%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG235-1 : 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 : n009.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 09:19:32 AM UTC 2026
% Result : Unsatisfiable 3.61s 1.20s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 1 def)
% Number of atoms : 23 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,mult(X1,mult(X0,X1))) = mult(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X1,mult(X0,X1))),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] : mult(X0,mult(X1,mult(X2,X3))) = mult(X2,mult(X1,mult(X0,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : mult(mult(X0,mult(X1,mult(X2,X1))),X3) = mult(X0,mult(X3,mult(mult(X2,X1),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f5,negated_conjecture,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f6,definition,
~ sP0(mult(a,mult(b,mult(a,mult(c,mult(d,c)))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f7,plain,
sP0(mult(a,mult(b,mult(d,c)))),
inference(inequality_splitting,[],[f5,f6]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : mult(X0,mult(X2,mult(X3,mult(X1,mult(X0,X1))))) = mult(X3,mult(X2,mult(X0,X1))),
inference(superposition,[],[f3,f2]) ).
fof(f18,plain,
! [X2,X0,X1] : mult(X2,mult(X0,X1)) = mult(X1,mult(X0,mult(X2,mult(X0,X1)))),
inference(superposition,[],[f3,f2]) ).
fof(f29,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(X0,mult(X2,mult(mult(X0,X1),X2))),
inference(superposition,[],[f4,f2]) ).
fof(f94,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,X1),mult(X1,mult(X0,X1))),
inference(superposition,[],[f18,f2]) ).
fof(f96,plain,
! [X2,X3,X0,X1] : mult(X0,mult(X1,mult(X2,X3))) = mult(mult(X0,X3),mult(X1,mult(X0,mult(X1,mult(X2,X3))))),
inference(superposition,[],[f18,f3]) ).
fof(f145,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X1,mult(mult(X0,X1),X1))),
inference(superposition,[],[f3,f94]) ).
fof(f159,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,X1),X1),
inference(forward_demodulation,[],[f145,f29]) ).
fof(f204,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(mult(X0,X1),mult(X2,mult(X0,X2))),
inference(superposition,[],[f3,f29]) ).
fof(f336,plain,
! [X2,X3,X0,X1] : mult(mult(X1,X3),mult(X0,X2)) = mult(mult(X1,X3),mult(X0,mult(X1,mult(mult(X0,X2),X2)))),
inference(superposition,[],[f204,f3]) ).
fof(f373,plain,
! [X2,X3,X0,X1] : mult(mult(X1,X3),mult(X0,X2)) = mult(mult(X1,X3),mult(X0,mult(X1,mult(X0,X2)))),
inference(forward_demodulation,[],[f336,f159]) ).
fof(f385,plain,
! [X2,X3,X0,X1] : mult(X0,mult(X1,mult(X2,X3))) = mult(mult(X0,X3),mult(X1,mult(X2,X3))),
inference(backward_demodulation,[],[f96,f373]) ).
fof(f469,plain,
! [X2,X3,X0,X1] : mult(X0,mult(X1,mult(X2,X3))) = mult(mult(X0,mult(X1,mult(X2,X3))),mult(X1,mult(X0,mult(X3,mult(X2,X3))))),
inference(superposition,[],[f159,f15]) ).
fof(f608,plain,
! [X2,X3,X0,X1,X4] : mult(X4,mult(X0,mult(X1,mult(X2,X3)))) = mult(mult(X4,mult(X0,X3)),mult(X0,mult(X1,mult(X2,X3)))),
inference(superposition,[],[f385,f3]) ).
fof(f699,plain,
! [X2,X3,X0,X1] : mult(X0,mult(X1,mult(X2,X3))) = mult(X0,mult(X1,mult(X0,mult(X3,mult(X2,X3))))),
inference(backward_demodulation,[],[f469,f608]) ).
fof(f716,plain,
~ sP0(mult(a,mult(b,mult(d,c)))),
inference(backward_demodulation,[],[f6,f699]) ).
fof(f722,plain,
$false,
inference(forward_subsumption_resolution,[],[f716,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG235-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 19:57:00 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 3.61/1.20 % (3396073)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.61/1.20 % (3396317)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=695693035:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.61/1.20 % (3396315)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=483548974:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.61/1.20 % (3396320)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=13470652:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.61/1.20 % (3396319)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1332771573:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.61/1.20 % (3396314)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=1611004441:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.61/1.20 % (3396324)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4016118130:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.61/1.20 % (3396322)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2808050884:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.61/1.20 % (3396319)First to succeed.
% 3.61/1.20 % (3396319)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3396073"
% 3.61/1.20 % (3396322)Also succeeded, but the first one will report.
% 3.61/1.20 % (3396320)Instruction limit reached!
% 3.61/1.20 % (3396320)------------------------------
% 3.61/1.20 % (3396320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.20 % (3396320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.20 % (3396320)CaDiCaL version: 2.1.3
% 3.61/1.20 % (3396320)Termination reason: Instruction limit
% 3.61/1.20 % (3396320)Termination phase: Saturation
% 3.61/1.20 % (3396320)Time elapsed: 0.102 s
% 3.61/1.20 % (3396320)Peak memory usage: 89 MB
% 3.61/1.20 % (3396320)Instructions burned: 181 (million)
% 3.61/1.20 % (3396324)Also succeeded, but the first one will report.
% 3.61/1.20 % (3396436)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1008319313:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.61/1.20 % (3396319)Refutation found. Thanks to Tanya!
% 3.61/1.20 % SZS status Unsatisfiable for theBenchmark
% 3.61/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.20 % (3396319)------------------------------
% 3.61/1.20 % (3396319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.20 % (3396319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.20 % (3396319)CaDiCaL version: 2.1.3
% 3.61/1.20 % (3396319)Termination reason: Refutation
% 3.61/1.20 % (3396319)Time elapsed: 0.035 s
% 3.61/1.20 % (3396319)Peak memory usage: 88 MB
% 3.61/1.20 % (3396319)Instructions burned: 57 (million)
% 3.61/1.20 % (3396319)------------------------------
% 3.61/1.20 % (3396319)------------------------------
% 3.61/1.20 % (3396073)Success in time 0.44 s
% 3.61/1.20 % Vampire exiting
%------------------------------------------------------------------------------