%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 10:14:50 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 60 unt; 11 def)
% Number of atoms : 60 ( 59 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 : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(definition_unfolding,[],[f5,f2,f2,f2,f2]) ).
fof(f7,definition,
! [X0,X1] : sF0(X0,X1) = divide(identity,divide(X0,X1)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f8,plain,
! [X0,X1] : divide(identity,divide(X0,X1)) = sF0(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF1(X1,X2,X0) = divide(divide(X1,X2),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : divide(divide(X1,X2),X0) = sF1(X1,X2,X0),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(sF0(X0,X1),sF1(X1,X2,X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(sF0(X0,X1),sF1(X1,X2,X0)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f12,f10,f8]) ).
fof(f14,definition,
! [X0] : sF3(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
! [X0] : divide(X0,X0) = sF3(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X0] : identity = sF3(X0),
inference(definition_folding,[],[f4,f15]) ).
fof(f17,definition,
sF4 = divide(identity,b3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
divide(identity,b3) = sF4,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF5 = divide(a3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
divide(a3,sF4) = sF5,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF6 = divide(identity,c3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
divide(identity,c3) = sF6,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF7 = divide(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
divide(sF5,sF6) = sF7,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF8 = divide(b3,sF6),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f26,plain,
divide(b3,sF6) = sF8,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF9 = divide(identity,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f28,plain,
divide(identity,sF8) = sF9,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF10 = divide(a3,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f30,plain,
divide(a3,sF9) = sF10,
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
sF7 != sF10,
inference(definition_folding,[],[f6,f30,f28,f26,f22,f24,f22,f20,f18]) ).
fof(f32,plain,
! [X0] : identity = divide(X0,X0),
inference(forward_demodulation,[],[f16,f15]) ).
fof(f33,plain,
! [X2,X0,X1] : divide(sF0(X0,X1),sF1(X1,X2,X0)) = X2,
inference(forward_demodulation,[],[f13,f12]) ).
fof(f34,plain,
! [X2,X0,X1] : divide(sF0(X0,X1),divide(divide(X1,X2),X0)) = X2,
inference(forward_demodulation,[],[f33,f10]) ).
fof(f35,plain,
! [X2,X0,X1] : divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
inference(forward_demodulation,[],[f34,f8]) ).
fof(f36,plain,
! [X0,X1] : divide(divide(identity,identity),divide(divide(X0,X1),X0)) = X1,
inference(superposition,[],[f35,f32]) ).
fof(f43,plain,
! [X0] : divide(divide(identity,sF8),divide(divide(sF6,X0),b3)) = X0,
inference(superposition,[],[f35,f26]) ).
fof(f56,plain,
! [X0] : divide(sF9,divide(divide(sF6,X0),b3)) = X0,
inference(forward_demodulation,[],[f43,f28]) ).
fof(f57,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[],[f36,f32]) ).
fof(f64,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(superposition,[],[f57,f32]) ).
fof(f66,plain,
b3 = divide(identity,divide(sF4,identity)),
inference(superposition,[],[f57,f18]) ).
fof(f71,plain,
sF4 = divide(identity,divide(sF5,a3)),
inference(superposition,[],[f57,f20]) ).
fof(f79,plain,
! [X0,X1] : divide(identity,X0) = divide(divide(X1,X0),X1),
inference(superposition,[],[f64,f57]) ).
fof(f159,plain,
divide(identity,divide(sF4,identity)) = divide(sF5,a3),
inference(superposition,[],[f57,f71]) ).
fof(f163,plain,
b3 = divide(sF5,a3),
inference(forward_demodulation,[],[f159,f66]) ).
fof(f396,plain,
! [X0] : divide(X0,identity) = X0,
inference(superposition,[],[f79,f57]) ).
fof(f493,plain,
! [X0,X1] : divide(divide(identity,divide(identity,X0)),divide(X0,X1)) = X1,
inference(superposition,[],[f35,f396]) ).
fof(f504,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f493,f64]) ).
fof(f569,plain,
sF9 = divide(a3,sF10),
inference(superposition,[],[f504,f30]) ).
fof(f580,plain,
sF6 = divide(sF5,sF7),
inference(superposition,[],[f504,f24]) ).
fof(f581,plain,
a3 = divide(sF5,b3),
inference(superposition,[],[f504,f163]) ).
fof(f623,plain,
divide(identity,sF10) = divide(sF9,a3),
inference(superposition,[],[f79,f569]) ).
fof(f635,plain,
divide(identity,sF7) = divide(sF6,sF5),
inference(superposition,[],[f79,f580]) ).
fof(f714,plain,
sF5 = divide(sF6,divide(identity,sF7)),
inference(superposition,[],[f504,f635]) ).
fof(f735,plain,
divide(identity,sF7) = divide(sF9,divide(sF5,b3)),
inference(superposition,[],[f56,f714]) ).
fof(f742,plain,
divide(identity,sF7) = divide(sF9,a3),
inference(forward_demodulation,[],[f735,f581]) ).
fof(f743,plain,
divide(identity,sF10) = divide(identity,sF7),
inference(forward_demodulation,[],[f742,f623]) ).
fof(f749,plain,
! [X0] : sF10 = divide(divide(identity,divide(X0,identity)),divide(divide(identity,sF7),X0)),
inference(superposition,[],[f35,f743]) ).
fof(f752,plain,
sF7 = sF10,
inference(forward_demodulation,[],[f749,f35]) ).
fof(f756,plain,
sF7 != sF7,
inference(superposition,[],[f31,f752]) ).
fof(f765,plain,
$false,
inference(trivial_inequality_removal,[],[f756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:07:04 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.18/1.30 % (2861725)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.18/1.30 % (2861734)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4003106446:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.18/1.30 % (2861734)First to succeed.
% 0.18/1.30 % (2861734)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2861725"
% 0.18/1.30 % (2861730)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=3383784488:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.18/1.30 % (2861732)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3626709976:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.18/1.30 % (2861733)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1192425284:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.18/1.30 % (2861731)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=217176881:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.18/1.30 % (2861735)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=656542424:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.18/1.30 % (2861736)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1359255933:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.18/1.30 % (2861733)Instruction limit reached!
% 0.18/1.30 % (2861733)------------------------------
% 0.18/1.30 % (2861733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (2861733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (2861733)CaDiCaL version: 2.1.3
% 0.18/1.30 % (2861733)Termination reason: Instruction limit
% 0.18/1.30 % (2861733)Termination phase: Saturation
% 0.18/1.30 % (2861733)Time elapsed: 0.080 s
% 0.18/1.30 % (2861733)Peak memory usage: 89 MB
% 0.18/1.30 % (2861733)Instructions burned: 136 (million)
% 0.18/1.30 % (2861734)Refutation found. Thanks to Tanya!
% 0.18/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.30 % (2861734)------------------------------
% 0.18/1.30 % (2861734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (2861734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (2861734)CaDiCaL version: 2.1.3
% 0.18/1.30 % (2861734)Termination reason: Refutation
% 0.18/1.30 % (2861734)Time elapsed: 0.010 s
% 0.18/1.30 % (2861734)Peak memory usage: 88 MB
% 0.18/1.30 % (2861734)Instructions burned: 29 (million)
% 0.18/1.30 % (2861734)------------------------------
% 0.18/1.30 % (2861734)------------------------------
% 0.18/1.30 % (2861725)Success in time 0.266 s
% 0.18/1.30 % Vampire exiting
%------------------------------------------------------------------------------