%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : FLD031-5 : 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 : n013.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 09:49:38 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 15 unt; 5 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 55 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f18,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
fof(f36,plain,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f39,plain,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f47,plain,
sum(additive_identity,a,additive_identity),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| ~ product(X0,X2,multiplicative_identity)
| ~ product(X1,X2,multiplicative_inverse(a)) ),
inference(resolution,[],[f6,f30]) ).
fof(f240,plain,
! [X0] :
( ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[],[f228,f8]) ).
fof(f244,definition,
( spl0_20
<=> defined(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f246,plain,
( ~ defined(multiplicative_inverse(a))
| spl0_20 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl0_21
<=> ! [X0] :
( ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(X0,multiplicative_inverse(a),multiplicative_identity) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f249,plain,
( ! [X0] :
( ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(X0,multiplicative_inverse(a),multiplicative_identity) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( ~ spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f240,f248,f244]) ).
fof(f261,plain,
( ~ defined(a)
| ~ sum(additive_identity,a,additive_identity)
| spl0_20 ),
inference(resolution,[],[f246,f39]) ).
fof(f263,definition,
( spl0_24
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f265,plain,
( ~ sum(additive_identity,a,additive_identity)
| spl0_24 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f267,definition,
( spl0_25
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f269,plain,
( ~ defined(a)
| spl0_25 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f270,plain,
( ~ spl0_24
| ~ spl0_25
| spl0_20 ),
inference(avatar_split_clause,[],[f261,f244,f267,f263]) ).
fof(f271,plain,
( $false
| spl0_25 ),
inference(resolution,[],[f269,f27]) ).
fof(f272,plain,
spl0_25,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f273,plain,
( $false
| spl0_24 ),
inference(resolution,[],[f265,f47]) ).
fof(f275,plain,
spl0_24,
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f285,plain,
( ! [X0] :
( ~ product(multiplicative_inverse(a),X0,multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) )
| ~ spl0_21 ),
inference(resolution,[],[f249,f10]) ).
fof(f309,plain,
( ~ product(multiplicative_identity,a,multiplicative_identity)
| ~ sum(additive_identity,a,additive_identity)
| ~ defined(a)
| ~ spl0_21 ),
inference(resolution,[],[f285,f36]) ).
fof(f313,definition,
( spl0_28
<=> product(multiplicative_identity,a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f315,plain,
( ~ product(multiplicative_identity,a,multiplicative_identity)
| spl0_28 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
( ~ spl0_25
| ~ spl0_24
| ~ spl0_28
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f309,f248,f313,f263,f267]) ).
fof(f335,plain,
( $false
| spl0_28 ),
inference(resolution,[],[f315,f28]) ).
fof(f339,plain,
spl0_28,
inference(avatar_contradiction_clause,[],[f335]) ).
cnf(s21,plain,
( ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f250]) ).
cnf(s24,plain,
( spl0_20
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f270]) ).
cnf(s25,plain,
spl0_25,
inference(sat_conversion,[],[f272]) ).
cnf(s26,plain,
spl0_24,
inference(sat_conversion,[],[f275]) ).
cnf(s28,plain,
( ~ spl0_21
| ~ spl0_24
| ~ spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f316]) ).
cnf(s29,plain,
spl0_28,
inference(sat_conversion,[],[f339]) ).
cnf(s30,plain,
( ~ spl0_21
| ~ spl0_24
| ~ spl0_25 ),
inference(rat,[],[s28,s29]) ).
cnf(s31,plain,
~ spl0_21,
inference(rat,[],[s30,s26,s25]) ).
cnf(s32,plain,
spl0_20,
inference(rat,[],[s24,s25,s26]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s21,s31,s32]) ).
fof(f340,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:29:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.29 % (1746511)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1746520)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1392278717:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1746517)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1746516)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2435857178_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (1746522)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2652307155:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (1746517)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3075859812:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1746518)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=966488613:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1746519)dis+10_1_sil=32000:sp=arity:random_seed=3041947117:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1746521)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2561462872:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % TRYING [1]
% 0.20/0.29 % TRYING [2]
% 0.20/0.29 % TRYING [3]
% 0.20/0.29 % (1746522) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1746511-1746522"...
% 0.20/0.29 % TRYING [4]
% 0.20/0.29 % (1746522)...printing done.
% 0.20/0.29 % (1746522)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1746522)------------------------------
% 0.20/0.29 % (1746522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1746522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1746522)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1746522)Termination reason: Refutation
% 0.20/0.29 % (1746522)Time elapsed: 0.007 s
% 0.20/0.29 % (1746522)Peak memory usage: 12 MB
% 0.20/0.29 % (1746522)Instructions burned: 9 (million)
% 0.20/0.29 % (1746511)Success in time 0.055 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------