%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP521-1 : 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 : n002.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 10:14:46 AM UTC 2026
% Result : Unsatisfiable 2.46s 1.29s
% Output : Refutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 52 unt; 10 def)
% Number of atoms : 52 ( 51 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 : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(X0,divide(X1,divide(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(X2,X0,X1) = divide(X2,divide(X0,X1)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : divide(X2,divide(X0,X1)) = sF0(X2,X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF1(X1,X2,X0) = divide(X1,sF0(X2,X0,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : divide(X1,sF0(X2,X0,X1)) = sF1(X1,X2,X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(X0,sF1(X1,X2,X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : divide(X0,sF1(X1,X2,X0)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f10,f8,f6]) ).
fof(f12,definition,
! [X2] : sF3(X2) = divide(X2,X2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f13,plain,
! [X2] : divide(X2,X2) = sF3(X2),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X1] : sF4(X2,X1) = divide(sF3(X2),X1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X2,X1] : divide(sF3(X2),X1) = sF4(X2,X1),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X2,X0,X1] : sF5(X0,X2,X1) = divide(X0,sF4(X2,X1)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
! [X2,X0,X1] : divide(X0,sF4(X2,X1)) = sF5(X0,X2,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF5(X0,X2,X1),
inference(definition_folding,[],[f2,f17,f15,f13]) ).
fof(f19,plain,
! [X0,X1] : inverse(X0) = sF4(X1,X0),
inference(definition_folding,[],[f3,f15,f13]) ).
fof(f20,definition,
sF6 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f21,plain,
inverse(a1) = sF6,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF7 = multiply(sF6,a1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f23,plain,
multiply(sF6,a1) = sF7,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF8 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f25,plain,
inverse(b1) = sF8,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF9 = multiply(sF8,b1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f27,plain,
multiply(sF8,b1) = sF9,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF7 != sF9,
inference(definition_folding,[],[f4,f27,f25,f23,f21]) ).
fof(f29,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF4(X2,X1)),
inference(forward_demodulation,[],[f18,f17]) ).
fof(f30,plain,
! [X2,X0,X1] : divide(X0,sF1(X1,X2,X0)) = X2,
inference(forward_demodulation,[],[f11,f10]) ).
fof(f31,plain,
! [X2,X0,X1] : divide(X0,divide(X1,sF0(X2,X0,X1))) = X2,
inference(forward_demodulation,[],[f30,f8]) ).
fof(f32,plain,
! [X2,X0,X1] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
inference(forward_demodulation,[],[f31,f6]) ).
fof(f34,plain,
! [X0,X1] : inverse(X0) = divide(sF3(X1),X0),
inference(superposition,[],[f15,f19]) ).
fof(f35,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(forward_demodulation,[],[f34,f13]) ).
fof(f38,plain,
! [X0] : sF6 = divide(divide(X0,X0),a1),
inference(superposition,[],[f35,f21]) ).
fof(f46,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f29,f19]) ).
fof(f47,plain,
! [X0] : multiply(X0,b1) = divide(X0,sF8),
inference(superposition,[],[f46,f25]) ).
fof(f48,plain,
! [X0] : multiply(X0,a1) = divide(X0,sF6),
inference(superposition,[],[f46,f21]) ).
fof(f58,plain,
sF9 = divide(sF8,sF8),
inference(superposition,[],[f47,f27]) ).
fof(f62,plain,
sF6 = divide(sF9,a1),
inference(superposition,[],[f38,f58]) ).
fof(f64,plain,
sF7 = divide(sF6,sF6),
inference(superposition,[],[f48,f23]) ).
fof(f73,plain,
! [X0] : divide(sF9,divide(a1,divide(X0,sF6))) = X0,
inference(superposition,[],[f32,f62]) ).
fof(f76,plain,
! [X0] : divide(sF8,divide(sF8,divide(X0,sF9))) = X0,
inference(superposition,[],[f32,f58]) ).
fof(f127,plain,
sF6 = divide(sF9,divide(a1,sF7)),
inference(superposition,[],[f73,f64]) ).
fof(f136,plain,
sF9 = divide(a1,divide(sF7,sF6)),
inference(superposition,[],[f32,f127]) ).
fof(f138,plain,
sF7 = divide(sF9,sF9),
inference(superposition,[],[f73,f136]) ).
fof(f141,plain,
sF9 = divide(sF8,divide(sF8,sF7)),
inference(superposition,[],[f76,f138]) ).
fof(f189,plain,
sF8 = divide(sF8,divide(sF7,sF9)),
inference(superposition,[],[f32,f141]) ).
fof(f197,plain,
sF7 = divide(sF8,sF8),
inference(superposition,[],[f76,f189]) ).
fof(f203,plain,
sF7 = sF9,
inference(forward_demodulation,[],[f197,f58]) ).
fof(f204,plain,
sF7 != sF7,
inference(superposition,[],[f28,f203]) ).
fof(f214,plain,
$false,
inference(trivial_inequality_removal,[],[f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP521-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:09:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.46/1.29 % (3312446)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.46/1.29 % (3312495)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1036578236:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.46/1.29 % (3312495)First to succeed.
% 2.46/1.29 % (3312495)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3312446"
% 2.46/1.29 % (3312491)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=1567013176:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.46/1.29 % (3312492)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=1212591488:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.46/1.29 % (3312493)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1663865927:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.46/1.29 % (3312494)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2135300192:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.46/1.29 % (3312494)Also succeeded, but the first one will report.
% 2.46/1.29 % (3312496)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3396014894:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.46/1.29 % (3312497)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=704896924:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.46/1.29 % (3312497)Also succeeded, but the first one will report.
% 2.46/1.29 % (3312496)Also succeeded, but the first one will report.
% 2.46/1.29 % (3312495)Refutation found. Thanks to Tanya!
% 2.46/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.46/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 2.46/1.29 % (3312495)------------------------------
% 2.46/1.29 % (3312495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.46/1.29 % (3312495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/1.29 % (3312495)CaDiCaL version: 2.1.3
% 2.46/1.29 % (3312495)Termination reason: Refutation
% 2.46/1.29 % (3312495)Time elapsed: 0.004 s
% 2.46/1.29 % (3312495)Peak memory usage: 88 MB
% 2.46/1.29 % (3312495)Instructions burned: 10 (million)
% 2.46/1.29 % (3312495)------------------------------
% 2.46/1.29 % (3312495)------------------------------
% 2.46/1.29 % (3312446)Success in time 0.271 s
% 2.46/1.29 % Vampire exiting
%------------------------------------------------------------------------------