%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:13:10 AM UTC 2026
% Result : Unsatisfiable 5.89s 1.98s
% Output : Refutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 17 unt; 1 def)
% Number of atoms : 17 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f17,axiom,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04a_1) ).
fof(f18,plain,
a = least_upper_bound(identity,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04a_2) ).
fof(f20,plain,
b = least_upper_bound(identity,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p04a) ).
fof(f22,plain,
multiply(a,b) != least_upper_bound(identity,multiply(a,b)),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
~ sP0(multiply(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(least_upper_bound(identity,multiply(a,b))),
inference(inequality_splitting,[],[f22,f23]) ).
fof(f86,plain,
! [X0] : least_upper_bound(b,X0) = least_upper_bound(identity,least_upper_bound(b,X0)),
inference(superposition,[],[f8,f20]) ).
fof(f210,plain,
! [X0] : multiply(a,X0) = least_upper_bound(multiply(identity,X0),multiply(a,X0)),
inference(superposition,[],[f15,f18]) ).
fof(f229,plain,
! [X0] : multiply(a,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(forward_demodulation,[],[f210,f1]) ).
fof(f433,plain,
multiply(a,b) = least_upper_bound(identity,multiply(a,b)),
inference(superposition,[],[f86,f229]) ).
fof(f434,plain,
sP0(multiply(a,b)),
inference(backward_demodulation,[],[f24,f433]) ).
fof(f439,plain,
$false,
inference(forward_subsumption_resolution,[],[f434,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 09:37:51 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 5.89/1.98 % (3290684)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.89/1.98 % (3290691)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3858966137:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.89/1.98 % (3290689)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=511864648:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.89/1.98 % (3290690)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=3454124273:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.89/1.98 % (3290695)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=120913207:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.89/1.98 % (3290693)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=436577715:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.89/1.98 % (3290692)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=584042775:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.89/1.98 % (3290694)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2768526180:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.89/1.98 % (3290692)First to succeed.
% 5.89/1.98 % (3290692)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3290684"
% 5.89/1.98 % (3290695)Also succeeded, but the first one will report.
% 5.89/1.98 % (3290693)Instruction limit reached!
% 5.89/1.98 % (3290693)------------------------------
% 5.89/1.98 % (3290693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.98 % (3290693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.98 % (3290693)CaDiCaL version: 2.1.3
% 5.89/1.98 % (3290693)Termination reason: Instruction limit
% 5.89/1.98 % (3290693)Termination phase: Saturation
% 5.89/1.98 % (3290693)Time elapsed: 0.171 s
% 5.89/1.98 % (3290693)Peak memory usage: 89 MB
% 5.89/1.98 % (3290693)Instructions burned: 181 (million)
% 5.89/1.98 % (3290694)Instruction limit reached!
% 5.89/1.98 % (3290694)------------------------------
% 5.89/1.98 % (3290694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.98 % (3290694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.98 % (3290694)CaDiCaL version: 2.1.3
% 5.89/1.98 % (3290694)Termination reason: Instruction limit
% 5.89/1.98 % (3290694)Termination phase: Saturation
% 5.89/1.98 % (3290694)Time elapsed: 0.270 s
% 5.89/1.98 % (3290694)Peak memory usage: 91 MB
% 5.89/1.98 % (3290694)Instructions burned: 257 (million)
% 5.89/1.98 % (3290703)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1568615507:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 5.89/1.98 % (3290692)Refutation found. Thanks to Tanya!
% 5.89/1.98 % SZS status Unsatisfiable for theBenchmark
% 5.89/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 5.89/1.98 % (3290692)------------------------------
% 5.89/1.98 % (3290692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.98 % (3290692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.98 % (3290692)CaDiCaL version: 2.1.3
% 5.89/1.98 % (3290692)Termination reason: Refutation
% 5.89/1.98 % (3290692)Time elapsed: 0.022 s
% 5.89/1.98 % (3290692)Peak memory usage: 88 MB
% 5.89/1.98 % (3290692)Instructions burned: 19 (million)
% 5.89/1.98 % (3290692)------------------------------
% 5.89/1.98 % (3290692)------------------------------
% 5.89/1.98 % (3290684)Success in time 0.731 s
% 5.89/1.98 % Vampire exiting
%------------------------------------------------------------------------------