%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP195-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 10:13:18 AM UTC 2026
% Result : Unsatisfiable 3.51s 1.39s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,multiply(X1,X1)) = multiply(X1,multiply(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f3,negated_conjecture,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f7,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,X0),X2)) = multiply(multiply(X0,multiply(X1,X1)),X2),
inference(superposition,[],[f1,f2]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(X1,X2))) = multiply(X1,multiply(X2,multiply(X0,X0))),
inference(superposition,[],[f1,f2]) ).
fof(f14,plain,
! [X2,X0,X1] : multiply(X2,multiply(multiply(X0,X1),multiply(X0,X1))) = multiply(multiply(X0,X1),multiply(X0,multiply(X1,X2))),
inference(superposition,[],[f2,f1]) ).
fof(f15,plain,
! [X2,X0,X1] : multiply(X2,multiply(multiply(X0,X1),multiply(X0,X1))) = multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f14,f1]) ).
fof(f20,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,X0),X2)) = multiply(X0,multiply(multiply(X1,X1),X2)),
inference(forward_demodulation,[],[f7,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,multiply(X1,multiply(X0,X1)))) = multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f15,f1]) ).
fof(f27,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,X0),X2)) = multiply(X0,multiply(X1,multiply(X1,X2))),
inference(forward_demodulation,[],[f20,f1]) ).
fof(f29,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(X1,X2))) = multiply(X1,multiply(X1,multiply(X0,X2))),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f139,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(X2,X2))) = multiply(X0,multiply(X2,multiply(X2,X1))),
inference(superposition,[],[f29,f9]) ).
fof(f689,plain,
multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) != multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,b))))))),
inference(superposition,[],[f3,f22]) ).
fof(f710,plain,
multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) != multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,b))))))),
inference(forward_demodulation,[],[f689,f29]) ).
fof(f781,plain,
multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(multiply(b,b),multiply(b,b)))))),
inference(forward_demodulation,[],[f710,f9]) ).
fof(f838,plain,
multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
inference(forward_demodulation,[],[f781,f139]) ).
fof(f839,plain,
$false,
inference(trivial_inequality_removal,[],[f838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP195-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:39:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 3.51/1.39 % (3296603)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.51/1.39 % (3296615)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=248696690:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.51/1.39 % (3296616)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=4109254816:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.51/1.39 % (3296618)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4160525147:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.51/1.39 % (3296621)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2936604235:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.51/1.39 % (3296617)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2050061130:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.51/1.39 % (3296620)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1614969345:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.51/1.39 % (3296619)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3879958504:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.51/1.39 % (3296621)First to succeed.
% 3.51/1.39 % (3296621)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3296603"
% 3.51/1.39 % (3296618)Also succeeded, but the first one will report.
% 3.51/1.39 % (3296619)Instruction limit reached!
% 3.51/1.39 % (3296619)------------------------------
% 3.51/1.39 % (3296619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (3296619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (3296619)CaDiCaL version: 2.1.3
% 3.51/1.39 % (3296619)Termination reason: Instruction limit
% 3.51/1.39 % (3296619)Termination phase: Saturation
% 3.51/1.39 % (3296619)Time elapsed: 0.086 s
% 3.51/1.39 % (3296619)Peak memory usage: 89 MB
% 3.51/1.39 % (3296619)Instructions burned: 181 (million)
% 3.51/1.39 % (3296620)Instruction limit reached!
% 3.51/1.39 % (3296620)------------------------------
% 3.51/1.39 % (3296620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (3296620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (3296620)CaDiCaL version: 2.1.3
% 3.51/1.39 % (3296620)Termination reason: Instruction limit
% 3.51/1.39 % (3296620)Termination phase: Saturation
% 3.51/1.39 % (3296620)Time elapsed: 0.139 s
% 3.51/1.39 % (3296620)Peak memory usage: 90 MB
% 3.51/1.39 % (3296620)Instructions burned: 258 (million)
% 3.51/1.39 % (3296707)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1181153201:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.51/1.39 % (3296621)Refutation found. Thanks to Tanya!
% 3.51/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.39 % (3296621)------------------------------
% 3.51/1.39 % (3296621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (3296621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (3296621)CaDiCaL version: 2.1.3
% 3.51/1.39 % (3296621)Termination reason: Refutation
% 3.51/1.39 % (3296621)Time elapsed: 0.018 s
% 3.51/1.39 % (3296621)Peak memory usage: 88 MB
% 3.51/1.39 % (3296621)Instructions burned: 33 (million)
% 3.51/1.39 % (3296621)------------------------------
% 3.51/1.39 % (3296621)------------------------------
% 3.51/1.39 % (3296603)Success in time 0.439 s
% 3.51/1.39 % Vampire exiting
%------------------------------------------------------------------------------