%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:14:46 AM UTC 2026
% Result : Unsatisfiable 2.81s 1.40s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 19 unt; 1 def)
% Number of atoms : 19 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f3,definition,
~ sP0(multiply(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f4,plain,
sP0(multiply(b,a)),
inference(inequality_splitting,[],[f2,f3]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(inverse(X0),X3),multiply(multiply(inverse(multiply(X1,X2)),X0),X2))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f6,plain,
! [X2,X3,X0,X1] : multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0),X3) = multiply(X1,multiply(X0,X2)),
inference(superposition,[],[f1,f1]) ).
fof(f13,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[],[f5,f1]) ).
fof(f19,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(inverse(multiply(inverse(X1),X2)),X0),X2),
inference(superposition,[],[f13,f1]) ).
fof(f20,plain,
! [X2,X3,X0,X1] : multiply(X0,X1) = multiply(multiply(inverse(X2),X0),multiply(multiply(inverse(multiply(inverse(X1),X3)),X2),X3)),
inference(superposition,[],[f13,f5]) ).
fof(f24,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(inverse(X2),X0),multiply(X2,X1)),
inference(backward_demodulation,[],[f20,f19]) ).
fof(f26,plain,
! [X2,X0,X1] : multiply(X1,multiply(X0,X2)) = multiply(X0,multiply(X1,X2)),
inference(backward_demodulation,[],[f6,f19]) ).
fof(f48,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,X3)) = multiply(multiply(multiply(inverse(multiply(inverse(X1),X2)),X0),X2),X3),
inference(superposition,[],[f24,f1]) ).
fof(f65,plain,
! [X3,X0,X1] : multiply(X0,multiply(X1,X3)) = multiply(multiply(X0,X1),X3),
inference(forward_demodulation,[],[f48,f19]) ).
fof(f81,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(backward_demodulation,[],[f13,f65]) ).
fof(f126,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(superposition,[],[f26,f81]) ).
fof(f164,plain,
! [X2,X0,X1] : multiply(X1,X0) = multiply(X0,multiply(X1,multiply(inverse(X2),X2))),
inference(superposition,[],[f26,f126]) ).
fof(f170,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f164,f126]) ).
fof(f285,plain,
sP0(multiply(a,b)),
inference(superposition,[],[f4,f170]) ).
fof(f286,plain,
$false,
inference(forward_subsumption_resolution,[],[f285,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:06:51 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.81/1.40 % (3278063)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.81/1.40 % (3278125)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4261348421:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.81/1.40 % (3278123)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=3733273489:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.81/1.40 % (3278126)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3205626083:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.81/1.40 % (3278124)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3750516180:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.81/1.40 % (3278122)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=3078015738:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.81/1.40 % (3278125)First to succeed.
% 2.81/1.40 % (3278125)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3278063"
% 2.81/1.40 % (3278127)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3094091409:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.81/1.40 % (3278127)Also succeeded, but the first one will report.
% 2.81/1.40 % (3278126)Instruction limit reached!
% 2.81/1.40 % (3278126)------------------------------
% 2.81/1.40 % (3278126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.40 % (3278126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.40 % (3278126)CaDiCaL version: 2.1.3
% 2.81/1.40 % (3278126)Termination reason: Instruction limit
% 2.81/1.40 % (3278126)Termination phase: Saturation
% 2.81/1.40 % (3278126)Time elapsed: 0.102 s
% 2.81/1.40 % (3278126)Peak memory usage: 89 MB
% 2.81/1.40 % (3278126)Instructions burned: 183 (million)
% 2.81/1.40 % (3278128)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4087789569:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.81/1.40 % (3278128)Also succeeded, but the first one will report.
% 2.81/1.40 % (3278125)Refutation found. Thanks to Tanya!
% 2.81/1.40 % SZS status Unsatisfiable for theBenchmark
% 2.81/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.40 % (3278125)------------------------------
% 2.81/1.40 % (3278125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.40 % (3278125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.40 % (3278125)CaDiCaL version: 2.1.3
% 2.81/1.40 % (3278125)Termination reason: Refutation
% 2.81/1.40 % (3278125)Time elapsed: 0.007 s
% 2.81/1.40 % (3278125)Peak memory usage: 88 MB
% 2.81/1.40 % (3278125)Instructions burned: 17 (million)
% 2.81/1.40 % (3278125)------------------------------
% 2.81/1.40 % (3278125)------------------------------
% 2.81/1.40 % (3278063)Success in time 0.333 s
% 2.81/1.40 % Vampire exiting
%------------------------------------------------------------------------------