%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP467-1 : 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 : n001.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 3.80s 1.53s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 45 unt; 9 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X3,X0,X1] : divide(divide(X0,X0),divide(X1,divide(divide(X2,divide(X3,X1)),inverse(X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2)),
inference(definition_unfolding,[],[f4,f2,f2]) ).
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,
! [X2,X3,X1] : sF1(X2,X3,X1) = divide(X2,divide(X3,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X2,X3,X1] : divide(X2,divide(X3,X1)) = sF1(X2,X3,X1),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X3,X1] : sF2(X2,X3,X1) = divide(sF1(X2,X3,X1),inverse(X3)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f11,plain,
! [X2,X3,X1] : divide(sF1(X2,X3,X1),inverse(X3)) = sF2(X2,X3,X1),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X3,X1] : sF3(X1,X2,X3) = divide(X1,sF2(X2,X3,X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f13,plain,
! [X2,X3,X1] : divide(X1,sF2(X2,X3,X1)) = sF3(X1,X2,X3),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X3,X0,X1] : sF4(X0,X1,X2,X3) = divide(sF0(X0),sF3(X1,X2,X3)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : divide(sF0(X0),sF3(X1,X2,X3)) = sF4(X0,X1,X2,X3),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : sF4(X0,X1,X2,X3) = X2,
inference(definition_folding,[],[f1,f15,f13,f11,f9,f7]) ).
fof(f17,definition,
sF5 = inverse(b2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f18,plain,
inverse(b2) = sF5,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF6 = divide(sF5,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f20,plain,
divide(sF5,sF5) = sF6,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF7 = inverse(a2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f22,plain,
inverse(a2) = sF7,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF8 = divide(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f24,plain,
divide(sF6,sF7) = sF8,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
a2 != sF8,
inference(definition_folding,[],[f5,f24,f22,f20,f18,f18]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : divide(sF0(X0),sF3(X1,X2,X3)) = X2,
inference(forward_demodulation,[],[f16,f15]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : divide(sF0(X0),divide(X1,sF2(X2,X3,X1))) = X2,
inference(forward_demodulation,[],[f26,f13]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : divide(sF0(X0),divide(X1,divide(sF1(X2,X3,X1),inverse(X3)))) = X2,
inference(forward_demodulation,[],[f27,f11]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : divide(sF0(X0),divide(X1,divide(divide(X2,divide(X3,X1)),inverse(X3)))) = X2,
inference(forward_demodulation,[],[f28,f9]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : divide(divide(X0,X0),divide(X1,divide(divide(X2,divide(X3,X1)),inverse(X3)))) = X2,
inference(forward_demodulation,[],[f29,f7]) ).
fof(f31,plain,
! [X2,X0,X1] : divide(sF6,divide(X0,divide(divide(X1,divide(X2,X0)),inverse(X2)))) = X1,
inference(superposition,[],[f30,f20]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] : divide(X4,X4) = divide(divide(X1,X1),divide(divide(divide(X0,divide(X2,X3)),inverse(X2)),divide(X0,inverse(X3)))),
inference(superposition,[],[f30,f30]) ).
fof(f38,plain,
! [X0] : divide(sF6,divide(sF7,divide(divide(X0,sF8),inverse(sF6)))) = X0,
inference(superposition,[],[f31,f24]) ).
fof(f44,plain,
! [X0,X1] : divide(sF6,divide(X0,divide(divide(X1,divide(a2,X0)),sF7))) = X1,
inference(superposition,[],[f31,f22]) ).
fof(f174,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(superposition,[],[f35,f35]) ).
fof(f197,plain,
! [X0] : divide(X0,X0) = sF6,
inference(superposition,[],[f174,f20]) ).
fof(f297,plain,
! [X0] : divide(a2,X0) = divide(sF6,divide(X0,divide(sF6,sF7))),
inference(superposition,[],[f44,f197]) ).
fof(f310,plain,
sF8 = divide(sF6,divide(sF7,divide(sF6,inverse(sF6)))),
inference(superposition,[],[f38,f197]) ).
fof(f327,plain,
! [X0] : divide(a2,X0) = divide(sF6,divide(X0,sF8)),
inference(forward_demodulation,[],[f297,f24]) ).
fof(f344,plain,
divide(sF6,sF6) = divide(a2,sF8),
inference(superposition,[],[f327,f197]) ).
fof(f370,plain,
sF6 = divide(a2,sF8),
inference(forward_demodulation,[],[f344,f197]) ).
fof(f389,plain,
a2 = divide(sF6,divide(sF7,divide(sF6,inverse(sF6)))),
inference(superposition,[],[f38,f370]) ).
fof(f429,plain,
a2 = sF8,
inference(forward_demodulation,[],[f389,f310]) ).
fof(f430,plain,
a2 != a2,
inference(superposition,[],[f25,f429]) ).
fof(f437,plain,
$false,
inference(trivial_inequality_removal,[],[f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP467-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:11:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.80/1.53 % (3325844)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.80/1.53 % (3325897)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=585438320:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.80/1.53 % (3325901)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2815550306:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.80/1.53 % (3325899)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1491458018:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.80/1.53 % (3325902)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=276877451:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.80/1.53 % (3325900)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1062086976:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.80/1.53 % (3325896)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=2394998162:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.80/1.53 % (3325898)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1383949176:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.80/1.53 % (3325900)First to succeed.
% 3.80/1.53 % (3325900)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3325844"
% 3.80/1.53 % (3325899)Also succeeded, but the first one will report.
% 3.80/1.53 % (3325901)Also succeeded, but the first one will report.
% 3.80/1.53 % (3325900)Refutation found. Thanks to Tanya!
% 3.80/1.53 % SZS status Unsatisfiable for theBenchmark
% 3.80/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.53 % (3325900)------------------------------
% 3.80/1.53 % (3325900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.53 % (3325900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.53 % (3325900)CaDiCaL version: 2.1.3
% 3.80/1.53 % (3325900)Termination reason: Refutation
% 3.80/1.53 % (3325900)Time elapsed: 0.016 s
% 3.80/1.53 % (3325900)Peak memory usage: 88 MB
% 3.80/1.53 % (3325900)Instructions burned: 25 (million)
% 3.80/1.53 % (3325900)------------------------------
% 3.80/1.53 % (3325900)------------------------------
% 3.80/1.53 % (3325844)Success in time 0.454 s
% 3.80/1.53 % Vampire exiting
%------------------------------------------------------------------------------