Instruction limit
% 46.70/7.48 % (1760651)Termination phase: Saturation
% 46.70/7.48 % (1760651)Time elapsed: 0.105 s
% 46.70/7.48 % (1760651)Peak memory usage: 91 MB
% 46.70/7.48 % (1760651)Instructions burned: 216 (million)
% 46.70/7.48 % (1760654)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1430243520:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 46.70/7.48 % (1760640)Instruction limit reached!
% 46.70/7.48 % (1760640)------------------------------
% 46.70/7.48 % (1760640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760640)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760640)Termination reason: Instruction limit
% 46.70/7.48 % (1760640)Termination phase: Saturation
% 46.70/7.48 % (1760640)Time elapsed: 0.628 s
% 46.70/7.48 % (1760640)Peak memory usage: 103 MB
% 46.70/7.48 % (1760640)Instructions burned: 1187 (million)
% 46.70/7.48 % (1760654)Instruction limit reached!
% 46.70/7.48 % (1760654)------------------------------
% 46.70/7.48 % (1760654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760654)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760654)Termination reason: Instruction limit
% 46.70/7.48 % (1760654)Termination phase: Saturation
% 46.70/7.48 % (1760654)Time elapsed: 0.203 s
% 46.70/7.48 % (1760654)Peak memory usage: 94 MB
% 46.70/7.48 % (1760654)Instructions burned: 318 (million)
% 46.70/7.48 % (1760656)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2931881050:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 46.70/7.48 % (1760657)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1868071962:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 46.70/7.48 % (1760648)Instruction limit reached!
% 46.70/7.48 % (1760648)------------------------------
% 46.70/7.48 % (1760648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760648)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760648)Termination reason: Instruction limit
% 46.70/7.48 % (1760648)Termination phase: Saturation
% 46.70/7.48 % (1760648)Time elapsed: 1.075 s
% 46.70/7.48 % (1760648)Peak memory usage: 141 MB
% 46.70/7.48 % (1760648)Instructions burned: 2053 (million)
% 46.70/7.48 % (1760660)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=4001452232:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2986 on theBenchmark for (2986ds/14534Mi)
% 46.70/7.48 % (1760657)Instruction limit reached!
% 46.70/7.48 % (1760657)------------------------------
% 46.70/7.48 % (1760657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760657)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760657)Termination reason: Instruction limit
% 46.70/7.48 % (1760657)Termination phase: Saturation
% 46.70/7.48 % (1760657)Time elapsed: 1.734 s
% 46.70/7.48 % (1760657)Peak memory usage: 138 MB
% 46.70/7.48 % (1760657)Instructions burned: 2837 (million)
% 46.70/7.48 % (1760662)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=811999985:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2971 on theBenchmark for (2971ds/11832Mi)
% 46.70/7.48 % (1760649)Instruction limit reached!
% 46.70/7.48 % (1760649)------------------------------
% 46.70/7.48 % (1760649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760649)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760649)Termination reason: Instruction limit
% 46.70/7.48 % (1760649)Termination phase: Saturation
% 46.70/7.48 % (1760649)Time elapsed: 2.819 s
% 46.70/7.48 % (1760649)Peak memory usage: 170 MB
% 46.70/7.48 % (1760649)Instructions burned: 4949 (million)
% 46.70/7.48 % (1760664)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=1937859992:i=2279:fgj=on:bd=all_2967 on theBenchmark for (2967ds/2279Mi)
% 46.70/7.48 % (1760664)Instruction limit reached!
% 46.70/7.48 % (1760664)------------------------------
% 46.70/7.48 % (1760664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 46.70/7.48 % (1760664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.70/7.48 % (1760664)CaDiCaL version: 2.1.3
% 46.70/7.48 % (1760664)Termination reason: Instruction limit
% 46.70/7.48 % (1760664)Termination phase: Saturation
% 46.70/7.48 % (1760664)Time elapsed: 1.381 s
% 46.70/7.48 % (1760664)Peak memory usage: 141 MB
% 46.70/7.48 % (1760664)Instructions burned: 2280 (million)
% 46.70/7.48 % (1760666)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=2341512010:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2952 on theBenchmark for (2952ds/6225Mi)
% 46.70/7.48 % (1760660)First to succeed.
% 46.70/7.48 % (1760660)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1760629"
% 46.70/7.48 % (1760660)Refutation found. Thanks to Tanya!
% 46.70/7.48 % SZS status Unsatisfiable for theBenchmark
% 46.70/7.48 % SZS output start Proof for theBenchmark
% See solution above
% 47.40/7.67 % (1760660)------------------------------
% 47.40/7.67 % (1760660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 47.40/7.67 % (1760660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.40/7.67 % (1760660)CaDiCaL version: 2.1.3
% 47.40/7.67 % (1760660)Termination reason: Refutation
% 47.40/7.67 % (1760660)Time elapsed: 4.764 s
% 47.40/7.67 % (1760660)Peak memory usage: 198 MB
% 47.40/7.67 % (1760660)Instructions burned: 7927 (million)
% 47.40/7.67 % (1760660)------------------------------
% 47.40/7.67 % (1760660)------------------------------
% 47.40/7.67 % (1760629)Success in time 6.606 s
% 47.40/7.67 % Vampire exiting
%------------------------------------------------------------------------------