%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : FLD009-3 : 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 : n004.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 09:49:31 AM UTC 2026
% Result : Unsatisfiable 0.67s 0.46s
% Output : Refutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 32 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| product(X0,X1,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(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f20,axiom,
! [X0,X1] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
! [X0] : ~ product(a,X0,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
fof(f42,plain,
! [X0,X1] :
( product(X1,X0,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f20,f10]) ).
fof(f75,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f9,f10]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ product(X1,X2,X3)
| ~ product(X0,X1,multiplicative_identity)
| product(X0,X3,X2)
| ~ defined(X2) ),
inference(resolution,[],[f6,f8]) ).
fof(f419,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,multiplicative_identity)
| product(X0,multiply(X2,X1),X2)
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X2) ),
inference(resolution,[],[f119,f42]) ).
fof(f423,plain,
! [X2,X0,X1] :
( product(X0,multiply(X2,X1),X2)
| ~ product(X0,X1,multiplicative_identity)
| ~ defined(X2)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f419]) ).
fof(f2323,plain,
! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ defined(b)
| ~ defined(X0) ),
inference(resolution,[],[f423,f30]) ).
fof(f2346,plain,
! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f2323,f28]) ).
fof(f2347,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[],[f2346,f75]) ).
fof(f2349,plain,
( ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f2347,f18]) ).
fof(f2350,plain,
sum(additive_identity,a,additive_identity),
inference(forward_subsumption_resolution,[],[f2349,f27]) ).
fof(f2351,plain,
$false,
inference(forward_subsumption_resolution,[],[f2350,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 % Computer : n004.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 00:22:22 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.30/0.32 Running first-order model finding
% 0.30/0.33 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
% 0.67/0.46 % (945108)Will run a generic schedule for satisfiability detection.
% 0.67/0.46 % (945114)% WARNING: option uhcvi not known.
% 0.67/0.46 % (945114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1170385951:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.67/0.46 % (945119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=839087768:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.67/0.46 % (945115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3290687494:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.67/0.46 % (945116)dis+10_1_sil=32000:sp=arity:random_seed=3277174181:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.67/0.46 % (945113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2754744748_2999 on theBenchmark for (2999ds/0Mi)
% 0.67/0.46 % (945117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2205654819:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.67/0.46 % (945118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3673360856:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.67/0.46 % TRYING [1]
% 0.67/0.46 % TRYING [2]
% 0.67/0.46 % TRYING [3]
% 0.67/0.46 % TRYING [4]
% 0.67/0.46 % TRYING [5]
% 0.67/0.46 % (945116) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-945108-945116"...
% 0.67/0.46 % (945116)...printing done.
% 0.67/0.46 % (945116)Refutation found. Thanks to Tanya!
% 0.67/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.67/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.67/0.46 % (945116)------------------------------
% 0.67/0.46 % (945116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (945116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (945116)CaDiCaL version: 2.1.3
% 0.67/0.46 % (945116)Termination reason: Refutation
% 0.67/0.46 % (945116)Time elapsed: 0.083 s
% 0.67/0.46 % (945116)Peak memory usage: 12 MB
% 0.67/0.46 % (945116)Instructions burned: 84 (million)
% 0.67/0.46 % (945108)Success in time 0.123 s
% 0.67/0.46 % Vampire exiting
%------------------------------------------------------------------------------