%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP529-1 : 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 : n013.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 10:14:47 AM UTC 2026
% Result : Unsatisfiable 2.53s 1.29s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 48 unt; 9 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(X0,divide(X1,X2)),divide(X0,X1)) = X2,
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,
! [X2,X0,X1] : sF0(X0,X1,X2) = divide(X0,divide(X1,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : divide(X0,divide(X1,X2)) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = divide(sF0(X0,X1,X2),divide(X0,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : divide(sF0(X0,X1,X2),divide(X0,X1)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
! [X2,X0,X1] : sF1(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f8,f6]) ).
fof(f10,definition,
! [X2] : sF2(X2) = divide(X2,X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f11,plain,
! [X2] : divide(X2,X2) = sF2(X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X1] : sF3(X2,X1) = divide(sF2(X2),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f13,plain,
! [X2,X1] : divide(sF2(X2),X1) = sF3(X2,X1),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF4(X0,X2,X1) = divide(X0,sF3(X2,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : divide(X0,sF3(X2,X1)) = sF4(X0,X2,X1),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF4(X0,X2,X1),
inference(definition_folding,[],[f2,f15,f13,f11]) ).
fof(f17,plain,
! [X0,X1] : inverse(X0) = sF3(X1,X0),
inference(definition_folding,[],[f3,f13,f11]) ).
fof(f18,definition,
sF5 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f19,plain,
inverse(a1) = sF5,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF6 = multiply(sF5,a1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f21,plain,
multiply(sF5,a1) = sF6,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF7 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f23,plain,
inverse(b1) = sF7,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF8 = multiply(sF7,b1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f25,plain,
multiply(sF7,b1) = sF8,
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
sF6 != sF8,
inference(definition_folding,[],[f4,f25,f23,f21,f19]) ).
fof(f27,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF3(X2,X1)),
inference(forward_demodulation,[],[f16,f15]) ).
fof(f28,plain,
! [X2,X0,X1] : divide(sF0(X0,X1,X2),divide(X0,X1)) = X2,
inference(forward_demodulation,[],[f9,f8]) ).
fof(f29,plain,
! [X2,X0,X1] : divide(divide(X0,divide(X1,X2)),divide(X0,X1)) = X2,
inference(forward_demodulation,[],[f28,f6]) ).
fof(f31,plain,
! [X0,X1] : inverse(X0) = divide(sF2(X1),X0),
inference(superposition,[],[f13,f17]) ).
fof(f32,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(forward_demodulation,[],[f31,f11]) ).
fof(f35,plain,
! [X0] : sF5 = divide(divide(X0,X0),a1),
inference(superposition,[],[f32,f19]) ).
fof(f43,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f27,f17]) ).
fof(f44,plain,
! [X0] : multiply(X0,b1) = divide(X0,sF7),
inference(superposition,[],[f43,f23]) ).
fof(f45,plain,
! [X0] : multiply(X0,a1) = divide(X0,sF5),
inference(superposition,[],[f43,f19]) ).
fof(f55,plain,
sF8 = divide(sF7,sF7),
inference(superposition,[],[f44,f25]) ).
fof(f59,plain,
sF5 = divide(sF8,a1),
inference(superposition,[],[f35,f55]) ).
fof(f61,plain,
sF6 = divide(sF5,sF5),
inference(superposition,[],[f45,f21]) ).
fof(f70,plain,
! [X0] : a1 = divide(divide(X0,sF5),divide(X0,sF8)),
inference(superposition,[],[f29,f59]) ).
fof(f92,plain,
sF5 = divide(sF6,a1),
inference(superposition,[],[f35,f61]) ).
fof(f97,plain,
! [X0] : a1 = divide(divide(X0,sF5),divide(X0,sF6)),
inference(superposition,[],[f29,f92]) ).
fof(f233,plain,
a1 = divide(sF6,divide(sF5,sF8)),
inference(superposition,[],[f70,f61]) ).
fof(f255,plain,
sF8 = divide(a1,divide(sF6,sF5)),
inference(superposition,[],[f29,f233]) ).
fof(f535,plain,
a1 = divide(sF6,divide(sF5,sF6)),
inference(superposition,[],[f97,f61]) ).
fof(f567,plain,
sF6 = divide(a1,divide(sF6,sF5)),
inference(superposition,[],[f29,f535]) ).
fof(f571,plain,
sF6 = sF8,
inference(forward_demodulation,[],[f567,f255]) ).
fof(f573,plain,
sF6 != sF6,
inference(superposition,[],[f26,f571]) ).
fof(f594,plain,
$false,
inference(trivial_inequality_removal,[],[f573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP529-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:06:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.53/1.29 % (4177146)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.53/1.29 % (4177256)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1215402616:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.53/1.29 % (4177256)First to succeed.
% 2.53/1.29 % (4177256)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4177146"
% 2.53/1.29 % (4177254)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1898860048:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.53/1.29 % (4177253)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=537860237:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.53/1.29 % (4177252)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=2836745693:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.53/1.29 % (4177257)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1788064225:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.53/1.29 % (4177257)Also succeeded, but the first one will report.
% 2.53/1.29 % (4177255)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1702715211:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.53/1.29 % (4177258)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4027133450:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.53/1.29 % (4177258)Also succeeded, but the first one will report.
% 2.53/1.29 % (4177255)Also succeeded, but the first one will report.
% 2.53/1.29 % (4177256)Refutation found. Thanks to Tanya!
% 2.53/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.29 % (4177256)------------------------------
% 2.53/1.29 % (4177256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.29 % (4177256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.29 % (4177256)CaDiCaL version: 2.1.3
% 2.53/1.29 % (4177256)Termination reason: Refutation
% 2.53/1.29 % (4177256)Time elapsed: 0.011 s
% 2.53/1.29 % (4177256)Peak memory usage: 88 MB
% 2.53/1.29 % (4177256)Instructions burned: 27 (million)
% 2.53/1.29 % (4177256)------------------------------
% 2.53/1.29 % (4177256)------------------------------
% 2.53/1.29 % (4177146)Success in time 0.292 s
% 2.53/1.29 % Vampire exiting
%------------------------------------------------------------------------------