%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO012-4 : 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 : n008.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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 2.75s 1.21s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 57 ( 57 unt; 8 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f4,negated_conjecture,
! [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(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f12,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f11]) ).
fof(f18,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = multiply(X0,add(X1,X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f19,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = add(multiply(X0,X1),multiply(X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f21,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X0,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X1,X2),
inference(definition_folding,[],[f4,f21,f19]) ).
fof(f23,definition,
! [X0] : sF4(X0) = add(X0,additive_identity),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f24,plain,
! [X0] : add(X0,additive_identity) = sF4(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF4(X0) = X0,
inference(definition_folding,[],[f5,f24]) ).
fof(f26,definition,
! [X0] : sF5(X0) = multiply(X0,multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f27,plain,
! [X0] : multiply(X0,multiplicative_identity) = sF5(X0),
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
! [X0] : sF5(X0) = X0,
inference(definition_folding,[],[f6,f27]) ).
fof(f29,definition,
! [X0] : sF6(X0) = add(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f30,plain,
! [X0] : add(X0,inverse(X0)) = sF6(X0),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
! [X0] : multiplicative_identity = sF6(X0),
inference(definition_folding,[],[f8,f30]) ).
fof(f32,definition,
! [X0] : sF7(X0) = multiply(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f33,plain,
! [X0] : multiply(X0,inverse(X0)) = sF7(X0),
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
! [X0] : additive_identity = sF7(X0),
inference(definition_folding,[],[f10,f33]) ).
fof(f35,definition,
sF8 = inverse(x),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f36,plain,
inverse(x) = sF8,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF9 = inverse(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f38,plain,
inverse(sF8) = sF9,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
x != sF9,
inference(definition_folding,[],[f12,f38,f36]) ).
fof(f40,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(forward_demodulation,[],[f34,f33]) ).
fof(f41,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(forward_demodulation,[],[f31,f30]) ).
fof(f42,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(forward_demodulation,[],[f28,f27]) ).
fof(f43,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f44,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X0,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f22,f21]) ).
fof(f46,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(forward_demodulation,[],[f44,f19]) ).
fof(f48,plain,
additive_identity = multiply(sF8,sF9),
inference(superposition,[],[f40,f38]) ).
fof(f49,plain,
additive_identity = multiply(x,sF8),
inference(superposition,[],[f40,f36]) ).
fof(f50,plain,
multiplicative_identity = add(sF8,sF9),
inference(superposition,[],[f41,f38]) ).
fof(f51,plain,
multiplicative_identity = add(x,sF8),
inference(superposition,[],[f41,f36]) ).
fof(f52,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f1,f43]) ).
fof(f81,plain,
! [X0] : multiply(X0,multiplicative_identity) = add(multiply(X0,x),multiply(X0,sF8)),
inference(superposition,[],[f46,f51]) ).
fof(f82,plain,
! [X0] : multiply(X0,multiplicative_identity) = add(multiply(X0,sF8),multiply(X0,sF9)),
inference(superposition,[],[f46,f50]) ).
fof(f91,plain,
! [X0] : add(multiply(X0,sF8),multiply(X0,sF9)) = X0,
inference(forward_demodulation,[],[f82,f42]) ).
fof(f92,plain,
! [X0] : add(multiply(X0,x),multiply(X0,sF8)) = X0,
inference(forward_demodulation,[],[f81,f42]) ).
fof(f99,plain,
x = add(additive_identity,multiply(x,sF9)),
inference(superposition,[],[f91,f49]) ).
fof(f107,plain,
x = multiply(x,sF9),
inference(forward_demodulation,[],[f99,f52]) ).
fof(f116,plain,
! [X0] : add(multiply(x,X0),multiply(X0,sF8)) = X0,
inference(superposition,[],[f92,f2]) ).
fof(f214,plain,
sF9 = add(x,multiply(sF9,sF8)),
inference(superposition,[],[f116,f107]) ).
fof(f238,plain,
sF9 = add(x,multiply(sF8,sF9)),
inference(forward_demodulation,[],[f214,f2]) ).
fof(f244,plain,
sF9 = add(x,additive_identity),
inference(forward_demodulation,[],[f238,f48]) ).
fof(f247,plain,
x = sF9,
inference(forward_demodulation,[],[f244,f43]) ).
fof(f248,plain,
x != x,
inference(superposition,[],[f39,f247]) ).
fof(f257,plain,
$false,
inference(trivial_inequality_removal,[],[f248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:04:39 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.75/1.21 % (2648774)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.75/1.21 % (2648814)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1995473277:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.75/1.21 % (2648814)First to succeed.
% 2.75/1.21 % (2648814)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2648774"
% 2.75/1.21 % (2648807)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=2979441539:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.75/1.21 % (2648809)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=2015901070:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.75/1.21 % (2648811)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1632534560:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.75/1.21 % (2648818)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2189465102:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.75/1.21 % (2648813)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1159082201:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.75/1.21 % (2648816)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1824935417:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.75/1.21 % (2648818)Also succeeded, but the first one will report.
% 2.75/1.21 % (2648816)Also succeeded, but the first one will report.
% 2.75/1.21 % (2648813)Also succeeded, but the first one will report.
% 2.75/1.21 % (2648814)Refutation found. Thanks to Tanya!
% 2.75/1.21 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.21 % (2648814)------------------------------
% 2.75/1.21 % (2648814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.21 % (2648814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.21 % (2648814)CaDiCaL version: 2.1.3
% 2.75/1.21 % (2648814)Termination reason: Refutation
% 2.75/1.21 % (2648814)Time elapsed: 0.004 s
% 2.75/1.21 % (2648814)Peak memory usage: 88 MB
% 2.75/1.21 % (2648814)Instructions burned: 9 (million)
% 2.75/1.21 % (2648814)------------------------------
% 2.75/1.21 % (2648814)------------------------------
% 2.75/1.21 % (2648774)Success in time 0.29 s
% 2.75/1.21 % Vampire exiting
%------------------------------------------------------------------------------