%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP464-1 : 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 10:14:04 AM UTC 2026
% Result : Unsatisfiable 2.65s 1.33s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 46 unt; 9 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(identity,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(f5,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,plain,
! [X0] : divide(X0,X0) = identity,
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f8,plain,
a2 != multiply(identity,a2),
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
a2 != divide(identity,divide(identity,a2)),
inference(definition_unfolding,[],[f8,f2]) ).
fof(f10,definition,
! [X0] : sF0(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f11,plain,
! [X0] : divide(X0,X0) = sF0(X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X0,X1] : sF1(X0,X1) = divide(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f13,plain,
! [X0,X1] : divide(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(sF1(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : divide(sF1(X0,X1),X2) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X0] : sF3(X0) = divide(identity,X0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f17,plain,
! [X0] : divide(identity,X0) = sF3(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
! [X2,X0] : sF4(X0,X2) = divide(sF3(X0),X2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f19,plain,
! [X2,X0] : divide(sF3(X0),X2) = sF4(X0,X2),
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
! [X2,X0,X1] : sF5(X0,X1,X2) = divide(sF2(X0,X1,X2),sF4(X0,X2)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f21,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),sF4(X0,X2)) = sF5(X0,X1,X2),
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = divide(X0,sF5(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
! [X2,X0,X1] : divide(X0,sF5(X0,X1,X2)) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] : sF6(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f23,f21,f19,f17,f15,f13,f11]) ).
fof(f25,plain,
! [X0] : identity = sF0(X0),
inference(definition_folding,[],[f6,f11]) ).
fof(f26,definition,
sF7 = divide(identity,a2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f27,plain,
divide(identity,a2) = sF7,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF8 = divide(identity,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f29,plain,
divide(identity,sF7) = sF8,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
a2 != sF8,
inference(definition_folding,[],[f9,f29,f27]) ).
fof(f31,plain,
! [X0] : divide(X0,X0) = identity,
inference(forward_demodulation,[],[f25,f11]) ).
fof(f32,plain,
! [X2,X0,X1] : divide(X0,sF5(X0,X1,X2)) = X1,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f33,plain,
! [X2,X0,X1] : divide(X0,divide(sF2(X0,X1,X2),sF4(X0,X2))) = X1,
inference(forward_demodulation,[],[f32,f21]) ).
fof(f34,plain,
! [X2,X0,X1] : divide(X0,divide(sF2(X0,X1,X2),divide(sF3(X0),X2))) = X1,
inference(forward_demodulation,[],[f33,f19]) ).
fof(f35,plain,
! [X2,X0,X1] : divide(X0,divide(sF2(X0,X1,X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f34,f17]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(X0,divide(divide(sF1(X0,X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f35,f15]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(sF0(X0),X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f36,f13]) ).
fof(f38,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f37,f11]) ).
fof(f39,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f38,f31]) ).
fof(f52,plain,
! [X0] : divide(X0,identity) = X0,
inference(superposition,[],[f39,f31]) ).
fof(f58,plain,
! [X0,X1] : divide(X1,divide(divide(identity,X0),divide(divide(identity,X1),identity))) = X0,
inference(superposition,[],[f39,f52]) ).
fof(f59,plain,
! [X0,X1] : divide(X1,divide(divide(identity,X0),divide(identity,X1))) = X0,
inference(forward_demodulation,[],[f58,f52]) ).
fof(f72,plain,
! [X0] : divide(identity,divide(divide(identity,X0),identity)) = X0,
inference(superposition,[],[f59,f52]) ).
fof(f80,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(forward_demodulation,[],[f72,f52]) ).
fof(f91,plain,
a2 = divide(identity,sF7),
inference(superposition,[],[f80,f27]) ).
fof(f102,plain,
a2 = sF8,
inference(forward_demodulation,[],[f91,f29]) ).
fof(f103,plain,
a2 != a2,
inference(superposition,[],[f30,f102]) ).
fof(f104,plain,
$false,
inference(trivial_inequality_removal,[],[f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP464-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:04:52 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.65/1.33 % (4173302)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.65/1.33 % (4173311)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1607417757:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.65/1.33 % (4173311)First to succeed.
% 2.65/1.33 % (4173311)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4173302"
% 2.65/1.33 % (4173310)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1084564270:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.65/1.33 % (4173309)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2743824746:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.65/1.33 % (4173307)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=3345286106:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.65/1.33 % (4173310)Also succeeded, but the first one will report.
% 2.65/1.33 % (4173308)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=1567269019:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.65/1.33 % (4173312)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2400421349:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.65/1.33 % (4173313)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1998774957:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.65/1.33 % (4173313)Also succeeded, but the first one will report.
% 2.65/1.33 % (4173312)Also succeeded, but the first one will report.
% 2.65/1.33 % (4173311)Refutation found. Thanks to Tanya!
% 2.65/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.33 % (4173311)------------------------------
% 2.65/1.33 % (4173311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.33 % (4173311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.33 % (4173311)CaDiCaL version: 2.1.3
% 2.65/1.33 % (4173311)Termination reason: Refutation
% 2.65/1.33 % (4173311)Time elapsed: 0.002 s
% 2.65/1.33 % (4173311)Peak memory usage: 88 MB
% 2.65/1.33 % (4173311)Instructions burned: 5 (million)
% 2.65/1.33 % (4173311)------------------------------
% 2.65/1.33 % (4173311)------------------------------
% 2.65/1.33 % (4173302)Success in time 0.286 s
% 2.65/1.33 % Vampire exiting
%------------------------------------------------------------------------------