%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP539-1 : 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 : 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 10:14:49 AM UTC 2026
% Result : Unsatisfiable 4.90s 1.82s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 66 unt; 9 def)
% Number of atoms : 66 ( 65 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 : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
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(f4,negated_conjecture,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,definition,
! [X2,X0,X1] : sF0(X0,X2,X1) = divide(divide(X0,X2),X1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X2,X0,X1] : divide(divide(X0,X2),X1) = sF0(X0,X2,X1),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = divide(divide(X0,X1),sF0(X0,X2,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : divide(divide(X0,X1),sF0(X0,X2,X1)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X2,X0,X1] : sF1(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f9,f7]) ).
fof(f11,definition,
! [X2] : sF2(X2) = divide(X2,X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
! [X2] : divide(X2,X2) = sF2(X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X1] : sF3(X2,X1) = divide(sF2(X2),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f14,plain,
! [X2,X1] : divide(sF2(X2),X1) = sF3(X2,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF4(X0,X2,X1) = divide(X0,sF3(X2,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : divide(X0,sF3(X2,X1)) = sF4(X0,X2,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,plain,
! [X2,X0,X1] : multiply(X0,X1) = sF4(X0,X2,X1),
inference(definition_folding,[],[f2,f16,f14,f12]) ).
fof(f19,plain,
! [X0] : identity = sF2(X0),
inference(definition_folding,[],[f4,f12]) ).
fof(f20,definition,
sF5 = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f21,plain,
multiply(a3,b3) = sF5,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF6 = multiply(sF5,c3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
multiply(sF5,c3) = sF6,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF7 = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f25,plain,
multiply(b3,c3) = sF7,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF8 = multiply(a3,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f27,plain,
multiply(a3,sF7) = sF8,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF6 != sF8,
inference(definition_folding,[],[f5,f27,f25,f23,f21]) ).
fof(f29,plain,
! [X0] : identity = divide(X0,X0),
inference(forward_demodulation,[],[f19,f12]) ).
fof(f31,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,sF3(X2,X1)),
inference(forward_demodulation,[],[f17,f16]) ).
fof(f32,plain,
! [X2,X0,X1] : divide(divide(X0,X1),sF0(X0,X2,X1)) = X2,
inference(forward_demodulation,[],[f10,f9]) ).
fof(f34,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(sF2(X2),X1)),
inference(forward_demodulation,[],[f31,f14]) ).
fof(f35,plain,
! [X2,X0,X1] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
inference(forward_demodulation,[],[f32,f7]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(forward_demodulation,[],[f34,f12]) ).
fof(f38,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(superposition,[],[f35,f29]) ).
fof(f40,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,X1)) = X0,
inference(superposition,[],[f35,f29]) ).
fof(f44,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(superposition,[],[f38,f29]) ).
fof(f49,plain,
! [X0,X1] : divide(identity,X0) = divide(divide(X1,X0),X1),
inference(superposition,[],[f44,f38]) ).
fof(f61,plain,
! [X0] : divide(divide(X0,identity),identity) = X0,
inference(superposition,[],[f40,f29]) ).
fof(f68,plain,
! [X0] : identity = divide(divide(X0,identity),X0),
inference(superposition,[],[f35,f61]) ).
fof(f83,plain,
! [X0,X1] : divide(divide(divide(X0,identity),X1),divide(identity,X1)) = X0,
inference(superposition,[],[f35,f68]) ).
fof(f85,plain,
! [X0] : divide(X0,identity) = X0,
inference(forward_demodulation,[],[f83,f40]) ).
fof(f97,plain,
! [X0,X1] : divide(divide(X0,identity),divide(X0,X1)) = X1,
inference(superposition,[],[f35,f85]) ).
fof(f103,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f97,f85]) ).
fof(f121,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(forward_demodulation,[],[f36,f29]) ).
fof(f122,plain,
sF8 = divide(a3,divide(identity,sF7)),
inference(superposition,[],[f121,f27]) ).
fof(f123,plain,
sF5 = divide(a3,divide(identity,b3)),
inference(superposition,[],[f121,f21]) ).
fof(f124,plain,
sF7 = divide(b3,divide(identity,c3)),
inference(superposition,[],[f121,f25]) ).
fof(f125,plain,
sF6 = divide(sF5,divide(identity,c3)),
inference(superposition,[],[f121,f23]) ).
fof(f147,plain,
a3 = divide(sF5,divide(identity,divide(identity,b3))),
inference(superposition,[],[f40,f123]) ).
fof(f151,plain,
a3 = divide(sF5,b3),
inference(forward_demodulation,[],[f147,f103]) ).
fof(f156,plain,
! [X0] : divide(a3,divide(divide(sF5,X0),b3)) = X0,
inference(superposition,[],[f35,f151]) ).
fof(f163,plain,
b3 = divide(sF7,divide(identity,divide(identity,c3))),
inference(superposition,[],[f40,f124]) ).
fof(f167,plain,
b3 = divide(sF7,c3),
inference(forward_demodulation,[],[f163,f103]) ).
fof(f170,plain,
c3 = divide(identity,divide(b3,sF7)),
inference(superposition,[],[f38,f167]) ).
fof(f179,plain,
sF5 = divide(sF6,divide(identity,divide(identity,c3))),
inference(superposition,[],[f40,f125]) ).
fof(f183,plain,
sF5 = divide(sF6,c3),
inference(forward_demodulation,[],[f179,f103]) ).
fof(f186,plain,
c3 = divide(identity,divide(sF5,sF6)),
inference(superposition,[],[f38,f183]) ).
fof(f211,plain,
divide(b3,sF7) = divide(identity,divide(c3,identity)),
inference(superposition,[],[f38,f170]) ).
fof(f214,plain,
divide(identity,c3) = divide(b3,sF7),
inference(forward_demodulation,[],[f211,f85]) ).
fof(f218,plain,
divide(sF5,sF6) = divide(identity,divide(c3,identity)),
inference(superposition,[],[f38,f186]) ).
fof(f221,plain,
divide(identity,c3) = divide(sF5,sF6),
inference(forward_demodulation,[],[f218,f85]) ).
fof(f247,plain,
divide(b3,sF7) = divide(sF5,sF6),
inference(forward_demodulation,[],[f221,f214]) ).
fof(f1164,plain,
sF6 = divide(a3,divide(divide(b3,sF7),b3)),
inference(superposition,[],[f156,f247]) ).
fof(f1188,plain,
sF6 = divide(a3,divide(identity,sF7)),
inference(forward_demodulation,[],[f1164,f49]) ).
fof(f1191,plain,
sF6 = sF8,
inference(forward_demodulation,[],[f1188,f122]) ).
fof(f1192,plain,
sF6 != sF6,
inference(superposition,[],[f28,f1191]) ).
fof(f1200,plain,
$false,
inference(trivial_inequality_removal,[],[f1192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP539-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:08:38 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 4.90/1.82 % (2101329)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.90/1.82 % (2101340)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=796444541:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.90/1.82 % (2101338)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3578756255:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.90/1.82 % (2101338)First to succeed.
% 4.90/1.82 % (2101338)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2101329"
% 4.90/1.82 % (2101337)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=229948098:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.90/1.82 % (2101334)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=1981719134:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.90/1.82 % (2101336)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3871277109:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.90/1.82 % (2101335)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=1401912993:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.90/1.82 % (2101340)Also succeeded, but the first one will report.
% 4.90/1.82 % (2101339)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=671483171:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.90/1.82 % (2101339)Also succeeded, but the first one will report.
% 4.90/1.82 % (2101337)Instruction limit reached!
% 4.90/1.82 % (2101337)------------------------------
% 4.90/1.82 % (2101337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/1.82 % (2101337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/1.82 % (2101337)CaDiCaL version: 2.1.3
% 4.90/1.82 % (2101337)Termination reason: Instruction limit
% 4.90/1.82 % (2101337)Termination phase: Saturation
% 4.90/1.82 % (2101337)Time elapsed: 0.119 s
% 4.90/1.82 % (2101337)Peak memory usage: 88 MB
% 4.90/1.82 % (2101337)Instructions burned: 136 (million)
% 4.90/1.82 % (2101338)Refutation found. Thanks to Tanya!
% 4.90/1.82 % SZS status Unsatisfiable for theBenchmark
% 4.90/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 4.90/1.82 % (2101338)------------------------------
% 4.90/1.82 % (2101338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/1.82 % (2101338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/1.82 % (2101338)CaDiCaL version: 2.1.3
% 4.90/1.82 % (2101338)Termination reason: Refutation
% 4.90/1.82 % (2101338)Time elapsed: 0.032 s
% 4.90/1.82 % (2101338)Peak memory usage: 89 MB
% 4.90/1.82 % (2101338)Instructions burned: 47 (million)
% 4.90/1.82 % (2101338)------------------------------
% 4.90/1.82 % (2101338)------------------------------
% 4.90/1.82 % (2101329)Success in time 0.574 s
% 4.90/1.82 % Vampire exiting
%------------------------------------------------------------------------------