%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP451-1 : 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 10:14:02 AM UTC 2026
% Result : Unsatisfiable 3.64s 1.47s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 59 unt; 13 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 106 ( 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f5,definition,
! [X0] : sF0(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X0] : divide(X0,X0) = sF0(X0),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X0] : sF1(X0) = divide(sF0(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X0] : divide(sF0(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0] : sF2(X0,X2) = divide(sF1(X0),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0] : divide(sF1(X0),X2) = sF2(X0,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X1,X0,X2) = divide(X1,sF2(X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(X1,sF2(X0,X2)) = sF3(X1,X0,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = divide(X0,sF3(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : divide(X0,sF3(X1,X0,X2)) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF5(X0,X1,X2) = divide(sF0(X0),sF4(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : divide(sF0(X0),sF4(X0,X1,X2)) = sF5(X0,X1,X2),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = divide(sF5(X0,X1,X2),X2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
! [X2,X0,X1] : divide(sF5(X0,X1,X2),X2) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] : sF6(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f18,f16,f14,f12,f10,f8,f6,f6]) ).
fof(f20,definition,
! [X2,X1] : sF7(X2,X1) = divide(sF0(X2),X1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
! [X2,X1] : divide(sF0(X2),X1) = sF7(X2,X1),
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
! [X2,X0,X1] : sF8(X0,X2,X1) = divide(X0,sF7(X2,X1)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
! [X2,X0,X1] : divide(X0,sF7(X2,X1)) = sF8(X0,X2,X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF8(X0,X2,X1),
inference(definition_folding,[],[f2,f23,f21,f6]) ).
fof(f25,plain,
! [X0,X1] : inverse(X0) = sF7(X1,X0),
inference(definition_folding,[],[f3,f21,f6]) ).
fof(f26,definition,
sF9 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f27,plain,
inverse(a1) = sF9,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF10 = multiply(sF9,a1),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f29,plain,
multiply(sF9,a1) = sF10,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF11 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f31,plain,
inverse(b1) = sF11,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF12 = multiply(sF11,b1),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f33,plain,
multiply(sF11,b1) = sF12,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sF10 != sF12,
inference(definition_folding,[],[f4,f33,f31,f29,f27]) ).
fof(f35,plain,
! [X0,X1] : inverse(X0) = divide(sF0(X1),X0),
inference(forward_demodulation,[],[f25,f21]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF7(X2,X1)),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(sF5(X0,X1,X2),X2) = X1,
inference(forward_demodulation,[],[f19,f18]) ).
fof(f38,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(forward_demodulation,[],[f35,f6]) ).
fof(f39,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(sF0(X2),X1)),
inference(forward_demodulation,[],[f36,f21]) ).
fof(f40,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),sF4(X0,X1,X2)),X2) = X1,
inference(forward_demodulation,[],[f37,f16]) ).
fof(f41,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(forward_demodulation,[],[f39,f6]) ).
fof(f42,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,sF3(X1,X0,X2))),X2) = X1,
inference(forward_demodulation,[],[f40,f14]) ).
fof(f43,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,sF2(X0,X2)))),X2) = X1,
inference(forward_demodulation,[],[f42,f12]) ).
fof(f44,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,divide(sF1(X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f43,f10]) ).
fof(f45,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,divide(divide(sF0(X0),X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f44,f8]) ).
fof(f46,plain,
! [X2,X0,X1] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f45,f6]) ).
fof(f47,plain,
! [X0] : sF11 = divide(divide(X0,X0),b1),
inference(superposition,[],[f38,f31]) ).
fof(f48,plain,
! [X0] : sF9 = divide(divide(X0,X0),a1),
inference(superposition,[],[f38,f27]) ).
fof(f49,plain,
! [X2,X0,X1] : divide(divide(X2,X2),X1) = divide(divide(X0,X0),X1),
inference(superposition,[],[f38,f38]) ).
fof(f64,plain,
! [X0] : sF12 = divide(sF11,divide(divide(X0,X0),b1)),
inference(superposition,[],[f33,f41]) ).
fof(f65,plain,
! [X0] : sF10 = divide(sF9,divide(divide(X0,X0),a1)),
inference(superposition,[],[f29,f41]) ).
fof(f67,plain,
sF10 = divide(sF9,sF9),
inference(forward_demodulation,[],[f65,f48]) ).
fof(f68,plain,
sF12 = divide(sF11,sF11),
inference(forward_demodulation,[],[f64,f47]) ).
fof(f177,plain,
! [X2,X3,X0,X1] : divide(X3,X3) = divide(divide(divide(X1,X1),divide(X1,divide(divide(X0,X0),divide(divide(divide(X1,X1),X1),X2)))),X2),
inference(superposition,[],[f46,f49]) ).
fof(f180,plain,
! [X3,X0] : divide(X0,X0) = divide(X3,X3),
inference(forward_demodulation,[],[f177,f46]) ).
fof(f186,plain,
! [X0] : divide(X0,X0) = sF10,
inference(superposition,[],[f180,f67]) ).
fof(f226,plain,
sF10 = sF12,
inference(superposition,[],[f186,f68]) ).
fof(f254,plain,
sF10 != sF10,
inference(superposition,[],[f34,f226]) ).
fof(f255,plain,
$false,
inference(trivial_inequality_removal,[],[f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP451-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:05:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.64/1.47 % (995982)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.64/1.47 % (996014)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=1254119027:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.64/1.47 % (996019)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3304911063:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.64/1.47 % (996013)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=2048170851:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.64/1.47 % (996017)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3554578273:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.64/1.47 % (996016)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2037332036:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.64/1.47 % (996015)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4027957577:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.64/1.47 % (996018)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1135701161:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.64/1.47 % (996017)First to succeed.
% 3.64/1.47 % (996017)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-995982"
% 3.64/1.47 % (996019)Also succeeded, but the first one will report.
% 3.64/1.47 % (996016)Also succeeded, but the first one will report.
% 3.64/1.47 % (996018)Also succeeded, but the first one will report.
% 3.64/1.47 % (996017)Refutation found. Thanks to Tanya!
% 3.64/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.47 % (996017)------------------------------
% 3.64/1.47 % (996017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.47 % (996017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.47 % (996017)CaDiCaL version: 2.1.3
% 3.64/1.47 % (996017)Termination reason: Refutation
% 3.64/1.47 % (996017)Time elapsed: 0.009 s
% 3.64/1.47 % (996017)Peak memory usage: 88 MB
% 3.64/1.47 % (996017)Instructions burned: 12 (million)
% 3.64/1.47 % (996017)------------------------------
% 3.64/1.47 % (996017)------------------------------
% 3.64/1.47 % (995982)Success in time 0.436 s
% 3.64/1.47 % Vampire exiting
%------------------------------------------------------------------------------