%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO069-1 : 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 : n016.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 09:36:00 AM UTC 2026
% Result : Unsatisfiable 2.97s 1.19s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 54 unt; 7 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-7 aty)
% Number of variables : 164 ( 164 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(a,b,inverse(b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_tba_axioms_3) ).
fof(f3,plain,
a != multiply(a,b,inverse(b)),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
! [X0,X1] : sF0(X0,X1) = multiply(X0,inverse(X0),X1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = sF0(X0,X1),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X2,X3,X6,X4,X5] : sF1(X2,X3,X4,X5,X6) = multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
! [X2,X3,X6,X4,X5] : multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6)) = sF1(X2,X3,X4,X5,X6),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X3,X6,X4,X5] : sF2(X2,X3,X4,X5,X6) = inverse(sF1(X2,X3,X4,X5,X6)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
! [X2,X3,X6,X4,X5] : inverse(sF1(X2,X3,X4,X5,X6)) = sF2(X2,X3,X4,X5,X6),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X3,X6,X4,X5] : sF3(X3,X6,X5,X4,X2) = multiply(X3,multiply(X6,X5,X4),X2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f11,plain,
! [X2,X3,X6,X4,X5] : multiply(X3,multiply(X6,X5,X4),X2) = sF3(X3,X6,X5,X4,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X3,X0,X1,X6,X4,X5] : sF4(X0,X1,X2,X3,X4,X5,X6) = multiply(sF0(X0,X1),sF2(X2,X3,X4,X5,X6),sF3(X3,X6,X5,X4,X2)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f13,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(sF0(X0,X1),sF2(X2,X3,X4,X5,X6),sF3(X3,X6,X5,X4,X2)) = sF4(X0,X1,X2,X3,X4,X5,X6),
inference(reorient_equations,[],[f12]) ).
fof(f14,plain,
! [X2,X3,X0,X1,X6,X4,X5] : sF4(X0,X1,X2,X3,X4,X5,X6) = X1,
inference(definition_folding,[],[f1,f13,f11,f9,f7,f5]) ).
fof(f15,definition,
sF5 = inverse(b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
inverse(b) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = multiply(a,b,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
multiply(a,b,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
a != sF6,
inference(definition_folding,[],[f3,f18,f16]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(sF0(X0,X1),sF2(X2,X3,X4,X5,X6),sF3(X3,X6,X5,X4,X2)) = X1,
inference(forward_demodulation,[],[f14,f13]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(sF0(X0,X1),sF2(X2,X3,X4,X5,X6),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(forward_demodulation,[],[f20,f11]) ).
fof(f22,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(sF0(X0,X1),inverse(sF1(X2,X3,X4,X5,X6)),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(forward_demodulation,[],[f21,f9]) ).
fof(f23,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(sF0(X0,X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(forward_demodulation,[],[f22,f7]) ).
fof(f24,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(forward_demodulation,[],[f23,f5]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(b,sF5,X0),inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1)) = X0,
inference(superposition,[],[f24,f16]) ).
fof(f26,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0) = multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X4,X5,X6),X7,multiply(X4,X5,X8))),multiply(X5,multiply(X8,X7,X6),X4)),
inference(superposition,[],[f24,f24]) ).
fof(f32,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,multiply(X5,multiply(X6,X7,X8),X9)),inverse(multiply(multiply(X9,X5,X8),X7,multiply(X9,X5,X6))),multiply(X3,X4,multiply(X10,inverse(X10),X0)))),multiply(X4,X0,X3)) = X2,
inference(superposition,[],[f24,f24]) ).
fof(f253,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1) = X0,
inference(superposition,[],[f26,f24]) ).
fof(f255,plain,
! [X0,X1] : multiply(sF5,multiply(X0,inverse(multiply(b,sF5,X1)),X1),b) = X0,
inference(superposition,[],[f26,f25]) ).
fof(f310,plain,
! [X2,X0,X1] : multiply(multiply(b,sF5,X1),inverse(multiply(multiply(b,sF5,X2),inverse(multiply(b,sF5,X2)),multiply(b,sF5,X0))),X0) = X1,
inference(superposition,[],[f25,f255]) ).
fof(f783,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X3,inverse(X3),X4),inverse(multiply(sF5,multiply(multiply(b,sF5,multiply(X0,inverse(X0),X1)),inverse(multiply(b,sF5,X2)),X2),b)),multiply(sF5,X1,b)) = X4,
inference(superposition,[],[f32,f310]) ).
fof(f829,plain,
! [X3,X0,X1,X4] : multiply(multiply(X3,inverse(X3),X4),inverse(multiply(b,sF5,multiply(X0,inverse(X0),X1))),multiply(sF5,X1,b)) = X4,
inference(forward_demodulation,[],[f783,f255]) ).
fof(f842,plain,
! [X2,X0,X1] : multiply(multiply(b,sF5,X0),inverse(multiply(b,sF5,multiply(X1,inverse(X1),X2))),multiply(sF5,X2,b)) = X0,
inference(superposition,[],[f829,f16]) ).
fof(f911,plain,
! [X2,X3,X0,X1] : multiply(sF5,X1,b) = multiply(multiply(X0,inverse(X0),X1),inverse(multiply(b,sF5,multiply(X2,inverse(X2),X3))),multiply(sF5,X3,b)),
inference(superposition,[],[f829,f842]) ).
fof(f931,plain,
! [X1] : multiply(sF5,X1,b) = X1,
inference(forward_demodulation,[],[f911,f829]) ).
fof(f944,plain,
! [X0,X1] : multiply(X0,inverse(multiply(b,sF5,X1)),X1) = X0,
inference(superposition,[],[f931,f255]) ).
fof(f978,plain,
! [X0] : multiply(inverse(sF5),multiply(X0,inverse(inverse(sF5)),b),sF5) = X0,
inference(superposition,[],[f253,f931]) ).
fof(f983,plain,
sF5 = multiply(sF5,inverse(multiply(b,sF5,b)),b),
inference(superposition,[],[f255,f931]) ).
fof(f1001,plain,
sF5 = inverse(multiply(b,sF5,b)),
inference(forward_demodulation,[],[f983,f931]) ).
fof(f1010,plain,
! [X0] : multiply(sF5,multiply(X0,sF5,b),b) = X0,
inference(superposition,[],[f255,f1001]) ).
fof(f1031,plain,
! [X0] : multiply(X0,sF5,b) = X0,
inference(forward_demodulation,[],[f1010,f931]) ).
fof(f1397,plain,
sF5 = multiply(inverse(sF5),inverse(inverse(sF5)),sF5),
inference(superposition,[],[f978,f931]) ).
fof(f1445,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(b,sF5,sF5)),multiply(sF5,sF5,b)) = X1,
inference(superposition,[],[f829,f1397]) ).
fof(f1479,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(b,sF5,sF5)),sF5) = X1,
inference(forward_demodulation,[],[f1445,f931]) ).
fof(f1481,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(forward_demodulation,[],[f1479,f944]) ).
fof(f1603,plain,
b = inverse(sF5),
inference(superposition,[],[f1481,f931]) ).
fof(f1802,plain,
! [X0] : multiply(b,multiply(X0,inverse(b),b),sF5) = X0,
inference(superposition,[],[f978,f1603]) ).
fof(f1827,plain,
! [X0] : multiply(b,multiply(X0,sF5,b),sF5) = X0,
inference(forward_demodulation,[],[f1802,f16]) ).
fof(f1832,plain,
! [X0] : multiply(b,X0,sF5) = X0,
inference(forward_demodulation,[],[f1827,f1031]) ).
fof(f1976,plain,
! [X0] : multiply(X0,inverse(sF5),sF5) = X0,
inference(superposition,[],[f944,f1832]) ).
fof(f2081,plain,
! [X0] : multiply(X0,b,sF5) = X0,
inference(forward_demodulation,[],[f1976,f1603]) ).
fof(f2158,plain,
a = sF6,
inference(superposition,[],[f2081,f18]) ).
fof(f2239,plain,
a != a,
inference(superposition,[],[f19,f2158]) ).
fof(f2254,plain,
$false,
inference(trivial_inequality_removal,[],[f2239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO069-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:12:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.23 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
% 2.97/1.19 % (4016350)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.97/1.19 % (4016359)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=978442095:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.97/1.19 % (4016361)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1488662732:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.97/1.19 % (4016355)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=1631166324:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.97/1.19 % (4016357)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4012816031:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.97/1.19 % (4016356)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=3910471545:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.97/1.19 % (4016358)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2680828263:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.97/1.19 % (4016360)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3794944126:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.97/1.19 % (4016359)First to succeed.
% 2.97/1.19 % (4016359)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4016350"
% 2.97/1.19 % (4016361)Also succeeded, but the first one will report.
% 2.97/1.19 % (4016358)Instruction limit reached!
% 2.97/1.19 % (4016358)------------------------------
% 2.97/1.19 % (4016358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.19 % (4016358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.19 % (4016358)CaDiCaL version: 2.1.3
% 2.97/1.19 % (4016358)Termination reason: Instruction limit
% 2.97/1.19 % (4016358)Termination phase: Saturation
% 2.97/1.19 % (4016358)Time elapsed: 0.084 s
% 2.97/1.19 % (4016358)Peak memory usage: 89 MB
% 2.97/1.19 % (4016358)Instructions burned: 137 (million)
% 2.97/1.19 % (4016360)Also succeeded, but the first one will report.
% 2.97/1.19 % (4016359)Refutation found. Thanks to Tanya!
% 2.97/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.97/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.97/1.19 % (4016359)------------------------------
% 2.97/1.19 % (4016359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.19 % (4016359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.19 % (4016359)CaDiCaL version: 2.1.3
% 2.97/1.19 % (4016359)Termination reason: Refutation
% 2.97/1.19 % (4016359)Time elapsed: 0.054 s
% 2.97/1.19 % (4016359)Peak memory usage: 89 MB
% 2.97/1.19 % (4016359)Instructions burned: 179 (million)
% 2.97/1.19 % (4016359)------------------------------
% 2.97/1.19 % (4016359)------------------------------
% 2.97/1.19 % (4016350)Success in time 0.332 s
% 2.97/1.19 % Vampire exiting
%------------------------------------------------------------------------------