%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 10:12:06 AM UTC 2026
% Result : Unsatisfiable 2.67s 1.44s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f2,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f3,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
multiply(b,c) = multiply(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_equality) ).
fof(f6,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation) ).
fof(f8,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f1,f4]) ).
fof(f9,plain,
! [X0] : multiply(d,multiply(c,X0)) = multiply(multiply(b,c),X0),
inference(superposition,[],[f1,f5]) ).
fof(f12,plain,
! [X0] : multiply(d,multiply(c,X0)) = multiply(b,multiply(c,X0)),
inference(forward_demodulation,[],[f9,f1]) ).
fof(f13,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f8,f2]) ).
fof(f16,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f13,f4]) ).
fof(f26,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f13,f16]) ).
fof(f50,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f13,f26]) ).
fof(f54,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f50,f16]) ).
fof(f57,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f16,f54]) ).
fof(f63,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f4,f54]) ).
fof(f90,plain,
multiply(d,identity) = multiply(b,identity),
inference(superposition,[],[f12,f63]) ).
fof(f95,plain,
b = multiply(d,identity),
inference(forward_demodulation,[],[f90,f57]) ).
fof(f98,plain,
b = d,
inference(forward_demodulation,[],[f95,f57]) ).
fof(f99,plain,
$false,
inference(forward_subsumption_resolution,[],[f98,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:13:30 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.67/1.44 % (2134799)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.67/1.44 % (2134857)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=727762621:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.67/1.44 % (2134857)First to succeed.
% 2.67/1.44 % (2134857)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2134799"
% 2.67/1.44 % (2134855)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4032314502:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.67/1.44 % (2134852)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3667934263:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.67/1.44 % (2134850)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1520783144:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.67/1.44 % (2134849)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=2257059239:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.67/1.44 % (2134847)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=4238229549:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.67/1.44 % (2134852)Also succeeded, but the first one will report.
% 2.67/1.44 % (2134855)Also succeeded, but the first one will report.
% 2.67/1.44 % (2134854)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1564640724:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.67/1.44 % (2134854)Also succeeded, but the first one will report.
% 2.67/1.44 % (2134857)Refutation found. Thanks to Tanya!
% 2.67/1.44 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.44 % (2134857)------------------------------
% 2.67/1.44 % (2134857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.44 % (2134857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.44 % (2134857)CaDiCaL version: 2.1.3
% 2.67/1.44 % (2134857)Termination reason: Refutation
% 2.67/1.44 % (2134857)Time elapsed: 0.002 s
% 2.67/1.44 % (2134857)Peak memory usage: 87 MB
% 2.67/1.44 % (2134857)Instructions burned: 4 (million)
% 2.67/1.44 % (2134857)------------------------------
% 2.67/1.44 % (2134857)------------------------------
% 2.67/1.44 % (2134799)Success in time 0.269 s
% 2.67/1.44 % Vampire exiting
%------------------------------------------------------------------------------