%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP751-1 : 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 10:16:06 AM UTC 2026
% Result : Unsatisfiable 0.17s 3.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(mult(X0,mult(X0,X0)),mult(X1,X2)) = mult(mult(X0,X1),mult(mult(X0,X0),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X2,X2)) = mult(mult(X0,X2),mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
mult(a,mult(b,c)) != mult(mult(rd(a,a),b),mult(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f72,plain,
! [X2,X0,X1] : mult(X0,X2) = rd(mult(mult(X0,X1),mult(X2,X1)),mult(X1,X1)),
inference(superposition,[],[f4,f7]) ).
fof(f81,plain,
! [X2,X0,X1] : mult(X0,mult(X2,X2)) = mult(mult(rd(X0,X1),X2),mult(X1,X2)),
inference(superposition,[],[f7,f3]) ).
fof(f82,plain,
! [X2,X0,X1] : mult(mult(rd(X0,X1),X2),mult(X1,X1)) = mult(X0,mult(X2,X1)),
inference(superposition,[],[f7,f3]) ).
fof(f99,plain,
! [X2,X0,X1] : mult(rd(X0,X2),X1) = rd(mult(X0,mult(X1,X1)),mult(X2,X1)),
inference(superposition,[],[f4,f81]) ).
fof(f116,plain,
! [X2,X0,X1] : mult(rd(X0,X2),X1) = rd(mult(X0,mult(X1,X2)),mult(X2,X2)),
inference(superposition,[],[f4,f82]) ).
fof(f225,plain,
! [X2,X3,X0,X1] : mult(rd(mult(rd(X0,X2),X1),X3),X2) = rd(mult(X0,mult(X1,X2)),mult(X3,X2)),
inference(superposition,[],[f99,f82]) ).
fof(f237,plain,
! [X2,X0,X1] : mult(rd(X1,rd(X0,X2)),X2) = rd(mult(X1,mult(X2,X2)),X0),
inference(superposition,[],[f99,f3]) ).
fof(f284,plain,
! [X2,X0,X1] : mult(rd(X1,X2),rd(X0,X2)) = rd(mult(X1,X0),mult(X2,X2)),
inference(superposition,[],[f116,f3]) ).
fof(f528,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f2670,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = rd(mult(mult(mult(X0,mult(X0,X0)),mult(X1,X2)),mult(X3,mult(mult(X0,X0),X2))),mult(mult(mult(X0,X0),X2),mult(mult(X0,X0),X2))),
inference(superposition,[],[f72,f5]) ).
fof(f2802,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(rd(mult(mult(X0,mult(X0,X0)),mult(X1,X2)),mult(mult(X0,X0),X2)),rd(mult(X3,mult(mult(X0,X0),X2)),mult(mult(X0,X0),X2))),
inference(forward_demodulation,[],[f2670,f284]) ).
fof(f2855,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(rd(mult(mult(X0,mult(X0,X0)),mult(X1,X2)),mult(mult(X0,X0),X2)),X3),
inference(forward_demodulation,[],[f2802,f4]) ).
fof(f2887,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(mult(rd(mult(rd(mult(X0,mult(X0,X0)),X2),X1),mult(X0,X0)),X2),X3),
inference(forward_demodulation,[],[f2855,f225]) ).
fof(f2906,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(mult(mult(rd(rd(mult(X0,mult(X0,X0)),X2),X0),rd(X1,X0)),X2),X3),
inference(forward_demodulation,[],[f2887,f284]) ).
fof(f2915,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(mult(mult(rd(mult(rd(X0,rd(X2,X0)),X0),X0),rd(X1,X0)),X2),X3),
inference(forward_demodulation,[],[f2906,f237]) ).
fof(f2919,plain,
! [X2,X3,X0,X1] : mult(mult(X0,X1),X3) = mult(mult(mult(rd(X0,rd(X2,X0)),rd(X1,X0)),X2),X3),
inference(forward_demodulation,[],[f2915,f4]) ).
fof(f3004,plain,
! [X2,X3,X0,X1] : mult(mult(rd(X0,rd(X3,X0)),rd(X1,X0)),X3) = rd(mult(mult(X0,X1),X2),X2),
inference(superposition,[],[f4,f2919]) ).
fof(f3099,plain,
! [X3,X0,X1] : mult(X0,X1) = mult(mult(rd(X0,rd(X3,X0)),rd(X1,X0)),X3),
inference(forward_demodulation,[],[f3004,f4]) ).
fof(f3252,plain,
! [X2,X0,X1] : mult(X1,mult(X0,X1)) = mult(mult(rd(X1,rd(X2,X1)),X0),X2),
inference(superposition,[],[f3099,f4]) ).
fof(f3385,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(rd(X1,X0),X2),mult(X0,X1)),
inference(superposition,[],[f3252,f4]) ).
fof(f3543,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(X0,X2),mult(ld(X0,X1),X1)),
inference(superposition,[],[f3385,f528]) ).
fof(f3551,plain,
! [X2,X0,X1] : mult(X0,mult(X2,X1)) = mult(X1,mult(ld(rd(X1,X2),X0),X1)),
inference(superposition,[],[f3385,f1]) ).
fof(f3763,plain,
! [X2,X0,X1] : rd(mult(X0,mult(X1,X0)),mult(X0,X0)) = mult(rd(mult(X2,X1),X0),ld(X2,X0)),
inference(superposition,[],[f116,f3543]) ).
fof(f3819,plain,
! [X2,X0,X1] : mult(rd(X0,X0),rd(mult(X1,X0),X0)) = mult(rd(mult(X2,X1),X0),ld(X2,X0)),
inference(forward_demodulation,[],[f3763,f284]) ).
fof(f3850,plain,
! [X2,X0,X1] : mult(rd(X0,X0),X1) = mult(rd(mult(X2,X1),X0),ld(X2,X0)),
inference(forward_demodulation,[],[f3819,f4]) ).
fof(f3891,plain,
! [X2,X0,X1] : mult(rd(X1,X1),X2) = mult(rd(X0,X1),ld(rd(X0,X2),X1)),
inference(superposition,[],[f3850,f3]) ).
fof(f4083,plain,
! [X2,X0,X1] : mult(X2,mult(ld(rd(X2,X1),X0),X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)),
inference(superposition,[],[f3385,f3891]) ).
fof(f4162,plain,
! [X2,X0,X1] : mult(X0,mult(X1,X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)),
inference(forward_demodulation,[],[f4083,f3551]) ).
fof(f4250,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(superposition,[],[f8,f4162]) ).
fof(f4315,plain,
$false,
inference(trivial_inequality_removal,[],[f4250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP751-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:45:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 14.74/3.07 % (1467317)Detected a unit-equality problem, will run specialized UEQ schedule.
% 14.74/3.07 % (1467367)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=602196639:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 14.74/3.07 % (1467365)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1235740582:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 14.74/3.07 % (1467360)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=3544747968:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 14.74/3.07 % (1467359)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=2646250569:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 14.74/3.07 % (1467363)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=590829115:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 14.74/3.07 % (1467364)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1712097030:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 14.74/3.07 % (1467361)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1905992828:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 14.74/3.07 % (1467363)Instruction limit reached!
% 14.74/3.07 % (1467363)------------------------------
% 14.74/3.07 % (1467363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.74/3.07 % (1467363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.74/3.07 % (1467363)CaDiCaL version: 2.1.3
% 14.74/3.07 % (1467363)Termination reason: Instruction limit
% 14.74/3.07 % (1467363)Termination phase: Saturation
% 14.74/3.07 % (1467363)Time elapsed: 0.094 s
% 14.74/3.07 % (1467363)Peak memory usage: 89 MB
% 14.74/3.07 % (1467363)Instructions burned: 137 (million)
% 14.74/3.07 % (1467364)Instruction limit reached!
% 14.74/3.07 % (1467364)------------------------------
% 14.74/3.07 % (1467364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.74/3.07 % (1467364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.74/3.07 % (1467364)CaDiCaL version: 2.1.3
% 14.74/3.07 % (1467364)Termination reason: Instruction limit
% 14.74/3.07 % (1467364)Termination phase: Saturation
% 14.74/3.07 % (1467364)Time elapsed: 0.102 s
% 14.74/3.07 % (1467364)Peak memory usage: 89 MB
% 14.74/3.07 % (1467364)Instructions burned: 182 (million)
% 14.74/3.07 % (1467365)Instruction limit reached!
% 14.74/3.07 % (1467365)------------------------------
% 14.74/3.07 % (1467365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.74/3.07 % (1467365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.74/3.07 % (1467365)CaDiCaL version: 2.1.3
% 14.74/3.07 % (1467365)Termination reason: Instruction limit
% 14.74/3.07 % (1467365)Termination phase: Saturation
% 14.74/3.07 % (1467365)Time elapsed: 0.166 s
% 14.74/3.07 % (1467365)Peak memory usage: 90 MB
% 14.74/3.07 % (1467365)Instructions burned: 259 (million)
% 14.74/3.07 % (1467426)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3930603061:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 14.74/3.07 % (1467427)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=900318408:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 14.74/3.07 % (1467437)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3890825168:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 14.74/3.07 % (1467367)Instruction limit reached!
% 14.74/3.07 % (1467367)------------------------------
% 14.74/3.07 % (1467367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.74/3.07 % (1467367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.74/3.07 % (1467367)CaDiCaL version: 2.1.3
% 14.74/3.07 % (1467367)Termination reason: Instruction limit
% 14.74/3.07 % (1467367)Termination phase: Saturation
% 14.74/3.07 % (1467367)Time elapsed: 0.353 s
% 0.17/3.31 % (1467367)Peak memory usage: 99 MB
% 0.17/3.31 % (1467367)Instructions burned: 1189 (million)
% 0.17/3.31 % (1467443)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=1453239785:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 0.17/3.31 % (1467437)Instruction limit reached!
% 0.17/3.31 % (1467437)------------------------------
% 0.17/3.31 % (1467437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/3.31 % (1467437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/3.31 % (1467437)CaDiCaL version: 2.1.3
% 0.17/3.31 % (1467437)Termination reason: Instruction limit
% 0.17/3.31 % (1467437)Termination phase: Saturation
% 0.17/3.31 % (1467437)Time elapsed: 0.118 s
% 0.17/3.31 % (1467437)Peak memory usage: 90 MB
% 0.17/3.31 % (1467437)Instructions burned: 216 (million)
% 0.17/3.31 % (1467443)Instruction limit reached!
% 0.17/3.31 % (1467443)------------------------------
% 0.17/3.31 % (1467443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/3.31 % (1467443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/3.31 % (1467443)CaDiCaL version: 2.1.3
% 0.17/3.31 % (1467443)Termination reason: Instruction limit
% 0.17/3.31 % (1467443)Termination phase: Saturation
% 0.17/3.31 % (1467443)Time elapsed: 0.156 s
% 0.17/3.31 % (1467443)Peak memory usage: 93 MB
% 0.17/3.31 % (1467443)Instructions burned: 317 (million)
% 0.17/3.31 % (1467449)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=1599912498:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 0.17/3.31 % (1467474)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2185122708:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2992 on theBenchmark for (2992ds/2836Mi)
% 0.17/3.31 % (1467360)First to succeed.
% 0.17/3.31 % (1467360)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1467317"
% 0.17/3.31 % (1467360)Refutation found. Thanks to Tanya!
% 0.17/3.31 % SZS status Unsatisfiable for theBenchmark
% 0.17/3.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/3.31 % (1467360)------------------------------
% 0.17/3.31 % (1467360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/3.31 % (1467360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/3.31 % (1467360)CaDiCaL version: 2.1.3
% 0.17/3.31 % (1467360)Termination reason: Refutation
% 0.17/3.31 % (1467360)Time elapsed: 1.574 s
% 0.17/3.31 % (1467360)Peak memory usage: 138 MB
% 0.17/3.31 % (1467360)Instructions burned: 1802 (million)
% 0.17/3.31 % (1467360)------------------------------
% 0.17/3.31 % (1467360)------------------------------
% 0.17/3.31 % (1467317)Success in time 2.21 s
% 0.17/3.31 % Vampire exiting
%------------------------------------------------------------------------------