%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 3.67s 1.42s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 1 def)
% Number of atoms : 36 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f9,definition,
~ sP0(rd(mult(x6,rd(x7,x8)),rd(x7,x8))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f10,plain,
sP0(rd(mult(x6,x8),x8)),
inference(inequality_splitting,[],[f8,f9]) ).
fof(f14,plain,
! [X0] : ld(X0,mult(X0,ld(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(superposition,[],[f7,f4]) ).
fof(f18,plain,
! [X0,X1] : rd(mult(mult(rd(X0,X0),X1),X1),X1) = mult(ld(X0,mult(X0,ld(X1,X1))),X1),
inference(superposition,[],[f4,f7]) ).
fof(f19,plain,
! [X0] : rd(X0,X0) = ld(X0,mult(X0,ld(X0,X0))),
inference(forward_demodulation,[],[f14,f2]) ).
fof(f20,plain,
! [X0] : rd(X0,X0) = ld(X0,ld(X0,mult(X0,X0))),
inference(forward_demodulation,[],[f19,f3]) ).
fof(f21,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(forward_demodulation,[],[f20,f1]) ).
fof(f24,plain,
! [X0,X1] : mult(ld(X0,mult(X0,ld(X1,X1))),X1) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(backward_demodulation,[],[f18,f21]) ).
fof(f26,plain,
! [X0] : rd(mult(X0,X0),X0) = mult(ld(X0,X0),X0),
inference(superposition,[],[f4,f21]) ).
fof(f27,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(forward_demodulation,[],[f26,f2]) ).
fof(f35,plain,
! [X2,X0,X1] : mult(ld(X0,mult(X0,X1)),X2) = ld(X0,mult(X0,mult(X1,X2))),
inference(superposition,[],[f5,f1]) ).
fof(f47,plain,
! [X2,X0,X1] : mult(X0,X2) = ld(ld(X0,X1),mult(ld(X0,X1),mult(X0,X2))),
inference(superposition,[],[f5,f1]) ).
fof(f59,plain,
! [X0,X1] : rd(mult(mult(ld(X0,X0),X1),X1),X1) = ld(X0,mult(X0,mult(ld(X1,X1),X1))),
inference(backward_demodulation,[],[f24,f35]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = ld(X0,mult(X0,mult(X2,X3))),
inference(backward_demodulation,[],[f5,f35]) ).
fof(f77,plain,
! [X2,X0] : mult(X0,X2) = ld(X0,mult(X0,mult(X0,X2))),
inference(backward_demodulation,[],[f47,f60]) ).
fof(f91,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(forward_demodulation,[],[f59,f27]) ).
fof(f105,plain,
! [X2,X0,X1] : mult(ld(X0,X0),rd(mult(X0,X2),X2)) = rd(mult(X0,rd(X1,X2)),rd(X1,X2)),
inference(superposition,[],[f6,f27]) ).
fof(f106,plain,
! [X2,X0,X1] : mult(X1,rd(mult(X2,X0),X0)) = rd(mult(mult(X1,X2),X0),X0),
inference(superposition,[],[f6,f2]) ).
fof(f123,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X0,X0),rd(mult(X1,X1),X1)),
inference(backward_demodulation,[],[f91,f106]) ).
fof(f127,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[],[f123,f2]) ).
fof(f131,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = ld(X0,mult(X0,rd(mult(X0,X2),X2))),
inference(backward_demodulation,[],[f105,f127]) ).
fof(f282,plain,
! [X2,X0,X1] : mult(ld(X0,X0),rd(mult(X1,X2),X2)) = rd(mult(ld(X0,mult(X0,X1)),X2),X2),
inference(superposition,[],[f106,f127]) ).
fof(f297,plain,
! [X2,X0,X1] : mult(ld(X0,X0),rd(mult(X1,X2),X2)) = rd(ld(X0,mult(X0,mult(X1,X2))),X2),
inference(forward_demodulation,[],[f282,f35]) ).
fof(f304,plain,
! [X2,X0,X1] : ld(X0,mult(X0,rd(mult(X1,X2),X2))) = rd(ld(X0,mult(X0,mult(X1,X2))),X2),
inference(forward_demodulation,[],[f297,f127]) ).
fof(f307,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(ld(X0,mult(X0,mult(X0,X2))),X2),
inference(backward_demodulation,[],[f131,f304]) ).
fof(f311,plain,
! [X2,X0,X1] : rd(mult(X0,X2),X2) = rd(mult(X0,rd(X1,X2)),rd(X1,X2)),
inference(forward_demodulation,[],[f307,f77]) ).
fof(f317,plain,
~ sP0(rd(mult(x6,x8),x8)),
inference(backward_demodulation,[],[f9,f311]) ).
fof(f318,plain,
$false,
inference(forward_subsumption_resolution,[],[f317,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n010.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 10:36:16 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.67/1.42 % (768825)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.67/1.42 % (768931)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=4001180653:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.67/1.42 % (768932)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=1807640969:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.67/1.42 % (768934)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2348285893:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.67/1.42 % (768935)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2504354973:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.67/1.42 % (768933)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4263982831:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.67/1.42 % (768937)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=913317997:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.67/1.42 % (768936)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1177411830:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.67/1.42 % (768934)First to succeed.
% 3.67/1.42 % (768934)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-768825"
% 3.67/1.42 % (768937)Also succeeded, but the first one will report.
% 3.67/1.42 % (768936)Also succeeded, but the first one will report.
% 3.67/1.42 % (768935)Also succeeded, but the first one will report.
% 3.67/1.42 % (768934)Refutation found. Thanks to Tanya!
% 3.67/1.42 % SZS status Unsatisfiable for theBenchmark
% 3.67/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.42 % (768934)------------------------------
% 3.67/1.42 % (768934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.42 % (768934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.42 % (768934)CaDiCaL version: 2.1.3
% 3.67/1.42 % (768934)Termination reason: Refutation
% 3.67/1.42 % (768934)Time elapsed: 0.019 s
% 3.67/1.42 % (768934)Peak memory usage: 87 MB
% 3.67/1.42 % (768934)Instructions burned: 26 (million)
% 3.67/1.42 % (768934)------------------------------
% 3.67/1.42 % (768934)------------------------------
% 3.67/1.42 % (768825)Success in time 0.444 s
% 3.67/1.42 % Vampire exiting
%------------------------------------------------------------------------------