%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 10:14:49 AM UTC 2026
% Result : Unsatisfiable 3.35s 1.32s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 45 unt; 7 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f4,negated_conjecture,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f6,definition,
! [X2,X0,X1] : sF0(X0,X2,X1) = divide(divide(X0,X2),X1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X2,X0,X1] : divide(divide(X0,X2),X1) = sF0(X0,X2,X1),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = divide(divide(X0,X1),sF0(X0,X2,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : divide(divide(X0,X1),sF0(X0,X2,X1)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X2,X0,X1] : sF1(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f9,f7]) ).
fof(f11,definition,
! [X2] : sF2(X2) = divide(X2,X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
! [X2] : divide(X2,X2) = sF2(X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X1] : sF3(X2,X1) = divide(sF2(X2),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f14,plain,
! [X2,X1] : divide(sF2(X2),X1) = sF3(X2,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF4(X0,X2,X1) = divide(X0,sF3(X2,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : divide(X0,sF3(X2,X1)) = sF4(X0,X2,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF4(X0,X2,X1),
inference(definition_folding,[],[f2,f16,f14,f12]) ).
fof(f19,plain,
! [X0] : identity = sF2(X0),
inference(definition_folding,[],[f4,f12]) ).
fof(f20,definition,
sF5 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f21,plain,
multiply(a,b) = sF5,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF6 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
multiply(b,a) = sF6,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
sF5 != sF6,
inference(definition_folding,[],[f5,f23,f21]) ).
fof(f25,plain,
! [X0] : identity = divide(X0,X0),
inference(forward_demodulation,[],[f19,f12]) ).
fof(f27,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF3(X2,X1)),
inference(forward_demodulation,[],[f17,f16]) ).
fof(f28,plain,
! [X2,X0,X1] : divide(divide(X0,X1),sF0(X0,X2,X1)) = X2,
inference(forward_demodulation,[],[f10,f9]) ).
fof(f30,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(sF2(X2),X1)),
inference(forward_demodulation,[],[f27,f14]) ).
fof(f31,plain,
! [X2,X0,X1] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
inference(forward_demodulation,[],[f28,f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(forward_demodulation,[],[f30,f12]) ).
fof(f36,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,X1)) = X0,
inference(superposition,[],[f31,f25]) ).
fof(f57,plain,
! [X0] : divide(divide(X0,identity),identity) = X0,
inference(superposition,[],[f36,f25]) ).
fof(f64,plain,
! [X0] : identity = divide(divide(X0,identity),X0),
inference(superposition,[],[f31,f57]) ).
fof(f79,plain,
! [X0,X1] : divide(divide(divide(X0,identity),X1),divide(identity,X1)) = X0,
inference(superposition,[],[f31,f64]) ).
fof(f81,plain,
! [X0] : divide(X0,identity) = X0,
inference(forward_demodulation,[],[f79,f36]) ).
fof(f93,plain,
! [X0,X1] : divide(divide(X0,identity),divide(X0,X1)) = X1,
inference(superposition,[],[f31,f81]) ).
fof(f99,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f93,f81]) ).
fof(f117,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(forward_demodulation,[],[f32,f25]) ).
fof(f118,plain,
sF6 = divide(b,divide(identity,a)),
inference(superposition,[],[f117,f23]) ).
fof(f119,plain,
sF5 = divide(a,divide(identity,b)),
inference(superposition,[],[f117,f21]) ).
fof(f139,plain,
a = divide(sF5,divide(identity,divide(identity,b))),
inference(superposition,[],[f36,f119]) ).
fof(f143,plain,
a = divide(sF5,b),
inference(forward_demodulation,[],[f139,f99]) ).
fof(f144,plain,
b = divide(sF5,a),
inference(superposition,[],[f99,f143]) ).
fof(f150,plain,
sF5 = divide(b,divide(identity,a)),
inference(superposition,[],[f36,f144]) ).
fof(f154,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f150,f118]) ).
fof(f157,plain,
sF5 != sF5,
inference(superposition,[],[f24,f154]) ).
fof(f158,plain,
$false,
inference(trivial_inequality_removal,[],[f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP540-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:04:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.35/1.32 % (1177371)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.35/1.32 % (1177417)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2818990729:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.35/1.32 % (1177419)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2820734176:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.35/1.32 % (1177420)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1291492317:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.35/1.32 % (1177416)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=2832202432:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.35/1.32 % (1177418)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3096887970:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.35/1.32 % (1177415)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=617736549:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.35/1.32 % (1177419)First to succeed.
% 3.35/1.32 % (1177419)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1177371"
% 3.35/1.32 % (1177420)Also succeeded, but the first one will report.
% 3.35/1.32 % (1177418)Also succeeded, but the first one will report.
% 3.35/1.32 % (1177421)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3003243579:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.35/1.32 % (1177421)Also succeeded, but the first one will report.
% 3.35/1.32 % (1177419)Refutation found. Thanks to Tanya!
% 3.35/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.35/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.32 % (1177419)------------------------------
% 3.35/1.32 % (1177419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.32 % (1177419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.32 % (1177419)CaDiCaL version: 2.1.3
% 3.35/1.32 % (1177419)Termination reason: Refutation
% 3.35/1.32 % (1177419)Time elapsed: 0.006 s
% 3.35/1.32 % (1177419)Peak memory usage: 88 MB
% 3.35/1.32 % (1177419)Instructions burned: 7 (million)
% 3.35/1.32 % (1177419)------------------------------
% 3.35/1.32 % (1177419)------------------------------
% 3.35/1.32 % (1177371)Success in time 0.392 s
% 3.35/1.32 % Vampire exiting
%------------------------------------------------------------------------------