%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP551-1 : 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 : n018.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 10:14:50 AM UTC 2026
% Result : Unsatisfiable 2.81s 1.26s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 83 unt; 12 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
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,negated_conjecture,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f7,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(definition_unfolding,[],[f6,f2,f2,f2,f2]) ).
fof(f8,definition,
! [X0] : sF0(X0) = divide(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X0] : divide(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF1(X1,X0,X2) = divide(divide(X1,X0),X2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : divide(divide(X1,X0),X2) = sF1(X1,X0,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X0,X1] : sF2(X1,X0,X2) = divide(sF1(X1,X0,X2),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
! [X2,X0,X1] : divide(sF1(X1,X0,X2),X1) = sF2(X1,X0,X2),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = divide(sF0(X0),sF2(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : divide(sF0(X0),sF2(X1,X0,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X2,X0,X1] : sF3(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f15,f13,f11,f9]) ).
fof(f17,definition,
! [X0] : sF4(X0) = divide(X0,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
! [X0] : divide(X0,X0) = sF4(X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : identity = sF4(X0),
inference(definition_folding,[],[f5,f18]) ).
fof(f20,definition,
sF5 = divide(identity,b3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f21,plain,
divide(identity,b3) = sF5,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF6 = divide(a3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
divide(a3,sF5) = sF6,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF7 = divide(identity,c3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f25,plain,
divide(identity,c3) = sF7,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF8 = divide(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f27,plain,
divide(sF6,sF7) = sF8,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF9 = divide(b3,sF7),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f29,plain,
divide(b3,sF7) = sF9,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF10 = divide(identity,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f31,plain,
divide(identity,sF9) = sF10,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF11 = divide(a3,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f33,plain,
divide(a3,sF10) = sF11,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sF8 != sF11,
inference(definition_folding,[],[f7,f33,f31,f29,f25,f27,f25,f23,f21]) ).
fof(f35,plain,
! [X0] : identity = divide(X0,X0),
inference(forward_demodulation,[],[f19,f18]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(sF0(X0),sF2(X1,X0,X2)) = X2,
inference(forward_demodulation,[],[f16,f15]) ).
fof(f37,plain,
! [X2,X0,X1] : divide(sF0(X0),divide(sF1(X1,X0,X2),X1)) = X2,
inference(forward_demodulation,[],[f36,f13]) ).
fof(f38,plain,
! [X2,X0,X1] : divide(sF0(X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[],[f37,f11]) ).
fof(f39,plain,
! [X2,X0,X1] : divide(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[],[f38,f9]) ).
fof(f40,plain,
! [X0,X1] : divide(sF10,divide(divide(divide(X0,sF9),X1),X0)) = X1,
inference(superposition,[],[f39,f31]) ).
fof(f43,plain,
! [X0,X1] : divide(identity,divide(divide(divide(X0,identity),X1),X0)) = X1,
inference(superposition,[],[f39,f35]) ).
fof(f45,plain,
! [X0] : divide(sF10,divide(divide(sF10,X0),identity)) = X0,
inference(superposition,[],[f39,f31]) ).
fof(f47,plain,
! [X0] : divide(sF5,divide(divide(sF5,X0),identity)) = X0,
inference(superposition,[],[f39,f21]) ).
fof(f49,plain,
! [X0] : divide(divide(identity,sF10),divide(divide(sF11,X0),a3)) = X0,
inference(superposition,[],[f39,f33]) ).
fof(f50,plain,
! [X0] : divide(divide(identity,sF5),divide(divide(sF6,X0),a3)) = X0,
inference(superposition,[],[f39,f23]) ).
fof(f56,plain,
sF10 = divide(sF10,divide(identity,identity)),
inference(superposition,[],[f45,f35]) ).
fof(f58,plain,
sF10 = divide(sF10,identity),
inference(forward_demodulation,[],[f56,f35]) ).
fof(f60,plain,
! [X0] : divide(divide(identity,identity),divide(divide(sF10,X0),sF10)) = X0,
inference(superposition,[],[f39,f58]) ).
fof(f61,plain,
! [X0] : divide(identity,divide(divide(sF10,X0),sF10)) = X0,
inference(forward_demodulation,[],[f60,f35]) ).
fof(f72,plain,
sF5 = divide(sF5,divide(identity,identity)),
inference(superposition,[],[f47,f35]) ).
fof(f74,plain,
sF5 = divide(sF5,identity),
inference(forward_demodulation,[],[f72,f35]) ).
fof(f83,plain,
! [X0,X1] : divide(X0,divide(divide(X0,X1),identity)) = X1,
inference(superposition,[],[f39,f61]) ).
fof(f103,plain,
! [X0] : divide(X0,divide(identity,identity)) = X0,
inference(superposition,[],[f83,f35]) ).
fof(f111,plain,
b3 = divide(identity,divide(sF5,identity)),
inference(superposition,[],[f83,f21]) ).
fof(f113,plain,
sF9 = divide(identity,divide(sF10,identity)),
inference(superposition,[],[f83,f31]) ).
fof(f117,plain,
sF7 = divide(b3,divide(sF9,identity)),
inference(superposition,[],[f83,f29]) ).
fof(f131,plain,
sF9 = divide(identity,sF10),
inference(forward_demodulation,[],[f113,f58]) ).
fof(f133,plain,
b3 = divide(identity,sF5),
inference(forward_demodulation,[],[f111,f74]) ).
fof(f134,plain,
! [X0] : divide(X0,identity) = X0,
inference(forward_demodulation,[],[f103,f35]) ).
fof(f135,plain,
! [X0] : divide(sF10,divide(divide(identity,X0),sF9)) = X0,
inference(superposition,[],[f40,f35]) ).
fof(f158,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(superposition,[],[f83,f134]) ).
fof(f181,plain,
sF7 = divide(b3,sF9),
inference(forward_demodulation,[],[f117,f134]) ).
fof(f245,plain,
sF5 = divide(sF10,divide(b3,sF9)),
inference(superposition,[],[f135,f133]) ).
fof(f262,plain,
sF5 = divide(sF10,sF7),
inference(forward_demodulation,[],[f245,f181]) ).
fof(f264,plain,
sF7 = divide(sF10,sF5),
inference(superposition,[],[f158,f262]) ).
fof(f269,plain,
sF5 = divide(identity,divide(sF7,sF10)),
inference(superposition,[],[f61,f264]) ).
fof(f361,plain,
divide(identity,sF5) = divide(sF7,sF10),
inference(superposition,[],[f158,f269]) ).
fof(f365,plain,
b3 = divide(sF7,sF10),
inference(forward_demodulation,[],[f361,f133]) ).
fof(f370,plain,
sF10 = divide(sF7,b3),
inference(superposition,[],[f158,f365]) ).
fof(f376,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[],[f43,f134]) ).
fof(f616,plain,
! [X0] : divide(sF9,divide(divide(sF11,X0),a3)) = X0,
inference(forward_demodulation,[],[f49,f131]) ).
fof(f685,plain,
sF11 = divide(sF9,divide(identity,a3)),
inference(superposition,[],[f616,f35]) ).
fof(f741,plain,
! [X0] : divide(b3,divide(divide(sF6,X0),a3)) = X0,
inference(forward_demodulation,[],[f50,f133]) ).
fof(f775,plain,
sF7 = divide(b3,divide(sF8,a3)),
inference(superposition,[],[f741,f27]) ).
fof(f789,plain,
divide(identity,divide(sF7,b3)) = divide(sF8,a3),
inference(superposition,[],[f376,f775]) ).
fof(f795,plain,
divide(identity,sF10) = divide(sF8,a3),
inference(forward_demodulation,[],[f789,f370]) ).
fof(f797,plain,
sF9 = divide(sF8,a3),
inference(forward_demodulation,[],[f795,f131]) ).
fof(f799,plain,
a3 = divide(identity,divide(sF9,sF8)),
inference(superposition,[],[f376,f797]) ).
fof(f817,plain,
divide(identity,divide(a3,identity)) = divide(sF9,sF8),
inference(superposition,[],[f83,f799]) ).
fof(f819,plain,
divide(identity,a3) = divide(sF9,sF8),
inference(forward_demodulation,[],[f817,f134]) ).
fof(f824,plain,
sF8 = divide(sF9,divide(divide(identity,a3),identity)),
inference(superposition,[],[f83,f819]) ).
fof(f826,plain,
sF8 = divide(sF9,divide(identity,a3)),
inference(forward_demodulation,[],[f824,f134]) ).
fof(f828,plain,
sF8 = sF11,
inference(forward_demodulation,[],[f826,f685]) ).
fof(f829,plain,
sF8 != sF8,
inference(superposition,[],[f34,f828]) ).
fof(f838,plain,
$false,
inference(trivial_inequality_removal,[],[f829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP551-1 : 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 : n018.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 10:09:08 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.81/1.26 % (2102318)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.81/1.26 % (2102325)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1644886024:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.81/1.26 % (2102329)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4028829069:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.81/1.26 % (2102327)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4150717373:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.81/1.26 % (2102323)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=27262021:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.81/1.26 % (2102324)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=1313667443:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.81/1.26 % (2102326)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3144347659:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.81/1.26 % (2102328)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2444377116:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.81/1.26 % (2102327)First to succeed.
% 2.81/1.26 % (2102327)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2102318"
% 2.81/1.26 % (2102328)Also succeeded, but the first one will report.
% 2.81/1.26 % (2102326)Instruction limit reached!
% 2.81/1.26 % (2102326)------------------------------
% 2.81/1.26 % (2102326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.26 % (2102326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.26 % (2102326)CaDiCaL version: 2.1.3
% 2.81/1.26 % (2102326)Termination reason: Instruction limit
% 2.81/1.26 % (2102326)Termination phase: Saturation
% 2.81/1.26 % (2102326)Time elapsed: 0.077 s
% 2.81/1.26 % (2102326)Peak memory usage: 88 MB
% 2.81/1.26 % (2102326)Instructions burned: 137 (million)
% 2.81/1.26 % (2102329)Also succeeded, but the first one will report.
% 2.81/1.26 % (2102337)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=71168110:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 2.81/1.26 % (2102327)Refutation found. Thanks to Tanya!
% 2.81/1.26 % SZS status Unsatisfiable for theBenchmark
% 2.81/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.45 % (2102327)------------------------------
% 3.52/1.45 % (2102327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.45 % (2102327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.45 % (2102327)CaDiCaL version: 2.1.3
% 3.52/1.45 % (2102327)Termination reason: Refutation
% 3.52/1.45 % (2102327)Time elapsed: 0.021 s
% 3.52/1.45 % (2102327)Peak memory usage: 88 MB
% 3.52/1.45 % (2102327)Instructions burned: 34 (million)
% 3.52/1.45 % (2102327)------------------------------
% 3.52/1.45 % (2102327)------------------------------
% 3.52/1.45 % (2102318)Success in time 0.414 s
% 3.52/1.45 % Vampire exiting
%------------------------------------------------------------------------------