%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP687-1 : 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 : n017.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 10:15:36 AM UTC 2026
% Result : Unsatisfiable 0.17s 2.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(X0,X0),mult(X1,X2)) = mult(mult(X0,mult(X0,X1)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f8,negated_conjecture,
mult(a,mult(b,mult(b,c))) != mult(mult(a,mult(b,b)),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,plain,
! [X2,X0,X1] : mult(mult(X0,X0),mult(ld(X0,X1),X2)) = mult(mult(X0,X1),X2),
inference(superposition,[],[f7,f1]) ).
fof(f25,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,X0),X2),
inference(superposition,[],[f19,f1]) ).
fof(f26,plain,
! [X2,X0,X1] : mult(ld(X1,X2),X0) = ld(mult(X1,X1),mult(mult(X1,X2),X0)),
inference(superposition,[],[f2,f19]) ).
fof(f31,plain,
! [X2,X0,X1] : mult(X1,mult(X1,X2)) = rd(mult(mult(X1,X1),mult(X2,X0)),X0),
inference(superposition,[],[f4,f7]) ).
fof(f52,plain,
! [X0] : unit = ld(X0,X0),
inference(superposition,[],[f2,f5]) ).
fof(f55,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),mult(X1,unit)),
inference(superposition,[],[f7,f5]) ).
fof(f56,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[],[f55,f5]) ).
fof(f65,plain,
! [X2,X0,X1] : mult(X1,mult(X1,X2)) = rd(mult(X1,mult(X1,mult(X2,X0))),X0),
inference(backward_demodulation,[],[f31,f56]) ).
fof(f72,plain,
! [X2,X0,X1] : mult(mult(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,mult(X0,X2)),
inference(backward_demodulation,[],[f25,f56]) ).
fof(f142,plain,
! [X2,X0,X1] : mult(X2,mult(X2,rd(X0,X1))) = rd(mult(X2,mult(X2,X0)),X1),
inference(superposition,[],[f65,f3]) ).
fof(f144,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f2,f3]) ).
fof(f161,plain,
! [X2,X0,X1] : mult(ld(X0,ld(X0,X1)),X2) = ld(mult(X0,X0),mult(X1,X2)),
inference(superposition,[],[f26,f1]) ).
fof(f167,plain,
! [X0,X1] : mult(ld(X0,X1),unit) = ld(mult(X0,X0),mult(X0,X1)),
inference(superposition,[],[f26,f5]) ).
fof(f170,plain,
! [X0,X1] : ld(X0,X1) = ld(mult(X0,X0),mult(X0,X1)),
inference(forward_demodulation,[],[f167,f5]) ).
fof(f180,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(X0,ld(X0,X0)),X1),
inference(forward_demodulation,[],[f170,f161]) ).
fof(f185,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(X0,unit),X1),
inference(forward_demodulation,[],[f180,f52]) ).
fof(f190,plain,
! [X2,X0,X1] : mult(X0,mult(X0,X2)) = mult(X1,ld(ld(X0,ld(X0,X1)),X2)),
inference(superposition,[],[f72,f1]) ).
fof(f323,plain,
! [X0,X1] : mult(X0,X1) = ld(rd(unit,X0),X1),
inference(superposition,[],[f185,f144]) ).
fof(f336,plain,
! [X0,X1] : mult(X0,mult(X0,rd(X1,mult(X0,X1)))) = X0,
inference(superposition,[],[f142,f4]) ).
fof(f374,plain,
! [X0,X1] : ld(X0,X0) = mult(X0,rd(X1,mult(X0,X1))),
inference(superposition,[],[f2,f336]) ).
fof(f377,plain,
! [X0,X1] : unit = mult(X0,rd(X1,mult(X0,X1))),
inference(forward_demodulation,[],[f374,f52]) ).
fof(f426,plain,
! [X0] : unit = mult(X0,rd(unit,X0)),
inference(superposition,[],[f377,f5]) ).
fof(f530,plain,
! [X0] : ld(X0,unit) = rd(unit,X0),
inference(superposition,[],[f2,f426]) ).
fof(f538,plain,
! [X0,X1] : mult(X0,X1) = ld(ld(X0,unit),X1),
inference(backward_demodulation,[],[f323,f530]) ).
fof(f966,plain,
! [X2,X0,X1] : ld(ld(X1,ld(X1,X2)),X0) = ld(X2,mult(X1,mult(X1,X0))),
inference(superposition,[],[f2,f190]) ).
fof(f2872,plain,
! [X2,X0,X1] : ld(ld(X1,ld(X1,X0)),X2) = mult(ld(X0,mult(X1,mult(X1,unit))),X2),
inference(superposition,[],[f185,f966]) ).
fof(f2873,plain,
! [X2,X0,X1] : ld(ld(X1,ld(X1,X0)),X2) = mult(ld(X0,mult(X1,X1)),X2),
inference(forward_demodulation,[],[f2872,f5]) ).
fof(f2912,plain,
! [X2,X0,X1] : ld(X2,mult(X1,mult(X1,X0))) = mult(ld(X2,mult(X1,X1)),X0),
inference(backward_demodulation,[],[f966,f2873]) ).
fof(f3071,plain,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X1,X2))) = mult(ld(ld(X0,unit),mult(X1,X1)),X2),
inference(superposition,[],[f2912,f538]) ).
fof(f3099,plain,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(X0,mult(X1,X1)),X2),
inference(forward_demodulation,[],[f3071,f538]) ).
fof(f3119,plain,
$false,
inference(backward_subsumption_resolution,[],[f8,f3099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP687-1 : 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 : n017.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 10:31:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.17/2.31 % (2351236)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.17/2.31 % (2351270)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2465649122:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.17/2.31 % (2351271)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=320997987:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.17/2.31 % (2351266)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=3644679871:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.17/2.31 % (2351268)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2743437052:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.17/2.31 % (2351267)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=423377251:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.17/2.31 % (2351265)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=1227593217:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.17/2.31 % (2351269)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1452704831:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.17/2.31 % (2351270)Instruction limit reached!
% 0.17/2.31 % (2351270)------------------------------
% 0.17/2.31 % (2351270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351270)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351270)Termination reason: Instruction limit
% 0.17/2.31 % (2351270)Termination phase: Saturation
% 0.17/2.31 % (2351270)Time elapsed: 0.081 s
% 0.17/2.31 % (2351270)Peak memory usage: 89 MB
% 0.17/2.31 % (2351270)Instructions burned: 259 (million)
% 0.17/2.31 % (2351268)Instruction limit reached!
% 0.17/2.31 % (2351268)------------------------------
% 0.17/2.31 % (2351268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351268)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351268)Termination reason: Instruction limit
% 0.17/2.31 % (2351268)Termination phase: Saturation
% 0.17/2.31 % (2351268)Time elapsed: 0.079 s
% 0.17/2.31 % (2351268)Peak memory usage: 88 MB
% 0.17/2.31 % (2351268)Instructions burned: 137 (million)
% 0.17/2.31 % (2351279)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3382233694:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 0.17/2.31 % (2351269)Instruction limit reached!
% 0.17/2.31 % (2351269)------------------------------
% 0.17/2.31 % (2351269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351269)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351269)Termination reason: Instruction limit
% 0.17/2.31 % (2351269)Termination phase: Saturation
% 0.17/2.31 % (2351269)Time elapsed: 0.169 s
% 0.17/2.31 % (2351269)Peak memory usage: 89 MB
% 0.17/2.31 % (2351269)Instructions burned: 181 (million)
% 0.17/2.31 % (2351280)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3351873763:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 0.17/2.31 % (2351282)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3810306437:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 0.17/2.31 % (2351282)Instruction limit reached!
% 0.17/2.31 % (2351282)------------------------------
% 0.17/2.31 % (2351282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351282)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351282)Termination reason: Instruction limit
% 0.17/2.31 % (2351282)Termination phase: Saturation
% 0.17/2.31 % (2351282)Time elapsed: 0.203 s
% 0.17/2.31 % (2351282)Peak memory usage: 90 MB
% 0.17/2.31 % (2351282)Instructions burned: 216 (million)
% 0.17/2.31 % (2351279)First to succeed.
% 0.17/2.31 % (2351279)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2351236"
% 0.17/2.31 % (2351271)Instruction limit reached!
% 0.17/2.31 % (2351271)------------------------------
% 0.17/2.31 % (2351271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351271)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351271)Termination reason: Instruction limit
% 0.17/2.31 % (2351271)Termination phase: Saturation
% 0.17/2.31 % (2351271)Time elapsed: 0.904 s
% 0.17/2.31 % (2351271)Peak memory usage: 101 MB
% 0.17/2.31 % (2351271)Instructions burned: 1187 (million)
% 0.17/2.31 % (2351303)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=2010650269: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)
% 0.17/2.31 % (2351279)Refutation found. Thanks to Tanya!
% 0.17/2.31 % SZS status Unsatisfiable for theBenchmark
% 0.17/2.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.31 % (2351279)------------------------------
% 0.17/2.31 % (2351279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.31 % (2351279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.31 % (2351279)CaDiCaL version: 2.1.3
% 0.17/2.31 % (2351279)Termination reason: Refutation
% 0.17/2.31 % (2351279)Time elapsed: 0.652 s
% 0.17/2.31 % (2351279)Peak memory usage: 134 MB
% 0.17/2.31 % (2351279)Instructions burned: 1451 (million)
% 0.17/2.31 % (2351279)------------------------------
% 0.17/2.31 % (2351279)------------------------------
% 0.17/2.31 % (2351236)Success in time 1.243 s
% 0.17/2.31 % Vampire exiting
%------------------------------------------------------------------------------