%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO015-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:35:54 AM UTC 2026
% Result : Unsatisfiable 9.00s 2.23s
% Output : Refutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 164 unt; 5 def)
% Number of atoms : 164 ( 163 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 165 ( 165 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f5,negated_conjecture,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f6,negated_conjecture,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
inverse(multiply(a,b)) != add(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
fof(f12,definition,
sF0 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f13,plain,
multiply(a,b) = sF0,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF1 = inverse(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f15,plain,
inverse(sF0) = sF1,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF2 = inverse(a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f17,plain,
inverse(a) = sF2,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF3 = inverse(b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f19,plain,
inverse(b) = sF3,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF4 = add(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f21,plain,
add(sF2,sF3) = sF4,
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
sF1 != sF4,
inference(definition_folding,[],[f11,f21,f19,f17,f15,f13]) ).
fof(f28,plain,
additive_identity = multiply(a,sF2),
inference(superposition,[],[f10,f17]) ).
fof(f29,plain,
additive_identity = multiply(b,sF3),
inference(superposition,[],[f10,f19]) ).
fof(f31,plain,
additive_identity = multiply(sF3,b),
inference(forward_demodulation,[],[f29,f2]) ).
fof(f32,plain,
additive_identity = multiply(sF2,a),
inference(forward_demodulation,[],[f28,f2]) ).
fof(f36,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f1,f5]) ).
fof(f40,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f2,f6]) ).
fof(f41,plain,
! [X0] : multiply(a,add(b,X0)) = add(sF0,multiply(a,X0)),
inference(superposition,[],[f4,f13]) ).
fof(f44,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(superposition,[],[f4,f10]) ).
fof(f49,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[],[f4,f10]) ).
fof(f50,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(multiply(X0,X1),X0),
inference(superposition,[],[f4,f6]) ).
fof(f55,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,multiplicative_identity)),
inference(forward_demodulation,[],[f50,f1]) ).
fof(f56,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(X1,inverse(X0))),
inference(forward_demodulation,[],[f49,f5]) ).
fof(f58,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f44,f36]) ).
fof(f59,plain,
! [X0] : add(sF2,multiply(sF3,X0)) = multiply(sF4,add(sF2,X0)),
inference(superposition,[],[f3,f21]) ).
fof(f62,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[],[f3,f8]) ).
fof(f63,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[],[f3,f5]) ).
fof(f68,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[],[f3,f8]) ).
fof(f69,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(add(X0,X1),X0),
inference(superposition,[],[f3,f5]) ).
fof(f77,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,additive_identity)),
inference(forward_demodulation,[],[f69,f2]) ).
fof(f78,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f68,f6]) ).
fof(f80,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f62,f40]) ).
fof(f90,plain,
! [X0] : multiply(sF2,add(a,X0)) = add(additive_identity,multiply(sF2,X0)),
inference(superposition,[],[f4,f32]) ).
fof(f91,plain,
! [X0] : multiply(sF2,X0) = multiply(sF2,add(a,X0)),
inference(forward_demodulation,[],[f90,f36]) ).
fof(f94,plain,
! [X0] : multiply(sF3,add(b,X0)) = add(additive_identity,multiply(sF3,X0)),
inference(superposition,[],[f4,f31]) ).
fof(f95,plain,
! [X0] : multiply(sF3,X0) = multiply(sF3,add(b,X0)),
inference(forward_demodulation,[],[f94,f36]) ).
fof(f102,plain,
! [X0] : add(X0,additive_identity) = add(X0,inverse(inverse(X0))),
inference(superposition,[],[f80,f10]) ).
fof(f103,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[],[f80,f6]) ).
fof(f108,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f103,f8]) ).
fof(f109,plain,
! [X0] : add(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f102,f5]) ).
fof(f110,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(backward_demodulation,[],[f55,f108]) ).
fof(f111,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f110,f6]) ).
fof(f114,plain,
! [X0,X1] : add(X1,multiply(X0,X1)) = X1,
inference(superposition,[],[f111,f2]) ).
fof(f152,plain,
b = add(b,sF0),
inference(superposition,[],[f114,f13]) ).
fof(f158,plain,
! [X2,X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,multiply(X2,X0))),
inference(superposition,[],[f3,f114]) ).
fof(f162,plain,
! [X2,X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,multiply(X2,X0))),
inference(forward_demodulation,[],[f158,f2]) ).
fof(f163,plain,
b = add(sF0,b),
inference(forward_demodulation,[],[f152,f1]) ).
fof(f164,plain,
! [X2,X0,X1] : add(X0,multiply(additive_identity,X1)) = add(X0,multiply(X1,multiply(X2,X0))),
inference(forward_demodulation,[],[f162,f63]) ).
fof(f180,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f111,f36]) ).
fof(f181,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(superposition,[],[f114,f36]) ).
fof(f185,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(X0,add(X0,X1)),
inference(backward_demodulation,[],[f77,f181]) ).
fof(f192,plain,
! [X2,X0,X1] : add(X0,additive_identity) = add(X0,multiply(X1,multiply(X2,X0))),
inference(backward_demodulation,[],[f164,f180]) ).
fof(f198,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(forward_demodulation,[],[f185,f5]) ).
fof(f199,plain,
! [X2,X0,X1] : add(X0,multiply(X1,multiply(X2,X0))) = X0,
inference(forward_demodulation,[],[f192,f5]) ).
fof(f213,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,multiply(inverse(inverse(X0)),X1)),
inference(superposition,[],[f58,f80]) ).
fof(f217,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(inverse(X0))),
inference(superposition,[],[f58,f8]) ).
fof(f223,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,add(inverse(inverse(X0)),X1)),
inference(superposition,[],[f80,f58]) ).
fof(f224,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(inverse(inverse(X0)),X1)),
inference(forward_demodulation,[],[f223,f80]) ).
fof(f229,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f217,f6]) ).
fof(f233,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(inverse(inverse(X0)),X1)),
inference(forward_demodulation,[],[f213,f58]) ).
fof(f237,plain,
! [X0] : inverse(inverse(X0)) = add(inverse(inverse(X0)),X0),
inference(superposition,[],[f114,f229]) ).
fof(f239,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,inverse(inverse(X0)))),
inference(superposition,[],[f4,f229]) ).
fof(f244,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,inverse(inverse(X0)))),
inference(forward_demodulation,[],[f239,f1]) ).
fof(f245,plain,
! [X0] : inverse(inverse(X0)) = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[],[f237,f1]) ).
fof(f246,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[],[f244,f111]) ).
fof(f247,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f245,f109]) ).
fof(f251,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(X0,X1)),
inference(backward_demodulation,[],[f224,f247]) ).
fof(f254,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(backward_demodulation,[],[f233,f247]) ).
fof(f257,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(backward_demodulation,[],[f246,f247]) ).
fof(f267,plain,
a = inverse(sF2),
inference(superposition,[],[f247,f17]) ).
fof(f269,plain,
sF0 = inverse(sF1),
inference(superposition,[],[f247,f15]) ).
fof(f286,plain,
! [X0,X1] : multiply(X1,X0) = multiply(multiply(X1,X0),X0),
inference(superposition,[],[f257,f114]) ).
fof(f294,plain,
sF3 = multiply(sF3,sF4),
inference(superposition,[],[f257,f21]) ).
fof(f300,plain,
! [X0,X1] : add(X1,X0) = add(add(X1,X0),X0),
inference(superposition,[],[f114,f257]) ).
fof(f309,plain,
! [X0,X1] : add(X1,X0) = add(X0,add(X1,X0)),
inference(forward_demodulation,[],[f300,f1]) ).
fof(f310,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f286,f2]) ).
fof(f319,plain,
sF4 = add(sF4,sF3),
inference(superposition,[],[f114,f294]) ).
fof(f325,plain,
sF4 = add(sF3,sF4),
inference(forward_demodulation,[],[f319,f1]) ).
fof(f356,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(inverse(X0),add(X1,X0)),
inference(superposition,[],[f56,f247]) ).
fof(f358,plain,
! [X0] : multiply(b,X0) = multiply(b,add(X0,sF3)),
inference(superposition,[],[f56,f19]) ).
fof(f374,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,add(X1,inverse(inverse(X0)))),
inference(superposition,[],[f80,f56]) ).
fof(f375,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,add(X1,X0)),
inference(forward_demodulation,[],[f374,f247]) ).
fof(f385,plain,
! [X0,X1] : add(X1,X0) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f375,f309]) ).
fof(f401,plain,
! [X0,X1] : add(inverse(X0),X1) = add(inverse(X0),multiply(X1,X0)),
inference(superposition,[],[f78,f247]) ).
fof(f420,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,multiply(X1,inverse(inverse(X0)))),
inference(superposition,[],[f58,f78]) ).
fof(f421,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f420,f247]) ).
fof(f431,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f421,f310]) ).
fof(f588,plain,
! [X0] : multiply(sF4,sF2) = add(sF2,multiply(sF3,multiply(X0,sF2))),
inference(superposition,[],[f59,f114]) ).
fof(f609,plain,
sF2 = multiply(sF4,sF2),
inference(forward_demodulation,[],[f588,f199]) ).
fof(f618,plain,
sF2 = multiply(sF2,sF4),
inference(forward_demodulation,[],[f609,f2]) ).
fof(f657,plain,
sF0 = multiply(sF0,b),
inference(superposition,[],[f198,f163]) ).
fof(f2559,plain,
multiply(b,sF2) = multiply(b,sF4),
inference(superposition,[],[f358,f21]) ).
fof(f2588,plain,
multiply(sF2,b) = multiply(b,sF4),
inference(forward_demodulation,[],[f2559,f2]) ).
fof(f2689,plain,
! [X0,X1] : add(inverse(add(X1,inverse(X0))),X0) = add(inverse(add(X1,inverse(X0))),multiply(X0,X1)),
inference(superposition,[],[f401,f56]) ).
fof(f2692,plain,
! [X0,X1] : add(inverse(multiply(X0,X1)),X0) = add(inverse(multiply(X0,X1)),multiply(X0,X1)),
inference(superposition,[],[f401,f254]) ).
fof(f2705,plain,
add(inverse(sF4),b) = add(inverse(sF4),multiply(sF2,b)),
inference(superposition,[],[f401,f2588]) ).
fof(f2763,plain,
add(inverse(sF4),multiply(sF2,b)) = add(b,inverse(sF4)),
inference(forward_demodulation,[],[f2705,f1]) ).
fof(f2773,plain,
! [X0,X1] : add(inverse(multiply(X0,X1)),X0) = add(multiply(X0,X1),inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f2692,f1]) ).
fof(f2776,plain,
! [X0,X1] : add(inverse(add(X1,inverse(X0))),X0) = add(multiply(X0,X1),inverse(add(X1,inverse(X0)))),
inference(forward_demodulation,[],[f2689,f1]) ).
fof(f2801,plain,
! [X0,X1] : multiplicative_identity = add(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f2773,f8]) ).
fof(f2804,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(add(X1,inverse(X0)))) = add(X0,inverse(add(X1,inverse(X0)))),
inference(forward_demodulation,[],[f2776,f1]) ).
fof(f2814,plain,
! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f2801,f1]) ).
fof(f2824,plain,
! [X0,X1] : multiplicative_identity = add(X1,inverse(multiply(X0,X1))),
inference(superposition,[],[f2814,f431]) ).
fof(f2836,plain,
multiplicative_identity = add(a,inverse(sF0)),
inference(superposition,[],[f2814,f13]) ).
fof(f2904,plain,
multiplicative_identity = add(a,sF1),
inference(forward_demodulation,[],[f2836,f15]) ).
fof(f2914,plain,
multiply(sF2,multiplicative_identity) = multiply(sF2,sF1),
inference(superposition,[],[f91,f2904]) ).
fof(f2933,plain,
sF2 = multiply(sF2,sF1),
inference(forward_demodulation,[],[f2914,f6]) ).
fof(f2941,plain,
sF1 = add(sF1,sF2),
inference(superposition,[],[f114,f2933]) ).
fof(f2944,plain,
sF1 = add(sF2,sF1),
inference(forward_demodulation,[],[f2941,f1]) ).
fof(f2953,plain,
multiply(sF4,sF1) = add(sF2,multiply(sF3,sF1)),
inference(superposition,[],[f59,f2944]) ).
fof(f2969,plain,
add(sF2,multiply(sF3,sF1)) = multiply(sF1,sF4),
inference(forward_demodulation,[],[f2953,f2]) ).
fof(f3073,plain,
multiplicative_identity = add(b,inverse(sF0)),
inference(superposition,[],[f2824,f657]) ).
fof(f3082,plain,
multiplicative_identity = add(sF4,inverse(sF2)),
inference(superposition,[],[f2824,f618]) ).
fof(f3132,plain,
multiplicative_identity = add(sF4,a),
inference(forward_demodulation,[],[f3082,f267]) ).
fof(f3138,plain,
multiplicative_identity = add(b,sF1),
inference(forward_demodulation,[],[f3073,f15]) ).
fof(f3153,plain,
multiplicative_identity = add(a,sF4),
inference(forward_demodulation,[],[f3132,f1]) ).
fof(f3157,plain,
multiply(sF3,multiplicative_identity) = multiply(sF3,sF1),
inference(superposition,[],[f95,f3138]) ).
fof(f3178,plain,
sF3 = multiply(sF3,sF1),
inference(forward_demodulation,[],[f3157,f6]) ).
fof(f3180,plain,
add(sF2,sF3) = multiply(sF1,sF4),
inference(backward_demodulation,[],[f2969,f3178]) ).
fof(f3181,plain,
sF4 = multiply(sF1,sF4),
inference(forward_demodulation,[],[f3180,f21]) ).
fof(f4010,plain,
! [X0,X1] : multiply(inverse(add(X0,X1)),X0) = multiply(inverse(add(X0,X1)),add(X0,X1)),
inference(superposition,[],[f356,f251]) ).
fof(f4028,plain,
multiply(inverse(sF4),multiplicative_identity) = multiply(inverse(sF4),a),
inference(superposition,[],[f356,f3153]) ).
fof(f4129,plain,
multiply(inverse(sF4),multiplicative_identity) = multiply(a,inverse(sF4)),
inference(forward_demodulation,[],[f4028,f2]) ).
fof(f4144,plain,
! [X0,X1] : multiply(inverse(add(X0,X1)),X0) = multiply(add(X0,X1),inverse(add(X0,X1))),
inference(forward_demodulation,[],[f4010,f2]) ).
fof(f4180,plain,
inverse(sF4) = multiply(a,inverse(sF4)),
inference(forward_demodulation,[],[f4129,f6]) ).
fof(f4195,plain,
! [X0,X1] : additive_identity = multiply(inverse(add(X0,X1)),X0),
inference(forward_demodulation,[],[f4144,f10]) ).
fof(f4227,plain,
! [X0,X1] : additive_identity = multiply(X0,inverse(add(X0,X1))),
inference(forward_demodulation,[],[f4195,f2]) ).
fof(f4317,plain,
! [X0,X1] : add(X0,additive_identity) = add(X0,inverse(add(inverse(X0),X1))),
inference(superposition,[],[f80,f4227]) ).
fof(f4326,plain,
! [X0,X1] : add(X0,inverse(add(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f4317,f5]) ).
fof(f4391,plain,
! [X0,X1] : add(X1,inverse(add(X0,inverse(X1)))) = X1,
inference(superposition,[],[f4326,f385]) ).
fof(f4457,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(add(X1,inverse(X0)))) = X0,
inference(backward_demodulation,[],[f2804,f4391]) ).
fof(f4509,plain,
b = add(multiply(sF2,b),inverse(add(sF4,inverse(b)))),
inference(superposition,[],[f4457,f2588]) ).
fof(f4515,plain,
sF1 = add(sF4,inverse(add(sF4,inverse(sF1)))),
inference(superposition,[],[f4457,f3181]) ).
fof(f4603,plain,
sF1 = add(sF4,inverse(add(sF4,sF0))),
inference(forward_demodulation,[],[f4515,f269]) ).
fof(f4607,plain,
b = add(multiply(sF2,b),inverse(add(sF4,sF3))),
inference(forward_demodulation,[],[f4509,f19]) ).
fof(f4649,plain,
sF1 = add(sF4,inverse(add(sF0,sF4))),
inference(forward_demodulation,[],[f4603,f1]) ).
fof(f4653,plain,
b = add(multiply(sF2,b),inverse(add(sF3,sF4))),
inference(forward_demodulation,[],[f4607,f1]) ).
fof(f4692,plain,
b = add(multiply(sF2,b),inverse(sF4)),
inference(forward_demodulation,[],[f4653,f325]) ).
fof(f4705,plain,
b = add(inverse(sF4),multiply(sF2,b)),
inference(forward_demodulation,[],[f4692,f1]) ).
fof(f4707,plain,
b = add(b,inverse(sF4)),
inference(backward_demodulation,[],[f2763,f4705]) ).
fof(f4723,plain,
additive_identity = multiply(sF4,inverse(sF1)),
inference(superposition,[],[f4227,f4649]) ).
fof(f4724,plain,
additive_identity = multiply(sF4,sF0),
inference(forward_demodulation,[],[f4723,f269]) ).
fof(f4737,plain,
additive_identity = multiply(sF0,sF4),
inference(forward_demodulation,[],[f4724,f2]) ).
fof(f4760,plain,
add(inverse(sF4),sF0) = add(inverse(sF4),additive_identity),
inference(superposition,[],[f401,f4737]) ).
fof(f4767,plain,
inverse(sF4) = add(inverse(sF4),sF0),
inference(forward_demodulation,[],[f4760,f5]) ).
fof(f4775,plain,
inverse(sF4) = add(sF0,inverse(sF4)),
inference(forward_demodulation,[],[f4767,f1]) ).
fof(f4780,plain,
multiply(a,b) = add(sF0,multiply(a,inverse(sF4))),
inference(superposition,[],[f41,f4707]) ).
fof(f4803,plain,
multiply(a,b) = add(sF0,inverse(sF4)),
inference(forward_demodulation,[],[f4780,f4180]) ).
fof(f4809,plain,
multiply(a,b) = inverse(sF4),
inference(forward_demodulation,[],[f4803,f4775]) ).
fof(f4811,plain,
sF0 = inverse(sF4),
inference(forward_demodulation,[],[f4809,f13]) ).
fof(f4856,plain,
! [X0] : sF4 = add(sF4,inverse(add(sF0,X0))),
inference(superposition,[],[f4326,f4811]) ).
fof(f4858,plain,
sF1 = sF4,
inference(backward_demodulation,[],[f4649,f4856]) ).
fof(f4863,plain,
$false,
inference(forward_subsumption_resolution,[],[f4858,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO015-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 % Computer : n002.cluster.edu
% 0.13/0.21 % Model : x86_64 x86_64
% 0.13/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.21 % Memory : 8046.5625MB
% 0.13/0.21 % OS : Linux 6.8.0-71-generic
% 0.13/0.22 % CPULimit : 300
% 0.13/0.22 % WCLimit : 300
% 0.13/0.22 % DateTime : Mon Sep 28 21:07:07 UTC 2026
% 0.13/0.22 % CPUTime :
% 0.13/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.28 Running first-order theorem proving
% 0.13/0.28 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.00/2.23 % (763303)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.00/2.23 % (763327)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2008198522:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.00/2.23 % (763323)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=797740601:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.00/2.23 % (763320)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=3536667571:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.00/2.23 % (763321)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3108437204:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.00/2.23 % (763322)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2913437624:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.00/2.23 % (763319)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=2740260750:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.00/2.23 % (763325)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3336624234:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.00/2.23 % (763322)Instruction limit reached!
% 9.00/2.23 % (763322)------------------------------
% 9.00/2.23 % (763322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763322)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763322)Termination reason: Instruction limit
% 9.00/2.23 % (763322)Termination phase: Saturation
% 9.00/2.23 % (763322)Time elapsed: 0.087 s
% 9.00/2.23 % (763322)Peak memory usage: 88 MB
% 9.00/2.23 % (763322)Instructions burned: 137 (million)
% 9.00/2.23 % (763323)Instruction limit reached!
% 9.00/2.23 % (763323)------------------------------
% 9.00/2.23 % (763323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763323)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763323)Termination reason: Instruction limit
% 9.00/2.23 % (763323)Termination phase: Saturation
% 9.00/2.23 % (763323)Time elapsed: 0.109 s
% 9.00/2.23 % (763323)Peak memory usage: 89 MB
% 9.00/2.23 % (763323)Instructions burned: 182 (million)
% 9.00/2.23 % (763325)Instruction limit reached!
% 9.00/2.23 % (763325)------------------------------
% 9.00/2.23 % (763325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763325)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763325)Termination reason: Instruction limit
% 9.00/2.23 % (763325)Termination phase: Saturation
% 9.00/2.23 % (763325)Time elapsed: 0.169 s
% 9.00/2.23 % (763325)Peak memory usage: 90 MB
% 9.00/2.23 % (763325)Instructions burned: 258 (million)
% 9.00/2.23 % (763424)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4276647416:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 9.00/2.23 % (763431)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=865041006:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 9.00/2.23 % (763327)Instruction limit reached!
% 9.00/2.23 % (763327)------------------------------
% 9.00/2.23 % (763327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763327)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763327)Termination reason: Instruction limit
% 9.00/2.23 % (763327)Termination phase: Saturation
% 9.00/2.23 % (763327)Time elapsed: 0.348 s
% 9.00/2.23 % (763327)Peak memory usage: 98 MB
% 9.00/2.23 % (763327)Instructions burned: 1190 (million)
% 9.00/2.23 % (763459)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1866801976:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 9.00/2.23 % (763490)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=924441901:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 9.00/2.23 % (763459)Instruction limit reached!
% 9.00/2.23 % (763459)------------------------------
% 9.00/2.23 % (763459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763459)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763459)Termination reason: Instruction limit
% 9.00/2.23 % (763459)Termination phase: Saturation
% 9.00/2.23 % (763459)Time elapsed: 0.111 s
% 9.00/2.23 % (763459)Peak memory usage: 90 MB
% 9.00/2.23 % (763459)Instructions burned: 217 (million)
% 9.00/2.23 % (763490)Instruction limit reached!
% 9.00/2.23 % (763490)------------------------------
% 9.00/2.23 % (763490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.00/2.23 % (763490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.00/2.23 % (763490)CaDiCaL version: 2.1.3
% 9.00/2.23 % (763490)Termination reason: Instruction limit
% 9.00/2.23 % (763490)Termination phase: Saturation
% 9.00/2.23 % (763490)Time elapsed: 0.100 s
% 9.00/2.23 % (763490)Peak memory usage: 92 MB
% 9.00/2.23 % (763490)Instructions burned: 318 (million)
% 9.00/2.23 % (763493)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=4071101126:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2993 on theBenchmark for (2993ds/12125Mi)
% 9.00/2.23 % (763494)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2962233784:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 9.00/2.23 % (763321)First to succeed.
% 9.00/2.23 % (763321)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-763303"
% 9.00/2.23 % (763319)Also succeeded, but the first one will report.
% 9.00/2.23 % (763424)Also succeeded, but the first one will report.
% 9.00/2.23 % (763320)Also succeeded, but the first one will report.
% 9.00/2.23 % (763321)Refutation found. Thanks to Tanya!
% 9.00/2.23 % SZS status Unsatisfiable for theBenchmark
% 9.00/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 10.76/2.43 % (763321)------------------------------
% 10.76/2.43 % (763321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.76/2.43 % (763321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.76/2.43 % (763321)CaDiCaL version: 2.1.3
% 10.76/2.43 % (763321)Termination reason: Refutation
% 10.76/2.43 % (763321)Time elapsed: 0.979 s
% 10.76/2.43 % (763321)Peak memory usage: 133 MB
% 10.76/2.43 % (763321)Instructions burned: 1489 (million)
% 10.76/2.43 % (763321)------------------------------
% 10.76/2.43 % (763321)------------------------------
% 10.76/2.43 % (763303)Success in time 1.41 s
% 10.76/2.43 % Vampire exiting
%------------------------------------------------------------------------------