%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:49:47 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 11 unt; 1 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 29 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
fof(f29,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
fof(f32,plain,
! [X0] :
( ~ sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ~ sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_or_equal(X0,X1)
| less_or_equal(X2,X3)
| sum(X2,X4,X0)
| sum(X3,X4,X1) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f51,plain,
~ less_or_equal(additive_identity,a),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f52,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f68,definition,
( spl0_3
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f69,plain,
( defined(additive_inverse(a))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
( ~ defined(additive_inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f76,plain,
( ~ defined(a)
| spl0_3 ),
inference(resolution,[],[f70,f15]) ).
fof(f77,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f76,f27]) ).
fof(f78,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f79,plain,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| sum(X0,X2,additive_inverse(a))
| sum(X1,X2,additive_identity) ),
inference(resolution,[],[f48,f52]) ).
fof(f108,plain,
! [X0] :
( less_or_equal(additive_identity,X0)
| sum(X0,additive_inverse(a),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f79,f32]) ).
fof(f119,plain,
( ! [X0] :
( sum(X0,additive_inverse(a),additive_identity)
| less_or_equal(additive_identity,X0) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f108,f69]) ).
fof(f133,plain,
( ! [X0] :
( sum(additive_inverse(a),X0,additive_identity)
| less_or_equal(additive_identity,X0) )
| ~ spl0_3 ),
inference(resolution,[],[f119,f34]) ).
fof(f394,plain,
( less_or_equal(additive_identity,a)
| ~ defined(a)
| ~ spl0_3 ),
inference(resolution,[],[f133,f33]) ).
fof(f399,plain,
( ~ defined(a)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f394,f51]) ).
fof(f400,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f399,f27]) ).
fof(f401,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f400]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
~ spl0_3,
inference(sat_conversion,[],[f401]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s10]) ).
fof(f402,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 00:53:34 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (913735)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (913746)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2584752277:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.26 % (913742)% WARNING: option uhcvi not known.
% 0.09/0.26 % (913742)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2082513354:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (913743)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=879214919:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (913747)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=991146393:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (913741)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2957128815_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (913745)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1409191646:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % TRYING [1]
% 0.09/0.26 % TRYING [2]
% 0.09/0.26 % TRYING [3]
% 0.09/0.26 % (913744)dis+10_1_sil=32000:sp=arity:random_seed=3880383559:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (913742) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-913735-913742"...
% 0.09/0.26 % TRYING [4]
% 0.09/0.26 % (913742)...printing done.
% 0.09/0.26 % (913742)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (913742)------------------------------
% 0.09/0.26 % (913742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (913742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (913742)CaDiCaL version: 2.1.3
% 0.09/0.26 % (913742)Termination reason: Refutation
% 0.09/0.26 % (913742)Time elapsed: 0.018 s
% 0.09/0.26 % (913742)Peak memory usage: 12 MB
% 0.09/0.26 % (913742)Instructions burned: 17 (million)
% 0.09/0.26 % (913735)Success in time 0.052 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------