%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO011-2 : 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 : n016.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 09:35:51 AM UTC 2026
% Result : Unsatisfiable 3.63s 1.33s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 9 unt; 1 def)
% Number of atoms : 9 ( 5 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 2 ( 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
fof(f17,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
fof(f18,plain,
multiplicative_identity != inverse(additive_identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
~ sP0(inverse(additive_identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f20,plain,
sP0(multiplicative_identity),
inference(inequality_splitting,[],[f18,f19]) ).
fof(f29,plain,
multiplicative_identity = inverse(additive_identity),
inference(superposition,[],[f16,f7]) ).
fof(f35,plain,
~ sP0(multiplicative_identity),
inference(backward_demodulation,[],[f19,f29]) ).
fof(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO011-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n016.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:08:34 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running first-order theorem proving
% 0.10/0.25 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
% 3.63/1.33 % (4010261)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.63/1.33 % (4010335)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=2332945730:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.63/1.33 % (4010337)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=2889312164:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.63/1.33 % (4010340)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3915892384:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.63/1.33 % (4010338)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=327328554:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.63/1.33 % (4010340)First to succeed.
% 3.63/1.33 % (4010340)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4010261"
% 3.63/1.33 % (4010343)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1392559388:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.63/1.33 % (4010341)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1619381480:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.63/1.33 % (4010342)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2353504454:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.63/1.33 % (4010343)Also succeeded, but the first one will report.
% 3.63/1.33 % (4010342)Also succeeded, but the first one will report.
% 3.63/1.33 % (4010341)Also succeeded, but the first one will report.
% 3.63/1.33 % (4010340)Refutation found. Thanks to Tanya!
% 3.63/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.33 % (4010340)------------------------------
% 3.63/1.33 % (4010340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.33 % (4010340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.33 % (4010340)CaDiCaL version: 2.1.3
% 3.63/1.33 % (4010340)Termination reason: Refutation
% 3.63/1.33 % (4010340)Time elapsed: 0.002 s
% 3.63/1.33 % (4010340)Peak memory usage: 88 MB
% 3.63/1.33 % (4010340)Instructions burned: 1 (million)
% 3.63/1.33 % (4010340)------------------------------
% 3.63/1.33 % (4010340)------------------------------
% 3.63/1.33 % (4010261)Success in time 0.434 s
% 3.63/1.33 % Vampire exiting
%------------------------------------------------------------------------------