%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP452-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 3.63s 1.52s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% 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 : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 114 ( 114 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f5,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X0] : sF0(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X0] : divide(X0,X0) = sF0(X0),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X0] : sF1(X0) = divide(sF0(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X0] : divide(sF0(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0] : sF2(X0,X2) = divide(sF1(X0),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f11,plain,
! [X2,X0] : divide(sF1(X0),X2) = sF2(X0,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X0,X1] : sF3(X1,X0,X2) = divide(X1,sF2(X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f13,plain,
! [X2,X0,X1] : divide(X1,sF2(X0,X2)) = sF3(X1,X0,X2),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = divide(X0,sF3(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : divide(X0,sF3(X1,X0,X2)) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X2,X0,X1] : sF5(X0,X1,X2) = divide(sF0(X0),sF4(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
! [X2,X0,X1] : divide(sF0(X0),sF4(X0,X1,X2)) = sF5(X0,X1,X2),
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = divide(sF5(X0,X1,X2),X2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
! [X2,X0,X1] : divide(sF5(X0,X1,X2),X2) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X2,X0,X1] : sF6(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f19,f17,f15,f13,f11,f9,f7,f7]) ).
fof(f21,definition,
! [X2,X1] : sF7(X2,X1) = divide(sF0(X2),X1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f22,plain,
! [X2,X1] : divide(sF0(X2),X1) = sF7(X2,X1),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
! [X2,X0,X1] : sF8(X0,X2,X1) = divide(X0,sF7(X2,X1)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f24,plain,
! [X2,X0,X1] : divide(X0,sF7(X2,X1)) = sF8(X0,X2,X1),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF8(X0,X2,X1),
inference(definition_folding,[],[f2,f24,f22,f7]) ).
fof(f26,plain,
! [X0,X1] : inverse(X0) = sF7(X1,X0),
inference(definition_folding,[],[f3,f22,f7]) ).
fof(f27,definition,
sF9 = inverse(b2),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f28,plain,
inverse(b2) = sF9,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF10 = multiply(sF9,b2),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f30,plain,
multiply(sF9,b2) = sF10,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF11 = multiply(sF10,a2),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f32,plain,
multiply(sF10,a2) = sF11,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
a2 != sF11,
inference(definition_folding,[],[f5,f32,f30,f28]) ).
fof(f34,plain,
! [X0,X1] : inverse(X0) = divide(sF0(X1),X0),
inference(forward_demodulation,[],[f26,f22]) ).
fof(f35,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF7(X2,X1)),
inference(forward_demodulation,[],[f25,f24]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(sF5(X0,X1,X2),X2) = X1,
inference(forward_demodulation,[],[f20,f19]) ).
fof(f37,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(forward_demodulation,[],[f34,f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(sF0(X2),X1)),
inference(forward_demodulation,[],[f35,f22]) ).
fof(f39,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),sF4(X0,X1,X2)),X2) = X1,
inference(forward_demodulation,[],[f36,f17]) ).
fof(f40,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(forward_demodulation,[],[f38,f7]) ).
fof(f41,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,sF3(X1,X0,X2))),X2) = X1,
inference(forward_demodulation,[],[f39,f15]) ).
fof(f42,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,sF2(X0,X2)))),X2) = X1,
inference(forward_demodulation,[],[f41,f13]) ).
fof(f43,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,divide(sF1(X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f42,f11]) ).
fof(f44,plain,
! [X2,X0,X1] : divide(divide(sF0(X0),divide(X0,divide(X1,divide(divide(sF0(X0),X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f43,f9]) ).
fof(f45,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,[],[f44,f7]) ).
fof(f46,plain,
! [X0] : sF9 = divide(divide(X0,X0),b2),
inference(superposition,[],[f37,f28]) ).
fof(f47,plain,
! [X2,X0,X1] : divide(divide(X2,X2),X1) = divide(divide(X0,X0),X1),
inference(superposition,[],[f37,f37]) ).
fof(f51,plain,
! [X0] : sF11 = divide(sF10,divide(divide(X0,X0),a2)),
inference(superposition,[],[f40,f32]) ).
fof(f59,plain,
! [X0] : sF10 = divide(sF9,divide(divide(X0,X0),b2)),
inference(superposition,[],[f30,f40]) ).
fof(f61,plain,
sF10 = divide(sF9,sF9),
inference(forward_demodulation,[],[f59,f46]) ).
fof(f77,plain,
sF11 = divide(sF10,divide(sF10,a2)),
inference(superposition,[],[f51,f61]) ).
fof(f147,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,[],[f45,f47]) ).
fof(f156,plain,
! [X3,X0] : divide(X0,X0) = divide(X3,X3),
inference(forward_demodulation,[],[f147,f45]) ).
fof(f162,plain,
! [X0] : divide(X0,X0) = sF10,
inference(superposition,[],[f156,f61]) ).
fof(f211,plain,
! [X0,X1] : divide(divide(divide(X0,X0),divide(X0,divide(X1,sF10))),divide(divide(X0,X0),X0)) = X1,
inference(superposition,[],[f45,f162]) ).
fof(f212,plain,
! [X0,X1] : divide(divide(sF10,divide(X0,divide(X1,sF10))),divide(sF10,X0)) = X1,
inference(forward_demodulation,[],[f211,f162]) ).
fof(f361,plain,
! [X0] : divide(divide(sF10,sF10),divide(sF10,divide(X0,sF10))) = X0,
inference(superposition,[],[f212,f162]) ).
fof(f390,plain,
! [X0] : divide(sF10,divide(sF10,divide(X0,sF10))) = X0,
inference(forward_demodulation,[],[f361,f162]) ).
fof(f421,plain,
! [X0] : divide(X0,divide(sF10,sF10)) = X0,
inference(superposition,[],[f212,f390]) ).
fof(f425,plain,
! [X0] : divide(X0,sF10) = X0,
inference(forward_demodulation,[],[f421,f162]) ).
fof(f447,plain,
! [X0] : divide(sF10,divide(sF10,X0)) = X0,
inference(superposition,[],[f390,f425]) ).
fof(f493,plain,
a2 = sF11,
inference(superposition,[],[f447,f77]) ).
fof(f515,plain,
a2 != a2,
inference(superposition,[],[f33,f493]) ).
fof(f516,plain,
$false,
inference(trivial_inequality_removal,[],[f515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP452-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 10:04:48 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.52 % (3760868)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.63/1.52 % (3760879)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1561689449:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.63/1.52 % (3760880)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2304159786:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.63/1.52 % (3760881)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2944945375:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.63/1.52 % (3760878)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=558344885:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.63/1.52 % (3760883)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3663578932:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.63/1.52 % (3760882)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2813091968:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.63/1.52 % (3760877)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=2829900800:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.63/1.52 % (3760881)First to succeed.
% 3.63/1.52 % (3760881)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3760868"
% 3.63/1.52 % (3760882)Also succeeded, but the first one will report.
% 3.63/1.52 % (3760883)Also succeeded, but the first one will report.
% 3.63/1.52 % (3760880)Instruction limit reached!
% 3.63/1.52 % (3760880)------------------------------
% 3.63/1.52 % (3760880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.52 % (3760880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.52 % (3760880)CaDiCaL version: 2.1.3
% 3.63/1.52 % (3760880)Termination reason: Instruction limit
% 3.63/1.52 % (3760880)Termination phase: Saturation
% 3.63/1.52 % (3760880)Time elapsed: 0.080 s
% 3.63/1.52 % (3760880)Peak memory usage: 89 MB
% 3.63/1.52 % (3760880)Instructions burned: 136 (million)
% 3.63/1.52 % (3760950)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2175275098:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.63/1.52 % (3760881)Refutation found. Thanks to Tanya!
% 3.63/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.52 % (3760881)------------------------------
% 3.63/1.52 % (3760881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.52 % (3760881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.52 % (3760881)CaDiCaL version: 2.1.3
% 3.63/1.52 % (3760881)Termination reason: Refutation
% 3.63/1.52 % (3760881)Time elapsed: 0.012 s
% 3.63/1.52 % (3760881)Peak memory usage: 88 MB
% 3.63/1.52 % (3760881)Instructions burned: 18 (million)
% 3.63/1.52 % (3760881)------------------------------
% 3.63/1.52 % (3760881)------------------------------
% 3.63/1.52 % (3760868)Success in time 0.407 s
% 3.63/1.52 % Vampire exiting
%------------------------------------------------------------------------------