%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : FLD020-3 : 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 : 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 09:49:35 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.29s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 13 unt; 3 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 34 ~; 30 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
sum(m,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,m,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X4,X1,X5)
| sum(X3,X4,X0)
| ~ sum(X0,X1,X2)
| sum(X3,X5,X2) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f34,plain,
! [X0] :
( ~ sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f47,plain,
~ sum(m,a,a),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f48,plain,
sum(additive_identity,m,additive_identity),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f49,plain,
~ sum(a,m,a),
inference(resolution,[],[f35,f47]) ).
fof(f469,definition,
( spl0_39
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f471,plain,
( ~ defined(a)
| spl0_39 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f488,plain,
( $false
| spl0_39 ),
inference(resolution,[],[f471,f27]) ).
fof(f489,plain,
spl0_39,
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f576,plain,
! [X2,X0,X1] :
( sum(X0,a,X2)
| ~ sum(X1,m,X2)
| sum(X0,a,X1) ),
inference(resolution,[],[f32,f49]) ).
fof(f855,plain,
! [X0] :
( ~ sum(X0,m,additive_identity)
| sum(additive_inverse(a),a,X0)
| ~ defined(a) ),
inference(resolution,[],[f576,f34]) ).
fof(f867,definition,
( spl0_68
<=> ! [X0] :
( ~ sum(X0,m,additive_identity)
| sum(additive_inverse(a),a,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_68])],[avatar_definition]) ).
fof(f868,plain,
( ! [X0] :
( sum(additive_inverse(a),a,X0)
| ~ sum(X0,m,additive_identity) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f869,plain,
( ~ spl0_39
| spl0_68 ),
inference(avatar_split_clause,[],[f855,f867,f469]) ).
fof(f948,plain,
( ~ sum(additive_identity,m,additive_identity)
| ~ defined(a)
| ~ spl0_68 ),
inference(resolution,[],[f868,f34]) ).
fof(f966,definition,
( spl0_76
<=> sum(additive_identity,m,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_76])],[avatar_definition]) ).
fof(f968,plain,
( ~ sum(additive_identity,m,additive_identity)
| spl0_76 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f969,plain,
( ~ spl0_39
| ~ spl0_76
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f948,f867,f966,f469]) ).
fof(f972,plain,
( $false
| spl0_76 ),
inference(resolution,[],[f968,f48]) ).
fof(f978,plain,
spl0_76,
inference(avatar_contradiction_clause,[],[f972]) ).
cnf(s46,plain,
spl0_39,
inference(sat_conversion,[],[f489]) ).
cnf(s74,plain,
( ~ spl0_39
| spl0_68 ),
inference(sat_conversion,[],[f869]) ).
cnf(s82,plain,
( ~ spl0_39
| ~ spl0_68
| ~ spl0_76 ),
inference(sat_conversion,[],[f969]) ).
cnf(s84,plain,
spl0_76,
inference(sat_conversion,[],[f978]) ).
cnf(s85,plain,
( ~ spl0_39
| ~ spl0_68 ),
inference(rat,[],[s82,s84]) ).
cnf(s98,plain,
~ spl0_68,
inference(rat,[],[s85,s46]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s74,s98,s46]) ).
fof(f979,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD020-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:23:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.29 % (421294)Will run a generic schedule for satisfiability detection.
% 0.18/0.29 % (421301)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=717901791:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.29 % (421300)% WARNING: option uhcvi not known.
% 0.18/0.29 % (421299)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2433853379_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.29 % (421300)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2895891569:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.29 % (421302)dis+10_1_sil=32000:sp=arity:random_seed=1923667254:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.29 % (421304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3694164473:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.29 % (421303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1903933505:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.29 % (421305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1901180656:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.29 % TRYING [1]
% 0.18/0.29 % TRYING [2]
% 0.18/0.29 % TRYING [3]
% 0.18/0.29 % TRYING [4]
% 0.18/0.29 % (421305) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-421294-421305"...
% 0.18/0.29 % (421305)...printing done.
% 0.18/0.29 % (421305)Refutation found. Thanks to Tanya!
% 0.18/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.29 % (421305)------------------------------
% 0.18/0.29 % (421305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (421305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (421305)CaDiCaL version: 2.1.3
% 0.18/0.29 % (421305)Termination reason: Refutation
% 0.18/0.29 % (421305)Time elapsed: 0.019 s
% 0.18/0.29 % (421305)Peak memory usage: 13 MB
% 0.18/0.29 % (421305)Instructions burned: 27 (million)
% 0.18/0.29 % (421294)Success in time 0.061 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------