%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:16:04 AM UTC 2026
% Result : Unsatisfiable 8.50s 2.39s
% Output : Refutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f5,axiom,
! [X0] : mult(i(X0),X0) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f6,plain,
! [X0] : unit = mult(i(X0),X0),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : i(mult(X0,X1)) = mult(i(X0),i(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
fof(f8,axiom,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
fof(f9,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f12,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,X2)),asoc(X0,X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
fof(f13,axiom,
! [X0,X1] : mult(X0,X1) = mult(mult(X1,X0),op_k(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
fof(f23,axiom,
! [X2,X3,X0,X1,X4] : asoc(asoc(X0,X1,X2),X3,X4) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21) ).
fof(f24,plain,
! [X2,X3,X0,X1,X4] : unit = asoc(asoc(X0,X1,X2),X3,X4),
inference(reorient_equations,[],[f23]) ).
fof(f25,axiom,
! [X2,X3,X0,X1,X4] : asoc(X0,X1,asoc(X2,X3,X4)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c22) ).
fof(f26,plain,
! [X2,X3,X0,X1,X4] : unit = asoc(X0,X1,asoc(X2,X3,X4)),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,plain,
unit != op_k(asoc(a,b,c),d),
inference(reorient_equations,[],[f27]) ).
fof(f58,plain,
! [X0,X1] : mult(X1,X0) = mult(i(i(X1)),X0),
inference(superposition,[],[f8,f8]) ).
fof(f72,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = mult(unit,asoc(i(mult(X0,X1)),X0,X1)),
inference(superposition,[],[f12,f6]) ).
fof(f74,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = asoc(i(mult(X0,X1)),X0,X1),
inference(forward_demodulation,[],[f72,f1]) ).
fof(f124,plain,
! [X0,X1] : op_k(X0,X1) = mult(i(mult(X1,X0)),mult(X0,X1)),
inference(superposition,[],[f8,f13]) ).
fof(f143,plain,
! [X0,X1] : op_k(i(X1),i(X0)) = mult(i(i(mult(X0,X1))),mult(i(X1),i(X0))),
inference(superposition,[],[f124,f7]) ).
fof(f153,plain,
! [X0,X1] : op_k(i(X0),i(X1)) = mult(i(mult(i(X1),i(X0))),i(mult(X0,X1))),
inference(superposition,[],[f124,f7]) ).
fof(f163,plain,
! [X0,X1] : op_k(i(X0),i(X1)) = i(mult(mult(i(X1),i(X0)),mult(X0,X1))),
inference(forward_demodulation,[],[f153,f7]) ).
fof(f168,plain,
! [X0,X1] : op_k(i(X1),i(X0)) = mult(mult(X0,X1),mult(i(X1),i(X0))),
inference(forward_demodulation,[],[f143,f58]) ).
fof(f173,plain,
! [X0,X1] : i(mult(i(mult(X1,X0)),mult(X0,X1))) = op_k(i(X0),i(X1)),
inference(forward_demodulation,[],[f163,f7]) ).
fof(f178,plain,
! [X0,X1] : op_k(i(X1),i(X0)) = mult(mult(X0,X1),i(mult(X1,X0))),
inference(forward_demodulation,[],[f168,f7]) ).
fof(f182,plain,
! [X0,X1] : i(op_k(X0,X1)) = op_k(i(X0),i(X1)),
inference(forward_demodulation,[],[f173,f124]) ).
fof(f298,plain,
! [X0,X1] : mult(mult(i(X0),i(X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(superposition,[],[f74,f8]) ).
fof(f320,plain,
! [X0,X1] : mult(i(mult(X0,X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f298,f7]) ).
fof(f334,plain,
! [X0,X1] : op_k(X1,X0) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f320,f124]) ).
fof(f361,plain,
! [X0,X1] : op_k(i(mult(X1,X0)),mult(X0,X1)) = asoc(i(mult(X0,X1)),i(i(mult(X1,X0))),op_k(X0,X1)),
inference(superposition,[],[f334,f124]) ).
fof(f364,plain,
! [X2,X3,X0,X1] : unit = asoc(X2,X3,op_k(X0,X1)),
inference(superposition,[],[f26,f334]) ).
fof(f366,plain,
! [X0,X1] : unit = op_k(i(mult(X1,X0)),mult(X0,X1)),
inference(forward_demodulation,[],[f361,f364]) ).
fof(f385,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(superposition,[],[f8,f58]) ).
fof(f396,plain,
! [X0] : mult(X0,unit) = i(i(X0)),
inference(superposition,[],[f2,f58]) ).
fof(f406,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[],[f396,f2]) ).
fof(f449,plain,
! [X0] : rd(X0,unit) = X0,
inference(superposition,[],[f9,f2]) ).
fof(f455,plain,
! [X0,X1] : mult(X1,X0) = rd(mult(X0,X1),op_k(X0,X1)),
inference(superposition,[],[f9,f13]) ).
fof(f828,plain,
! [X0,X1] : mult(mult(X0,X1),i(mult(X1,X0))) = rd(op_k(X0,X1),op_k(i(mult(X1,X0)),mult(X0,X1))),
inference(superposition,[],[f455,f124]) ).
fof(f847,plain,
! [X0,X1] : mult(mult(X0,X1),i(mult(X1,X0))) = rd(op_k(X0,X1),unit),
inference(forward_demodulation,[],[f828,f366]) ).
fof(f859,plain,
! [X0,X1] : op_k(X0,X1) = mult(mult(X0,X1),i(mult(X1,X0))),
inference(forward_demodulation,[],[f847,f449]) ).
fof(f1030,plain,
! [X0,X1] : i(X1) = mult(X0,i(mult(X0,X1))),
inference(superposition,[],[f385,f7]) ).
fof(f1087,plain,
! [X0,X1] : i(op_k(X0,X1)) = mult(mult(X1,X0),i(mult(X0,X1))),
inference(superposition,[],[f1030,f13]) ).
fof(f1105,plain,
! [X0,X1] : mult(mult(i(i(X0)),X1),i(mult(X1,X0))) = asoc(i(i(X0)),X1,i(mult(X1,X0))),
inference(superposition,[],[f74,f1030]) ).
fof(f1125,plain,
! [X0,X1] : mult(mult(X0,X1),i(mult(X1,X0))) = asoc(X0,X1,i(mult(X1,X0))),
inference(forward_demodulation,[],[f1105,f406]) ).
fof(f1136,plain,
! [X0,X1] : op_k(X1,X0) = i(op_k(X0,X1)),
inference(forward_demodulation,[],[f1087,f859]) ).
fof(f1145,plain,
! [X0,X1] : op_k(i(X1),i(X0)) = asoc(X0,X1,i(mult(X1,X0))),
inference(forward_demodulation,[],[f1125,f178]) ).
fof(f1155,plain,
! [X0,X1] : i(op_k(X1,X0)) = asoc(X0,X1,i(mult(X1,X0))),
inference(forward_demodulation,[],[f1145,f182]) ).
fof(f1160,plain,
! [X0,X1] : op_k(X0,X1) = asoc(X0,X1,i(mult(X1,X0))),
inference(forward_demodulation,[],[f1155,f1136]) ).
fof(f2945,plain,
! [X2,X3,X0,X1] : unit = op_k(asoc(X0,X1,X2),X3),
inference(superposition,[],[f24,f1160]) ).
fof(f3026,plain,
unit != unit,
inference(superposition,[],[f28,f2945]) ).
fof(f3045,plain,
$false,
inference(trivial_inequality_removal,[],[f3026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:40:37 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 8.50/2.39 % (31765)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.50/2.39 % (31784)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=3084343575:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.50/2.39 % (31788)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3178125724:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.50/2.39 % (31783)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=3679297329:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.50/2.39 % (31787)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1799063985:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.50/2.39 % (31785)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2766776836:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.50/2.39 % (31786)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3767687852:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.50/2.39 % (31789)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=166701425:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.50/2.39 % (31786)Instruction limit reached!
% 8.50/2.39 % (31786)------------------------------
% 8.50/2.39 % (31786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.39 % (31786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.39 % (31786)CaDiCaL version: 2.1.3
% 8.50/2.39 % (31786)Termination reason: Instruction limit
% 8.50/2.39 % (31786)Termination phase: Saturation
% 8.50/2.39 % (31786)Time elapsed: 0.136 s
% 8.50/2.39 % (31786)Peak memory usage: 89 MB
% 8.50/2.39 % (31786)Instructions burned: 136 (million)
% 8.50/2.39 % (31787)Instruction limit reached!
% 8.50/2.39 % (31787)------------------------------
% 8.50/2.39 % (31787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.39 % (31787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.39 % (31787)CaDiCaL version: 2.1.3
% 8.50/2.39 % (31787)Termination reason: Instruction limit
% 8.50/2.39 % (31787)Termination phase: Saturation
% 8.50/2.39 % (31787)Time elapsed: 0.174 s
% 8.50/2.39 % (31787)Peak memory usage: 90 MB
% 8.50/2.39 % (31787)Instructions burned: 181 (million)
% 8.50/2.39 % (31788)Instruction limit reached!
% 8.50/2.39 % (31788)------------------------------
% 8.50/2.39 % (31788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.39 % (31788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.39 % (31788)CaDiCaL version: 2.1.3
% 8.50/2.39 % (31788)Termination reason: Instruction limit
% 8.50/2.39 % (31788)Termination phase: Saturation
% 8.50/2.39 % (31788)Time elapsed: 0.261 s
% 8.50/2.39 % (31788)Peak memory usage: 90 MB
% 8.50/2.39 % (31788)Instructions burned: 257 (million)
% 8.50/2.39 % (31799)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1218137958:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 8.50/2.39 % (31800)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2579004793:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 8.50/2.39 % (31802)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3166130736:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 8.50/2.39 % (31802)Instruction limit reached!
% 8.50/2.39 % (31802)------------------------------
% 8.50/2.39 % (31802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.39 % (31802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.39 % (31802)CaDiCaL version: 2.1.3
% 8.50/2.39 % (31802)Termination reason: Instruction limit
% 8.50/2.39 % (31802)Termination phase: Saturation
% 8.50/2.39 % (31802)Time elapsed: 0.151 s
% 8.50/2.39 % (31802)Peak memory usage: 90 MB
% 8.50/2.39 % (31802)Instructions burned: 215 (million)
% 8.50/2.39 % (31784)First to succeed.
% 8.50/2.39 % (31784)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31765"
% 8.50/2.39 % (31808)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1628332888:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 8.50/2.39 % (31784)Refutation found. Thanks to Tanya!
% 8.50/2.39 % SZS status Unsatisfiable for theBenchmark
% 8.50/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 8.50/2.39 % (31784)------------------------------
% 8.50/2.39 % (31784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.50/2.39 % (31784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.50/2.39 % (31784)CaDiCaL version: 2.1.3
% 8.50/2.39 % (31784)Termination reason: Refutation
% 8.50/2.39 % (31784)Time elapsed: 0.708 s
% 8.50/2.39 % (31784)Peak memory usage: 132 MB
% 8.50/2.39 % (31784)Instructions burned: 1267 (million)
% 8.50/2.39 % (31784)------------------------------
% 8.50/2.39 % (31784)------------------------------
% 8.50/2.39 % (31765)Success in time 1.102 s
% 8.50/2.39 % Vampire exiting
%------------------------------------------------------------------------------