%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO011-4 : 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 : n019.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 2.73s 1.17s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 22 unt; 3 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f5,negated_conjecture,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
fof(f12,plain,
multiplicative_identity != inverse(additive_identity),
inference(reorient_equations,[],[f11]) ).
fof(f23,definition,
! [X0] : sF4(X0) = add(X0,additive_identity),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f24,plain,
! [X0] : add(X0,additive_identity) = sF4(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : sF4(X0) = X0,
inference(definition_folding,[],[f5,f24]) ).
fof(f29,definition,
! [X0] : sF6(X0) = add(X0,inverse(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f30,plain,
! [X0] : add(X0,inverse(X0)) = sF6(X0),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
! [X0] : multiplicative_identity = sF6(X0),
inference(definition_folding,[],[f8,f30]) ).
fof(f35,definition,
sF8 = inverse(additive_identity),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f36,plain,
inverse(additive_identity) = sF8,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
multiplicative_identity != sF8,
inference(definition_folding,[],[f12,f36]) ).
fof(f39,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(forward_demodulation,[],[f31,f30]) ).
fof(f41,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f47,plain,
multiplicative_identity = add(additive_identity,sF8),
inference(superposition,[],[f39,f36]) ).
fof(f48,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f1,f41]) ).
fof(f52,plain,
multiplicative_identity = sF8,
inference(superposition,[],[f48,f47]) ).
fof(f64,plain,
multiplicative_identity != multiplicative_identity,
inference(superposition,[],[f37,f52]) ).
fof(f65,plain,
$false,
inference(trivial_inequality_removal,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 21:03:48 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.73/1.17 % (278263)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.73/1.17 % (278414)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3929932196:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.73/1.17 % (278414)First to succeed.
% 2.73/1.17 % (278414)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-278263"
% 2.73/1.17 % (278409)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=3627876443:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.73/1.17 % (278413)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3804916551:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.73/1.17 % (278417)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=329547280:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.73/1.17 % (278412)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3184150251:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.73/1.17 % (278415)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3461373760:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.73/1.17 % (278410)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=2506017020:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.73/1.17 % (278417)Also succeeded, but the first one will report.
% 2.73/1.17 % (278413)Also succeeded, but the first one will report.
% 2.73/1.17 % (278415)Also succeeded, but the first one will report.
% 2.73/1.17 % (278414)Refutation found. Thanks to Tanya!
% 2.73/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.17 % (278414)------------------------------
% 2.73/1.17 % (278414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (278414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (278414)CaDiCaL version: 2.1.3
% 2.73/1.17 % (278414)Termination reason: Refutation
% 2.73/1.17 % (278414)Time elapsed: 0.002 s
% 2.73/1.17 % (278414)Peak memory usage: 88 MB
% 2.73/1.17 % (278414)Instructions burned: 2 (million)
% 2.73/1.17 % (278414)------------------------------
% 2.73/1.17 % (278414)------------------------------
% 2.73/1.17 % (278263)Success in time 0.291 s
% 2.73/1.17 % Vampire exiting
%------------------------------------------------------------------------------