%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:35:47 AM UTC 2026
% Result : Unsatisfiable 0.30s 1.91s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 33 unt; 6 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
fof(f5,negated_conjecture,
! [X0,X1] : multiply(X0,X1,inverse(X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f6,negated_conjecture,
inverse(inverse(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
fof(f7,plain,
a != inverse(inverse(a)),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X3,X0,X1,X4] : sF0(X0,X1,X2,X3,X4) = multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = sF0(X0,X1,X2,X3,X4),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X3,X0,X1,X4] : sF1(X0,X1,X2,X3,X4) = multiply(X0,X1,multiply(X2,X3,X4)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,X1,multiply(X2,X3,X4)) = sF1(X0,X1,X2,X3,X4),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X2,X3,X0,X1,X4] : sF0(X0,X1,X2,X3,X4) = sF1(X0,X1,X2,X3,X4),
inference(definition_folding,[],[f1,f11,f9]) ).
fof(f13,definition,
! [X0,X1] : sF2(X0,X1) = multiply(X0,X1,X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X0,X1] : multiply(X0,X1,X1) = sF2(X0,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X0,X1] : sF2(X0,X1) = X1,
inference(definition_folding,[],[f2,f14]) ).
fof(f22,definition,
! [X0,X1] : sF5(X0,X1) = multiply(X0,X1,inverse(X1)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f23,plain,
! [X0,X1] : multiply(X0,X1,inverse(X1)) = sF5(X0,X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0,X1] : sF5(X0,X1) = X0,
inference(definition_folding,[],[f5,f23]) ).
fof(f25,definition,
sF6 = inverse(a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f26,plain,
inverse(a) = sF6,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF7 = inverse(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f28,plain,
inverse(sF6) = sF7,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
a != sF7,
inference(definition_folding,[],[f7,f28,f26]) ).
fof(f30,plain,
! [X0,X1] : multiply(X0,X1,inverse(X1)) = X0,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f33,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,X1,multiply(X2,X3,X4)) = sF0(X0,X1,X2,X3,X4),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(forward_demodulation,[],[f34,f9]) ).
fof(f36,plain,
! [X0] : multiply(X0,sF6,sF7) = X0,
inference(superposition,[],[f30,f28]) ).
fof(f37,plain,
! [X0] : multiply(X0,a,sF6) = X0,
inference(superposition,[],[f30,f26]) ).
fof(f49,plain,
! [X2,X3,X0,X1] : multiply(X1,X0,multiply(X0,X2,X3)) = multiply(X0,X2,multiply(X1,X0,X3)),
inference(superposition,[],[f35,f33]) ).
fof(f86,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X2,X0,multiply(X1,X2,X0)),
inference(superposition,[],[f49,f33]) ).
fof(f275,plain,
! [X0] : multiply(a,sF6,X0) = X0,
inference(superposition,[],[f86,f37]) ).
fof(f297,plain,
a = sF7,
inference(superposition,[],[f275,f36]) ).
fof(f321,plain,
a != a,
inference(superposition,[],[f29,f297]) ).
fof(f322,plain,
$false,
inference(trivial_inequality_removal,[],[f321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 % Computer : n018.cluster.edu
% 0.23/0.31 % Model : x86_64 x86_64
% 0.23/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.31 % Memory : 8046.5625MB
% 0.23/0.31 % OS : Linux 6.8.0-71-generic
% 0.23/0.31 % CPULimit : 300
% 0.23/0.31 % WCLimit : 300
% 0.23/0.31 % DateTime : Mon Sep 28 21:04:55 UTC 2026
% 0.23/0.31 % CPUTime :
% 0.23/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.37 Running first-order theorem proving
% 0.23/0.37 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
% 0.30/1.91 % (3782161)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.30/1.91 % (3782170)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2678469437:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.30/1.91 % (3782170)First to succeed.
% 0.30/1.91 % (3782170)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3782161"
% 0.30/1.91 % (3782167)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=991231075:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.30/1.91 % (3782166)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=829489671:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.30/1.91 % (3782168)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=546091954:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.30/1.91 % (3782169)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=974364132:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.30/1.91 % (3782171)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=797984961:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.30/1.91 % (3782171)Also succeeded, but the first one will report.
% 0.30/1.91 % (3782172)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3551925717:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.30/1.91 % (3782169)Also succeeded, but the first one will report.
% 0.30/1.91 % (3782172)Also succeeded, but the first one will report.
% 0.30/1.91 % (3782170)Refutation found. Thanks to Tanya!
% 0.30/1.91 % SZS status Unsatisfiable for theBenchmark
% 0.30/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/1.91 % (3782170)------------------------------
% 0.30/1.91 % (3782170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.91 % (3782170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.91 % (3782170)CaDiCaL version: 2.1.3
% 0.30/1.91 % (3782170)Termination reason: Refutation
% 0.30/1.91 % (3782170)Time elapsed: 0.008 s
% 0.30/1.91 % (3782170)Peak memory usage: 88 MB
% 0.30/1.91 % (3782170)Instructions burned: 13 (million)
% 0.30/1.91 % (3782170)------------------------------
% 0.30/1.91 % (3782170)------------------------------
% 0.30/1.91 % (3782161)Success in time 0.484 s
% 0.30/1.91 % Vampire exiting
%------------------------------------------------------------------------------