%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 11:58:44 AM UTC 2026
% Result : Theorem 0.21s 10.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 29 unt; 0 def)
% Number of atoms : 69 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 16 ~; 12 |; 0 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f53,conjecture,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f54,negated_conjecture,
~ r3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r3,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> r3 ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f69,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f69]) ).
fof(f88,plain,
( r3
| ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f89,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f90,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f91,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f92,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f109,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(cnf_transformation,[],[f88]) ).
fof(f110,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f89]) ).
fof(f111,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f90]) ).
fof(f112,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f113,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f115,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f116,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f119,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f133,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f134,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f136,plain,
~ r3,
inference(cnf_transformation,[],[f55]) ).
fof(f138,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f113,f133]) ).
fof(f139,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f112,f116]) ).
fof(f140,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f111,f134]) ).
fof(f141,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f110,f115]) ).
fof(f142,plain,
~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
inference(forward_subsumption_resolution,[],[f109,f136]) ).
fof(f155,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f96,f119]) ).
fof(f158,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f140,f138]) ).
fof(f159,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f141,f139]) ).
fof(f186,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f159,f139]) ).
fof(f196,plain,
! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[],[f138,f158]) ).
fof(f210,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(not(X0))),or(X0,X1))),
inference(superposition,[],[f155,f159]) ).
fof(f211,plain,
! [X0,X1] : is_a_theorem(or(and(not(X1),not(X0)),or(X0,X1))),
inference(forward_demodulation,[],[f210,f196]) ).
fof(f217,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),X0),or(X0,X1))),
inference(forward_demodulation,[],[f211,f186]) ).
fof(f220,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1))),
inference(forward_demodulation,[],[f217,f159]) ).
fof(f276,plain,
$false,
inference(resolution,[],[f220,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/10.45 % Computer : n005.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Sun Sep 27 15:44:13 UTC 2026
% 0.17/10.46 % CPUTime :
% 0.17/10.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/10.49 Running first-order model finding
% 0.17/10.49 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/10.54 % (4162805)Will run a generic schedule for satisfiability detection.
% 0.21/10.54 % (4162812)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3254775440:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/10.54 % (4162814)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1019225563:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/10.54 % (4162811)% WARNING: option uhcvi not known.
% 0.21/10.54 % (4162814) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4162805-4162814"...
% 0.21/10.54 % (4162814)...printing done.
% 0.21/10.54 % (4162814)Refutation found. Thanks to Tanya!
% 0.21/10.54 % SZS status Theorem for theBenchmark
% 0.21/10.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/10.54 % (4162814)------------------------------
% 0.21/10.54 % (4162814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/10.54 % (4162814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/10.54 % (4162814)CaDiCaL version: 2.1.3
% 0.21/10.54 % (4162814)Termination reason: Refutation
% 0.21/10.54 % (4162814)Time elapsed: 0.005 s
% 0.21/10.54 % (4162814)Peak memory usage: 12 MB
% 0.21/10.54 % (4162814)Instructions burned: 7 (million)
% 0.21/10.54 % (4162805)Success in time 0.035 s
% 0.21/10.54 % Vampire exiting
%------------------------------------------------------------------------------