%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP728-1 : 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 : n015.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 10:16:03 AM UTC 2026
% Result : Unsatisfiable 14.06s 3.29s
% Output : Refutation 14.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 91 ( 91 !; 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(f3,axiom,
! [X0] : mult(X0,i(X0)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f4,plain,
! [X0] : unit = mult(X0,i(X0)),
inference(reorient_equations,[],[f3]) ).
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(f27,negated_conjecture,
op_k(op_k(a,b),c) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,plain,
unit != op_k(op_k(a,b),c),
inference(reorient_equations,[],[f27]) ).
fof(f35,plain,
! [X0,X1] : mult(X1,X0) = mult(i(i(X1)),X0),
inference(superposition,[],[f8,f8]) ).
fof(f62,plain,
! [X0,X1] : op_k(X0,X1) = mult(i(mult(X1,X0)),mult(X0,X1)),
inference(superposition,[],[f8,f13]) ).
fof(f140,plain,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = mult(mult(X0,unit),asoc(X0,X1,i(X1))),
inference(superposition,[],[f12,f4]) ).
fof(f150,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(f156,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = asoc(i(mult(X0,X1)),X0,X1),
inference(forward_demodulation,[],[f150,f1]) ).
fof(f162,plain,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = mult(X0,asoc(X0,X1,i(X1))),
inference(forward_demodulation,[],[f140,f2]) ).
fof(f248,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(superposition,[],[f8,f35]) ).
fof(f250,plain,
! [X0,X1] : mult(X0,i(X1)) = i(mult(i(X0),X1)),
inference(superposition,[],[f7,f35]) ).
fof(f257,plain,
! [X0] : mult(X0,unit) = i(i(X0)),
inference(superposition,[],[f2,f35]) ).
fof(f267,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[],[f257,f2]) ).
fof(f299,plain,
! [X0,X1] : mult(mult(i(X0),i(X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(superposition,[],[f156,f8]) ).
fof(f324,plain,
! [X0,X1] : mult(i(mult(X0,X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f299,f7]) ).
fof(f337,plain,
! [X0,X1] : op_k(X1,X0) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f324,f62]) ).
fof(f482,plain,
! [X2,X3,X0,X1] : unit = asoc(op_k(X0,X1),X2,X3),
inference(superposition,[],[f24,f337]) ).
fof(f1904,plain,
! [X2,X0,X1] : mult(mult(op_k(X0,X1),X2),i(X2)) = mult(op_k(X0,X1),unit),
inference(superposition,[],[f162,f482]) ).
fof(f1909,plain,
! [X2,X0,X1] : op_k(X0,X1) = mult(mult(op_k(X0,X1),X2),i(X2)),
inference(forward_demodulation,[],[f1904,f2]) ).
fof(f1919,plain,
! [X2,X0,X1] : op_k(X1,X2) = mult(X0,i(mult(i(op_k(X1,X2)),X0))),
inference(superposition,[],[f1909,f248]) ).
fof(f1936,plain,
! [X2,X0,X1] : mult(op_k(X0,X1),X2) = rd(op_k(X0,X1),i(X2)),
inference(superposition,[],[f9,f1909]) ).
fof(f1980,plain,
! [X2,X0,X1] : op_k(X1,X2) = mult(X0,mult(op_k(X1,X2),i(X0))),
inference(forward_demodulation,[],[f1919,f250]) ).
fof(f2018,plain,
! [X2,X0,X1] : rd(op_k(X1,X2),X0) = mult(op_k(X1,X2),i(X0)),
inference(superposition,[],[f1936,f267]) ).
fof(f2057,plain,
! [X2,X0,X1] : mult(op_k(X0,X1),i(X2)) = mult(i(X2),op_k(X0,X1)),
inference(superposition,[],[f8,f1980]) ).
fof(f2111,plain,
! [X2,X0,X1] : rd(op_k(X0,X1),X2) = mult(i(X2),op_k(X0,X1)),
inference(forward_demodulation,[],[f2057,f2018]) ).
fof(f2181,plain,
! [X2,X0,X1] : op_k(op_k(X0,X1),i(X2)) = mult(i(rd(op_k(X0,X1),X2)),mult(op_k(X0,X1),i(X2))),
inference(superposition,[],[f62,f2111]) ).
fof(f2207,plain,
! [X2,X0,X1] : op_k(op_k(X0,X1),i(X2)) = mult(i(rd(op_k(X0,X1),X2)),rd(op_k(X0,X1),X2)),
inference(forward_demodulation,[],[f2181,f2018]) ).
fof(f2229,plain,
! [X2,X0,X1] : unit = op_k(op_k(X0,X1),i(X2)),
inference(forward_demodulation,[],[f2207,f6]) ).
fof(f2286,plain,
! [X2,X0,X1] : unit = op_k(op_k(X1,X2),X0),
inference(superposition,[],[f2229,f267]) ).
fof(f2318,plain,
unit != unit,
inference(superposition,[],[f28,f2286]) ).
fof(f2330,plain,
$false,
inference(trivial_inequality_removal,[],[f2318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:41:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 12.23/2.98 % (1464246)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.23/2.98 % (1464265)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=255286564:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 12.23/2.98 % (1464266)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3888531930:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 12.23/2.98 % (1464268)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=605181499:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 12.23/2.98 % (1464263)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=1506100218:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 12.23/2.98 % (1464264)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=1590545909:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 12.23/2.98 % (1464269)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1706002654:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 12.23/2.98 % (1464267)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2189983568:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 12.23/2.98 % (1464266)Instruction limit reached!
% 12.23/2.98 % (1464266)------------------------------
% 12.23/2.98 % (1464266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.23/2.98 % (1464266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.98 % (1464266)CaDiCaL version: 2.1.3
% 12.23/2.98 % (1464266)Termination reason: Instruction limit
% 12.23/2.98 % (1464266)Termination phase: Saturation
% 12.23/2.98 % (1464266)Time elapsed: 0.132 s
% 12.23/2.98 % (1464266)Peak memory usage: 89 MB
% 12.23/2.98 % (1464266)Instructions burned: 137 (million)
% 12.23/2.98 % (1464267)Instruction limit reached!
% 12.23/2.98 % (1464267)------------------------------
% 12.23/2.98 % (1464267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.23/2.98 % (1464267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.98 % (1464267)CaDiCaL version: 2.1.3
% 12.23/2.98 % (1464267)Termination reason: Instruction limit
% 12.23/2.98 % (1464267)Termination phase: Saturation
% 12.23/2.98 % (1464267)Time elapsed: 0.169 s
% 12.23/2.98 % (1464267)Peak memory usage: 90 MB
% 12.23/2.98 % (1464267)Instructions burned: 181 (million)
% 12.23/2.98 % (1464268)Instruction limit reached!
% 12.23/2.98 % (1464268)------------------------------
% 12.23/2.98 % (1464268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.23/2.98 % (1464268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.98 % (1464268)CaDiCaL version: 2.1.3
% 12.23/2.98 % (1464268)Termination reason: Instruction limit
% 12.23/2.98 % (1464268)Termination phase: Saturation
% 12.23/2.98 % (1464268)Time elapsed: 0.233 s
% 12.23/2.98 % (1464268)Peak memory usage: 90 MB
% 12.23/2.98 % (1464268)Instructions burned: 257 (million)
% 12.23/2.98 % (1464281)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3579988690:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 12.23/2.98 % (1464286)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3076052647:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 12.23/2.98 % (1464287)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=4233114954:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 12.23/2.98 % (1464287)Instruction limit reached!
% 12.23/2.98 % (1464287)------------------------------
% 12.23/2.98 % (1464287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.23/2.98 % (1464287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.98 % (1464287)CaDiCaL version: 2.1.3
% 12.23/2.98 % (1464287)Termination reason: Instruction limit
% 12.23/2.98 % (1464287)Termination phase: Saturation
% 12.23/2.98 % (1464287)Time elapsed: 0.208 s
% 14.06/3.29 % (1464287)Peak memory usage: 90 MB
% 14.06/3.29 % (1464287)Instructions burned: 216 (million)
% 14.06/3.29 % (1464291)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=77476543:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 14.06/3.29 % (1464291)Instruction limit reached!
% 14.06/3.29 % (1464291)------------------------------
% 14.06/3.29 % (1464291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.06/3.29 % (1464291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.06/3.29 % (1464291)CaDiCaL version: 2.1.3
% 14.06/3.29 % (1464291)Termination reason: Instruction limit
% 14.06/3.29 % (1464291)Termination phase: Saturation
% 14.06/3.29 % (1464291)Time elapsed: 0.173 s
% 14.06/3.29 % (1464291)Peak memory usage: 94 MB
% 14.06/3.29 % (1464291)Instructions burned: 317 (million)
% 14.06/3.29 % (1464269)Instruction limit reached!
% 14.06/3.29 % (1464269)------------------------------
% 14.06/3.29 % (1464269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.06/3.29 % (1464269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.06/3.29 % (1464269)CaDiCaL version: 2.1.3
% 14.06/3.29 % (1464269)Termination reason: Instruction limit
% 14.06/3.29 % (1464269)Termination phase: Saturation
% 14.06/3.29 % (1464269)Time elapsed: 1.013 s
% 14.06/3.29 % (1464269)Peak memory usage: 101 MB
% 14.06/3.29 % (1464269)Instructions burned: 1187 (million)
% 14.06/3.29 % (1464295)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2788647104:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 14.06/3.29 % (1464264)First to succeed.
% 14.06/3.29 % (1464264)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1464246"
% 14.06/3.29 % (1464263)Also succeeded, but the first one will report.
% 14.06/3.29 % (1464296)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2463296305:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2987 on theBenchmark for (2987ds/2836Mi)
% 14.06/3.29 % (1464281)Also succeeded, but the first one will report.
% 14.06/3.29 % (1464264)Refutation found. Thanks to Tanya!
% 14.06/3.29 % SZS status Unsatisfiable for theBenchmark
% 14.06/3.29 % SZS output start Proof for theBenchmark
% See solution above
% 14.06/3.29 % (1464264)------------------------------
% 14.06/3.29 % (1464264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.06/3.29 % (1464264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.06/3.29 % (1464264)CaDiCaL version: 2.1.3
% 14.06/3.29 % (1464264)Termination reason: Refutation
% 14.06/3.29 % (1464264)Time elapsed: 1.235 s
% 14.06/3.29 % (1464264)Peak memory usage: 132 MB
% 14.06/3.29 % (1464264)Instructions burned: 1227 (million)
% 14.06/3.29 % (1464264)------------------------------
% 14.06/3.29 % (1464264)------------------------------
% 14.06/3.29 % (1464246)Success in time 1.879 s
% 14.06/3.29 % Vampire exiting
%------------------------------------------------------------------------------