%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 2.65s 1.23s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 141 ( 141 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f9,plain,
! [X0] : mult(X0,ld(X0,X0)) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f11,plain,
! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f3,f9]) ).
fof(f13,plain,
! [X0] : mult(rd(X0,X0),X0) = X0,
inference(superposition,[],[f4,f2]) ).
fof(f14,plain,
rd(mult(x6,x8),x8) != mult(rd(x6,ld(x7,x8)),ld(x7,x8)),
inference(superposition,[],[f8,f4]) ).
fof(f16,plain,
mult(rd(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(forward_demodulation,[],[f14,f4]) ).
fof(f17,plain,
! [X0] : rd(X0,X0) = mult(rd(rd(X0,X0),X0),X0),
inference(superposition,[],[f4,f13]) ).
fof(f19,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(forward_demodulation,[],[f7,f4]) ).
fof(f20,plain,
! [X0,X1] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(forward_demodulation,[],[f19,f3]) ).
fof(f26,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[],[f20,f13]) ).
fof(f27,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f17,f20]) ).
fof(f31,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(forward_demodulation,[],[f27,f11]) ).
fof(f33,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
inference(superposition,[],[f20,f31]) ).
fof(f35,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(superposition,[],[f13,f31]) ).
fof(f41,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[],[f5,f3]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : mult(mult(X0,ld(X0,X2)),X3) = mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))),
inference(forward_demodulation,[],[f41,f3]) ).
fof(f52,plain,
! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))),
inference(forward_demodulation,[],[f26,f31]) ).
fof(f57,plain,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(forward_demodulation,[],[f6,f4]) ).
fof(f58,plain,
! [X2,X3,X0,X1] : mult(X0,mult(rd(X1,X3),X3)) = mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)),
inference(forward_demodulation,[],[f57,f4]) ).
fof(f76,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(superposition,[],[f42,f1]) ).
fof(f93,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X0,X1))),X2) = mult(ld(X0,X1),mult(ld(X0,X1),ld(ld(X0,X1),X2))),
inference(superposition,[],[f42,f3]) ).
fof(f106,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(superposition,[],[f76,f9]) ).
fof(f131,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f106,f3]) ).
fof(f138,plain,
! [X0] : mult(X0,ld(X0,X0)) = mult(X0,ld(ld(X0,X0),ld(X0,X0))),
inference(superposition,[],[f131,f52]) ).
fof(f154,plain,
! [X0] : mult(X0,ld(ld(X0,X0),ld(X0,X0))) = X0,
inference(forward_demodulation,[],[f138,f9]) ).
fof(f193,plain,
! [X2,X0,X1] : mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,X0)),ld(ld(X0,X0),ld(X0,X0))),
inference(superposition,[],[f42,f154]) ).
fof(f197,plain,
! [X2,X0,X1] : mult(ld(X1,X2),ld(ld(X1,X2),X0)) = mult(X1,ld(X1,mult(X0,ld(ld(X0,X0),ld(X0,X0))))),
inference(forward_demodulation,[],[f193,f76]) ).
fof(f198,plain,
! [X2,X0,X1] : mult(X1,ld(X1,X0)) = mult(ld(X1,X2),ld(ld(X1,X2),X0)),
inference(forward_demodulation,[],[f197,f154]) ).
fof(f248,plain,
! [X2,X0,X1] : mult(X1,mult(rd(X2,X0),X0)) = mult(rd(mult(X1,X2),X0),X0),
inference(superposition,[],[f58,f2]) ).
fof(f279,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(rd(ld(X0,X0),X1),X1)),
inference(superposition,[],[f248,f9]) ).
fof(f301,plain,
! [X0,X1] : mult(X0,mult(rd(X1,X1),X1)) = mult(mult(rd(X0,X1),X1),X1),
inference(superposition,[],[f248,f4]) ).
fof(f316,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(rd(X0,X1),X1),X1),
inference(forward_demodulation,[],[f301,f13]) ).
fof(f334,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f279,f33]) ).
fof(f344,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[],[f334,f131]) ).
fof(f348,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(superposition,[],[f316,f20]) ).
fof(f364,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(X0,ld(X0,mult(ld(X1,X1),X1))),
inference(forward_demodulation,[],[f348,f76]) ).
fof(f368,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(rd(X0,X0),X1),
inference(forward_demodulation,[],[f364,f35]) ).
fof(f369,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[],[f368,f31]) ).
fof(f390,plain,
mult(rd(x6,x8),x8) != mult(x6,ld(ld(x7,x8),ld(x7,x8))),
inference(superposition,[],[f16,f344]) ).
fof(f404,plain,
mult(x6,ld(ld(x7,x8),ld(x7,x8))) != mult(x6,ld(x8,x8)),
inference(forward_demodulation,[],[f390,f344]) ).
fof(f460,plain,
! [X0,X1] : mult(rd(ld(X0,X0),X1),X1) = rd(mult(X0,ld(X0,X1)),X1),
inference(superposition,[],[f4,f369]) ).
fof(f476,plain,
! [X0,X1] : mult(ld(X0,X0),ld(X1,X1)) = rd(mult(X0,ld(X0,X1)),X1),
inference(forward_demodulation,[],[f460,f344]) ).
fof(f495,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(X0,ld(X0,X1)),X1),
inference(forward_demodulation,[],[f476,f369]) ).
fof(f1862,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
inference(superposition,[],[f198,f9]) ).
fof(f1979,plain,
! [X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(X0,mult(rd(ld(X0,X1),X1),X1)),
inference(superposition,[],[f248,f495]) ).
fof(f1997,plain,
! [X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(X0,mult(ld(X0,X1),ld(X1,X1))),
inference(forward_demodulation,[],[f1979,f344]) ).
fof(f2026,plain,
! [X0,X1] : mult(X0,ld(X0,mult(ld(X1,X1),X1))) = mult(X0,mult(ld(X0,X1),ld(X1,X1))),
inference(forward_demodulation,[],[f1997,f76]) ).
fof(f2042,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(X0,mult(ld(X0,X1),ld(X1,X1))),
inference(forward_demodulation,[],[f2026,f35]) ).
fof(f2496,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,ld(X0,X1))),X2) = mult(ld(X0,X1),X2),
inference(forward_demodulation,[],[f93,f131]) ).
fof(f2497,plain,
! [X2,X0,X1] : mult(ld(X0,X1),X2) = mult(X0,ld(X0,mult(ld(X0,X1),X2))),
inference(forward_demodulation,[],[f2496,f76]) ).
fof(f3771,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X0,X1))) = mult(X0,ld(X0,mult(ld(X0,X1),ld(X1,X1)))),
inference(superposition,[],[f3,f2042]) ).
fof(f3796,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X0,X1))) = mult(ld(X0,X1),ld(X1,X1)),
inference(forward_demodulation,[],[f3771,f2497]) ).
fof(f3811,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X0,X1))) = mult(ld(X0,X1),ld(X1,X1)),
inference(forward_demodulation,[],[f3796,f3]) ).
fof(f3819,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(X0,X1),ld(X1,X1)),
inference(forward_demodulation,[],[f3811,f1862]) ).
fof(f3860,plain,
! [X0,X1] : ld(ld(X0,X1),ld(X0,X1)) = mult(ld(X0,X1),ld(ld(X0,X1),ld(X1,X1))),
inference(superposition,[],[f3,f3819]) ).
fof(f3880,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(ld(X0,X1),ld(X0,X1)),
inference(forward_demodulation,[],[f3860,f198]) ).
fof(f5798,plain,
mult(x6,ld(x8,x8)) != mult(x6,mult(x7,ld(x7,ld(x8,x8)))),
inference(superposition,[],[f404,f3880]) ).
fof(f5814,plain,
! [X2,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,ld(X0,ld(X1,X1))),X2),
inference(superposition,[],[f369,f3880]) ).
fof(f5887,plain,
! [X2,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(ld(X1,X1),X2))),
inference(forward_demodulation,[],[f5814,f76]) ).
fof(f5928,plain,
! [X2,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(X1,ld(X1,X2)))),
inference(forward_demodulation,[],[f5887,f369]) ).
fof(f5957,plain,
! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(X0,ld(X0,mult(X1,ld(X1,X2)))),
inference(forward_demodulation,[],[f5928,f198]) ).
fof(f9422,plain,
! [X2,X0,X1] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,mult(X2,ld(X2,X1))),
inference(superposition,[],[f131,f5957]) ).
fof(f9520,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(X0,mult(X2,ld(X2,X1))),
inference(forward_demodulation,[],[f9422,f131]) ).
fof(f9754,plain,
mult(x6,ld(x8,x8)) != mult(x6,ld(x8,x8)),
inference(superposition,[],[f5798,f9520]) ).
fof(f9755,plain,
$false,
inference(trivial_inequality_removal,[],[f9754]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:38:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.65/1.23 % (2141157)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.65/1.23 % (2141168)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1005348584:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.65/1.23 % (2141167)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2032705012:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.65/1.23 % (2141164)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1785950840:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.65/1.23 % (2141166)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3641979329:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.65/1.23 % (2141165)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2845929691:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.65/1.23 % (2141162)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=3453779552:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.65/1.23 % (2141163)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=944138929:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.65/1.23 % (2141168)First to succeed.
% 2.65/1.23 % (2141168)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2141157"
% 2.65/1.23 % (2141165)Instruction limit reached!
% 2.65/1.23 % (2141165)------------------------------
% 2.65/1.23 % (2141165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.23 % (2141165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.23 % (2141165)CaDiCaL version: 2.1.3
% 2.65/1.23 % (2141165)Termination reason: Instruction limit
% 2.65/1.23 % (2141165)Termination phase: Saturation
% 2.65/1.23 % (2141165)Time elapsed: 0.086 s
% 2.65/1.23 % (2141165)Peak memory usage: 88 MB
% 2.65/1.23 % (2141165)Instructions burned: 136 (million)
% 2.65/1.23 % (2141166)Instruction limit reached!
% 2.65/1.23 % (2141166)------------------------------
% 2.65/1.23 % (2141166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.23 % (2141166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.23 % (2141166)CaDiCaL version: 2.1.3
% 2.65/1.23 % (2141166)Termination reason: Instruction limit
% 2.65/1.23 % (2141166)Termination phase: Saturation
% 2.65/1.23 % (2141166)Time elapsed: 0.106 s
% 2.65/1.23 % (2141166)Peak memory usage: 89 MB
% 2.65/1.23 % (2141166)Instructions burned: 181 (million)
% 2.65/1.23 % (2141167)Instruction limit reached!
% 2.65/1.23 % (2141167)------------------------------
% 2.65/1.23 % (2141167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.23 % (2141167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.23 % (2141167)CaDiCaL version: 2.1.3
% 2.65/1.23 % (2141167)Termination reason: Instruction limit
% 2.65/1.23 % (2141167)Termination phase: Saturation
% 2.65/1.23 % (2141167)Time elapsed: 0.169 s
% 2.65/1.23 % (2141167)Peak memory usage: 89 MB
% 2.65/1.23 % (2141167)Instructions burned: 257 (million)
% 2.65/1.23 % (2141168)Refutation found. Thanks to Tanya!
% 2.65/1.23 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.23/1.42 % (2141168)------------------------------
% 3.23/1.42 % (2141168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.42 % (2141168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.42 % (2141168)CaDiCaL version: 2.1.3
% 3.23/1.42 % (2141168)Termination reason: Refutation
% 3.23/1.42 % (2141168)Time elapsed: 0.099 s
% 3.23/1.42 % (2141168)Peak memory usage: 91 MB
% 3.23/1.42 % (2141168)Instructions burned: 333 (million)
% 3.23/1.42 % (2141168)------------------------------
% 3.23/1.42 % (2141168)------------------------------
% 3.23/1.42 % (2141157)Success in time 0.361 s
% 3.23/1.42 % Vampire exiting
%------------------------------------------------------------------------------