%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 10:13:09 AM UTC 2026
% Result : Unsatisfiable 3.49s 1.36s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 15 ( 15 unt; 1 def)
% Number of atoms : 15 ( 11 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 : 4 ( 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p01b_1) ).
fof(f18,plain,
a = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p01b) ).
fof(f20,plain,
multiply(inverse(c),multiply(a,c)) != greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
~ sP0(multiply(inverse(c),multiply(a,c))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f22,plain,
sP0(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))),
inference(inequality_splitting,[],[f20,f21]) ).
fof(f169,plain,
! [X0] : multiply(X0,a) = greatest_lower_bound(multiply(X0,a),multiply(X0,b)),
inference(superposition,[],[f14,f18]) ).
fof(f443,plain,
! [X0,X1] : multiply(multiply(X0,a),X1) = greatest_lower_bound(multiply(multiply(X0,a),X1),multiply(multiply(X0,b),X1)),
inference(superposition,[],[f16,f169]) ).
fof(f446,plain,
! [X0,X1] : multiply(multiply(X0,a),X1) = greatest_lower_bound(multiply(multiply(X0,a),X1),multiply(X0,multiply(b,X1))),
inference(forward_demodulation,[],[f443,f4]) ).
fof(f455,plain,
! [X0,X1] : multiply(X0,multiply(a,X1)) = greatest_lower_bound(multiply(X0,multiply(a,X1)),multiply(X0,multiply(b,X1))),
inference(forward_demodulation,[],[f446,f4]) ).
fof(f460,plain,
sP0(multiply(inverse(c),multiply(a,c))),
inference(backward_demodulation,[],[f22,f455]) ).
fof(f463,plain,
$false,
inference(forward_subsumption_resolution,[],[f460,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:40:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 3.49/1.36 % (3299277)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.49/1.36 % (3299286)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4047334862:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.49/1.36 % (3299283)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=613709276:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.49/1.36 % (3299282)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=3651919949:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.49/1.36 % (3299285)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3469118536:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.49/1.36 % (3299284)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=977696793:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.49/1.36 % (3299288)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1789850866:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.49/1.36 % (3299287)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1714008030:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.49/1.36 % (3299285)First to succeed.
% 3.49/1.36 % (3299285)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3299277"
% 3.49/1.36 % (3299288)Also succeeded, but the first one will report.
% 3.49/1.36 % (3299286)Instruction limit reached!
% 3.49/1.36 % (3299286)------------------------------
% 3.49/1.36 % (3299286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.36 % (3299286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.36 % (3299286)CaDiCaL version: 2.1.3
% 3.49/1.36 % (3299286)Termination reason: Instruction limit
% 3.49/1.36 % (3299286)Termination phase: Saturation
% 3.49/1.36 % (3299286)Time elapsed: 0.059 s
% 3.49/1.36 % (3299286)Peak memory usage: 89 MB
% 3.49/1.36 % (3299286)Instructions burned: 184 (million)
% 3.49/1.36 % (3299287)Also succeeded, but the first one will report.
% 3.49/1.36 % (3299296)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2660243918:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.49/1.36 % (3299285)Refutation found. Thanks to Tanya!
% 3.49/1.36 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.37 % (3299285)------------------------------
% 3.49/1.37 % (3299285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.37 % (3299285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.37 % (3299285)CaDiCaL version: 2.1.3
% 3.49/1.37 % (3299285)Termination reason: Refutation
% 3.49/1.37 % (3299285)Time elapsed: 0.013 s
% 3.49/1.37 % (3299285)Peak memory usage: 88 MB
% 3.49/1.37 % (3299285)Instructions burned: 19 (million)
% 3.49/1.37 % (3299285)------------------------------
% 3.49/1.37 % (3299285)------------------------------
% 3.49/1.37 % (3299277)Success in time 0.424 s
% 3.49/1.37 % Vampire exiting
%------------------------------------------------------------------------------