%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP543-1 : TPTP v9.3.1. Released v2.6.0.
% 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 10:14:49 AM UTC 2026
% Result : Unsatisfiable 2.59s 1.25s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 64 unt; 12 def)
% Number of atoms : 64 ( 63 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f4,negated_conjecture,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/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,
! [X2,X0,X1] : sF0(X0,X1,X2) = divide(divide(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : divide(divide(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = divide(sF0(X0,X1,X2),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : divide(sF0(X0,X1,X2),X0) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(identity,sF1(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(identity,sF1(X0,X1,X2)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = divide(sF2(X0,X1,X2),X2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : sF3(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f14,f12,f10,f8]) ).
fof(f16,definition,
! [X0] : sF4(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f17,plain,
! [X0] : divide(X0,X0) = sF4(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : identity = sF4(X0),
inference(definition_folding,[],[f4,f17]) ).
fof(f19,definition,
sF5 = divide(identity,b3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
divide(identity,b3) = sF5,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF6 = divide(a3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
divide(a3,sF5) = sF6,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF7 = divide(identity,c3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
divide(identity,c3) = sF7,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF8 = divide(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f26,plain,
divide(sF6,sF7) = sF8,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF9 = divide(b3,sF7),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f28,plain,
divide(b3,sF7) = sF9,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF10 = divide(identity,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f30,plain,
divide(identity,sF9) = sF10,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF11 = divide(a3,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f32,plain,
divide(a3,sF10) = sF11,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
sF8 != sF11,
inference(definition_folding,[],[f6,f32,f30,f28,f24,f26,f24,f22,f20]) ).
fof(f34,plain,
! [X0] : identity = divide(X0,X0),
inference(forward_demodulation,[],[f18,f17]) ).
fof(f35,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = X1,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(divide(identity,sF1(X0,X1,X2)),X2) = X1,
inference(forward_demodulation,[],[f35,f12]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(divide(identity,divide(sF0(X0,X1,X2),X0)),X2) = X1,
inference(forward_demodulation,[],[f36,f10]) ).
fof(f38,plain,
! [X2,X0,X1] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
inference(forward_demodulation,[],[f37,f8]) ).
fof(f39,plain,
! [X0,X1] : divide(divide(identity,divide(divide(identity,X1),X0)),X1) = X0,
inference(superposition,[],[f38,f34]) ).
fof(f45,plain,
! [X0] : sF5 = divide(divide(identity,divide(divide(sF6,X0),a3)),X0),
inference(superposition,[],[f38,f22]) ).
fof(f48,plain,
! [X2,X0,X1] : divide(divide(divide(X1,X0),X2),X1) = divide(divide(identity,divide(X0,identity)),X2),
inference(superposition,[],[f38,f38]) ).
fof(f49,plain,
! [X0,X1] : divide(divide(identity,divide(identity,X0)),divide(X0,X1)) = X1,
inference(superposition,[],[f38,f34]) ).
fof(f52,plain,
! [X0] : divide(divide(identity,divide(sF5,X0)),b3) = X0,
inference(superposition,[],[f39,f20]) ).
fof(f53,plain,
! [X0] : divide(divide(identity,divide(identity,X0)),identity) = X0,
inference(superposition,[],[f39,f34]) ).
fof(f70,plain,
! [X0] : b3 = divide(divide(identity,X0),divide(sF5,X0)),
inference(superposition,[],[f39,f52]) ).
fof(f183,plain,
b3 = divide(identity,divide(sF5,identity)),
inference(superposition,[],[f70,f34]) ).
fof(f414,plain,
sF5 = divide(divide(identity,divide(sF8,a3)),sF7),
inference(superposition,[],[f45,f26]) ).
fof(f422,plain,
divide(sF8,a3) = divide(divide(identity,divide(sF5,identity)),sF7),
inference(superposition,[],[f38,f414]) ).
fof(f424,plain,
divide(b3,sF7) = divide(sF8,a3),
inference(forward_demodulation,[],[f422,f183]) ).
fof(f426,plain,
sF9 = divide(sF8,a3),
inference(forward_demodulation,[],[f424,f28]) ).
fof(f643,plain,
! [X0] : divide(divide(identity,identity),divide(identity,X0)) = X0,
inference(superposition,[],[f49,f34]) ).
fof(f831,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(forward_demodulation,[],[f643,f34]) ).
fof(f929,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(superposition,[],[f49,f831]) ).
fof(f930,plain,
! [X0] : divide(X0,identity) = X0,
inference(superposition,[],[f53,f831]) ).
fof(f1167,plain,
! [X2,X0,X1] : divide(divide(divide(X1,X0),X2),X1) = divide(divide(identity,X0),X2),
inference(forward_demodulation,[],[f48,f930]) ).
fof(f1245,plain,
a3 = divide(sF8,sF9),
inference(superposition,[],[f929,f426]) ).
fof(f1365,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,divide(identity,X0))) = divide(divide(identity,identity),X1),
inference(superposition,[],[f1167,f53]) ).
fof(f1551,plain,
! [X0,X1] : divide(identity,X1) = divide(divide(X0,X1),divide(identity,divide(identity,X0))),
inference(forward_demodulation,[],[f1365,f34]) ).
fof(f1565,plain,
! [X0,X1] : divide(identity,X1) = divide(divide(X0,X1),X0),
inference(forward_demodulation,[],[f1551,f929]) ).
fof(f1873,plain,
divide(identity,sF9) = divide(a3,sF8),
inference(superposition,[],[f1565,f1245]) ).
fof(f1966,plain,
sF10 = divide(a3,sF8),
inference(forward_demodulation,[],[f1873,f30]) ).
fof(f2056,plain,
sF8 = divide(a3,sF10),
inference(superposition,[],[f929,f1966]) ).
fof(f2060,plain,
sF8 = sF11,
inference(forward_demodulation,[],[f2056,f32]) ).
fof(f2062,plain,
sF8 != sF8,
inference(superposition,[],[f33,f2060]) ).
fof(f2070,plain,
$false,
inference(trivial_inequality_removal,[],[f2062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP543-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:07:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 2.59/1.25 % (1001721)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.59/1.25 % (1001882)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2724806106:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.59/1.25 % (1001882)First to succeed.
% 2.59/1.25 % (1001882)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1001721"
% 2.59/1.25 % (1001880)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4209545472:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.59/1.25 % (1001883)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3950917898:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.59/1.25 % (1001881)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3154299131:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.59/1.25 % (1001879)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=2607141834:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.59/1.25 % (1001878)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=3532450305:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.59/1.25 % (1001881)Also succeeded, but the first one will report.
% 2.59/1.25 % (1001884)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3376438147:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.59/1.25 % (1001882)Refutation found. Thanks to Tanya!
% 2.59/1.25 % SZS status Unsatisfiable for theBenchmark
% 2.59/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.25 % (1001882)------------------------------
% 2.59/1.25 % (1001882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.25 % (1001882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.25 % (1001882)CaDiCaL version: 2.1.3
% 2.59/1.25 % (1001882)Termination reason: Refutation
% 2.59/1.25 % (1001882)Time elapsed: 0.022 s
% 2.59/1.25 % (1001882)Peak memory usage: 89 MB
% 2.59/1.25 % (1001882)Instructions burned: 69 (million)
% 2.59/1.25 % (1001882)------------------------------
% 2.59/1.25 % (1001882)------------------------------
% 2.59/1.25 % (1001721)Success in time 0.306 s
% 2.59/1.25 % Vampire exiting
%------------------------------------------------------------------------------