%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP001-2 : 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 : n012.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 10:12:03 AM UTC 2026
% Result : Unsatisfiable 1.97s 0.87s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 19 unt; 1 def)
% Number of atoms : 19 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f8,axiom,
! [X0] : multiply(X0,X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',squareness) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f11,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f12,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
~ sP0(multiply(b,a)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f14,plain,
sP0(c),
inference(inequality_splitting,[],[f12,f13]) ).
fof(f21,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f9]) ).
fof(f27,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[],[f4,f10]) ).
fof(f37,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f21,f1]) ).
fof(f65,plain,
identity = multiply(a,multiply(b,c)),
inference(superposition,[],[f9,f27]) ).
fof(f121,plain,
multiply(b,c) = multiply(a,identity),
inference(superposition,[],[f37,f65]) ).
fof(f124,plain,
a = multiply(b,c),
inference(forward_demodulation,[],[f121,f5]) ).
fof(f128,plain,
c = multiply(b,a),
inference(superposition,[],[f37,f124]) ).
fof(f131,plain,
~ sP0(c),
inference(backward_demodulation,[],[f13,f128]) ).
fof(f132,plain,
$false,
inference(forward_subsumption_resolution,[],[f131,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 27 09:12:05 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 Running first-order theorem proving
% 0.05/0.32 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
% 1.97/0.87 % (2097981)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.97/0.87 % (2097989)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3922714270:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.97/0.87 % (2097987)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=528080129:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.97/0.87 % (2097989)First to succeed.
% 1.97/0.87 % (2097989)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2097981"
% 1.97/0.87 % (2097988)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2710548843:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.97/0.87 % (2097990)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=550695773:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.97/0.87 % (2097986)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=204257719:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.97/0.87 % (2097990)Also succeeded, but the first one will report.
% 1.97/0.87 % (2097991)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=239863561:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.97/0.87 % (2097992)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2557771538:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.97/0.87 % (2097992)Also succeeded, but the first one will report.
% 1.97/0.87 % (2097991)Also succeeded, but the first one will report.
% 1.97/0.87 % (2097989)Refutation found. Thanks to Tanya!
% 1.97/0.87 % SZS status Unsatisfiable for theBenchmark
% 1.97/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 1.97/0.87 % (2097989)------------------------------
% 1.97/0.87 % (2097989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.97/0.87 % (2097989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.87 % (2097989)CaDiCaL version: 2.1.3
% 1.97/0.87 % (2097989)Termination reason: Refutation
% 1.97/0.87 % (2097989)Time elapsed: 0.002 s
% 1.97/0.87 % (2097989)Peak memory usage: 87 MB
% 1.97/0.87 % (2097989)Instructions burned: 5 (million)
% 1.97/0.87 % (2097989)------------------------------
% 1.97/0.87 % (2097989)------------------------------
% 1.97/0.87 % (2097981)Success in time 0.253 s
% 1.97/0.87 % Vampire exiting
%------------------------------------------------------------------------------