%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP729-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 10:16:04 AM UTC 2026
% Result : Unsatisfiable 0.29s 3.42s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
fof(f5,axiom,
! [X0] : mult(i(X0),X0) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
fof(f6,plain,
! [X0] : unit = mult(i(X0),X0),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : i(mult(X0,X1)) = mult(i(X0),i(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
fof(f8,axiom,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
fof(f12,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,X2)),asoc(X0,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
fof(f13,axiom,
! [X0,X1] : mult(X0,X1) = mult(mult(X1,X0),op_k(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
fof(f25,axiom,
! [X2,X3,X0,X1,X4] : asoc(X0,X1,asoc(X2,X3,X4)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22) ).
fof(f26,plain,
! [X2,X3,X0,X1,X4] : unit = asoc(X0,X1,asoc(X2,X3,X4)),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
asoc(a,b,op_k(c,d)) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,plain,
unit != asoc(a,b,op_k(c,d)),
inference(reorient_equations,[],[f27]) ).
fof(f58,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = mult(unit,asoc(i(mult(X0,X1)),X0,X1)),
inference(superposition,[],[f12,f6]) ).
fof(f60,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = asoc(i(mult(X0,X1)),X0,X1),
inference(forward_demodulation,[],[f58,f1]) ).
fof(f84,plain,
! [X0,X1] : op_k(X0,X1) = mult(i(mult(X1,X0)),mult(X0,X1)),
inference(superposition,[],[f8,f13]) ).
fof(f99,plain,
! [X0,X1] : mult(mult(i(X0),i(X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(superposition,[],[f60,f8]) ).
fof(f112,plain,
! [X0,X1] : mult(i(mult(X0,X1)),mult(X1,X0)) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f99,f7]) ).
fof(f122,plain,
! [X0,X1] : op_k(X1,X0) = asoc(i(X0),i(X1),mult(X1,X0)),
inference(forward_demodulation,[],[f112,f84]) ).
fof(f217,plain,
! [X2,X3,X0,X1] : unit = asoc(X2,X3,op_k(X0,X1)),
inference(superposition,[],[f26,f122]) ).
fof(f234,plain,
unit != unit,
inference(superposition,[],[f28,f217]) ).
fof(f235,plain,
$false,
inference(trivial_inequality_removal,[],[f234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP729-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n001.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 27 10:47:15 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 0.29/3.42 % (3374266)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.29/3.42 % (3374277)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3124805206:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.29/3.42 % (3374271)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=2553807388:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.29/3.42 % (3374274)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=651050174:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.29/3.42 % (3374272)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=2580916993:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.29/3.42 % (3374273)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2060293894:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.29/3.42 % (3374275)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1963052002:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.29/3.42 % (3374276)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2252440909:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.29/3.42 % (3374274)Instruction limit reached!
% 0.29/3.42 % (3374274)------------------------------
% 0.29/3.42 % (3374274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374274)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374274)Termination reason: Instruction limit
% 0.29/3.42 % (3374274)Termination phase: Saturation
% 0.29/3.42 % (3374274)Time elapsed: 0.130 s
% 0.29/3.42 % (3374274)Peak memory usage: 89 MB
% 0.29/3.42 % (3374274)Instructions burned: 136 (million)
% 0.29/3.42 % (3374275)Instruction limit reached!
% 0.29/3.42 % (3374275)------------------------------
% 0.29/3.42 % (3374275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374275)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374275)Termination reason: Instruction limit
% 0.29/3.42 % (3374275)Termination phase: Saturation
% 0.29/3.42 % (3374275)Time elapsed: 0.170 s
% 0.29/3.42 % (3374275)Peak memory usage: 90 MB
% 0.29/3.42 % (3374275)Instructions burned: 182 (million)
% 0.29/3.42 % (3374276)Instruction limit reached!
% 0.29/3.42 % (3374276)------------------------------
% 0.29/3.42 % (3374276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374276)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374276)Termination reason: Instruction limit
% 0.29/3.42 % (3374276)Termination phase: Saturation
% 0.29/3.42 % (3374276)Time elapsed: 0.256 s
% 0.29/3.42 % (3374276)Peak memory usage: 90 MB
% 0.29/3.42 % (3374276)Instructions burned: 257 (million)
% 0.29/3.42 % (3374285)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=846404359:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 0.29/3.42 % (3374286)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1933748652:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 0.29/3.42 % (3374277)Instruction limit reached!
% 0.29/3.42 % (3374277)------------------------------
% 0.29/3.42 % (3374277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374277)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374277)Termination reason: Instruction limit
% 0.29/3.42 % (3374277)Termination phase: Saturation
% 0.29/3.42 % (3374277)Time elapsed: 0.591 s
% 0.29/3.42 % (3374277)Peak memory usage: 101 MB
% 0.29/3.42 % (3374277)Instructions burned: 1188 (million)
% 0.29/3.42 % (3374287)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1314887263:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 0.29/3.42 % (3374290)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=3068530338: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)
% 0.29/3.42 % (3374287)Instruction limit reached!
% 0.29/3.42 % (3374287)------------------------------
% 0.29/3.42 % (3374287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374287)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374287)Termination reason: Instruction limit
% 0.29/3.42 % (3374287)Termination phase: Saturation
% 0.29/3.42 % (3374287)Time elapsed: 0.213 s
% 0.29/3.42 % (3374287)Peak memory usage: 90 MB
% 0.29/3.42 % (3374287)Instructions burned: 215 (million)
% 0.29/3.42 % (3374290)Instruction limit reached!
% 0.29/3.42 % (3374290)------------------------------
% 0.29/3.42 % (3374290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374290)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374290)Termination reason: Instruction limit
% 0.29/3.42 % (3374290)Termination phase: Saturation
% 0.29/3.42 % (3374290)Time elapsed: 0.171 s
% 0.29/3.42 % (3374290)Peak memory usage: 93 MB
% 0.29/3.42 % (3374290)Instructions burned: 317 (million)
% 0.29/3.42 % (3374272)First to succeed.
% 0.29/3.42 % (3374272)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3374266"
% 0.29/3.42 % (3374293)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=3548902377:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/12125Mi)
% 0.29/3.42 % (3374294)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2984119218:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2987 on theBenchmark for (2987ds/2836Mi)
% 0.29/3.42 % (3374272)Refutation found. Thanks to Tanya!
% 0.29/3.42 % SZS status Unsatisfiable for theBenchmark
% 0.29/3.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/3.42 % (3374272)------------------------------
% 0.29/3.42 % (3374272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/3.42 % (3374272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/3.42 % (3374272)CaDiCaL version: 2.1.3
% 0.29/3.42 % (3374272)Termination reason: Refutation
% 0.29/3.42 % (3374272)Time elapsed: 1.027 s
% 0.29/3.42 % (3374272)Peak memory usage: 129 MB
% 0.29/3.42 % (3374272)Instructions burned: 957 (million)
% 0.29/3.42 % (3374272)------------------------------
% 0.29/3.42 % (3374272)------------------------------
% 0.29/3.42 % (3374266)Success in time 1.753 s
% 0.29/3.42 % Vampire exiting
%------------------------------------------------------------------------------