%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO003-2 : 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 : n005.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 09:35:48 AM UTC 2026
% Result : Unsatisfiable 6.60s 1.95s
% Output : Refutation 6.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 21 unt; 1 def)
% Number of atoms : 21 ( 17 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 : 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 : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f8,axiom,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f9,plain,
! [X0] : multiplicative_identity = add(inverse(X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f11,axiom,
! [X0] : multiply(inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f12,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f11]) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
fof(f17,negated_conjecture,
multiply(a,a) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_a_is_a) ).
fof(f18,plain,
a != multiply(a,a),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
~ sP0(multiply(a,a)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f20,plain,
sP0(a),
inference(inequality_splitting,[],[f18,f19]) ).
fof(f35,plain,
additive_identity = inverse(multiplicative_identity),
inference(superposition,[],[f14,f10]) ).
fof(f38,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(multiplicative_identity),
inference(backward_demodulation,[],[f12,f35]) ).
fof(f40,plain,
! [X0] : add(inverse(multiplicative_identity),X0) = X0,
inference(backward_demodulation,[],[f16,f35]) ).
fof(f77,plain,
! [X0,X1] : multiply(multiplicative_identity,X1) = add(multiply(inverse(X0),X1),multiply(X0,X1)),
inference(superposition,[],[f5,f9]) ).
fof(f89,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f77,f14]) ).
fof(f120,plain,
! [X0] : add(inverse(multiplicative_identity),multiply(X0,X0)) = X0,
inference(superposition,[],[f89,f38]) ).
fof(f147,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f120,f40]) ).
fof(f150,plain,
~ sP0(a),
inference(backward_demodulation,[],[f19,f147]) ).
fof(f151,plain,
$false,
inference(forward_subsumption_resolution,[],[f150,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n005.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 21:02:46 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running first-order theorem proving
% 0.24/0.30 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
% 6.60/1.95 % (1170760)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.60/1.95 % (1170769)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=32883611:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.60/1.95 % (1170767)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=3626243071:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.60/1.95 % (1170768)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=13983532:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.60/1.95 % (1170772)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3160253113:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.60/1.95 % (1170773)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2831810322:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.60/1.95 % (1170770)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=971490881:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.60/1.95 % (1170771)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2805048443:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.60/1.95 % (1170770)First to succeed.
% 6.60/1.95 % (1170770)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1170760"
% 6.60/1.95 % (1170771)Also succeeded, but the first one will report.
% 6.60/1.95 % (1170773)Also succeeded, but the first one will report.
% 6.60/1.95 % (1170772)Also succeeded, but the first one will report.
% 6.60/1.95 % (1170769)Also succeeded, but the first one will report.
% 6.60/1.95 % (1170770)Refutation found. Thanks to Tanya!
% 6.60/1.95 % SZS status Unsatisfiable for theBenchmark
% 6.60/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 6.60/1.95 % (1170770)------------------------------
% 6.60/1.95 % (1170770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/1.95 % (1170770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/1.95 % (1170770)CaDiCaL version: 2.1.3
% 6.60/1.95 % (1170770)Termination reason: Refutation
% 6.60/1.95 % (1170770)Time elapsed: 0.009 s
% 6.60/1.95 % (1170770)Peak memory usage: 88 MB
% 6.60/1.95 % (1170770)Instructions burned: 7 (million)
% 6.60/1.95 % (1170770)------------------------------
% 6.60/1.95 % (1170770)------------------------------
% 6.60/1.95 % (1170760)Success in time 0.833 s
% 6.60/1.95 % Vampire exiting
%------------------------------------------------------------------------------