%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 11:58:49 AM UTC 2026
% Result : Theorem 0.30s 0.46s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 87 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 26 ~; 22 |; 2 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 56 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f45,conjecture,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f46,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ kn1,
inference(flattening,[],[f46]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f52,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f53,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f55,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f62,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f66,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f72,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0] :
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f79,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f83,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f84,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f86,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f87,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f89,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f96,plain,
~ kn1,
inference(cnf_transformation,[],[f47]) ).
fof(f98,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f81,f83]) ).
fof(f100,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f79,f84]) ).
fof(f104,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f75,f89]) ).
fof(f106,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f73,f87]) ).
fof(f107,plain,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(forward_subsumption_resolution,[],[f72,f96]) ).
fof(f109,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f70,f86]) ).
fof(f110,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f100,f98]) ).
fof(f113,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[],[f106,f98]) ).
fof(f119,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f109,f104]) ).
fof(f135,plain,
! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[],[f98,f110]) ).
fof(f378,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(superposition,[],[f113,f135]) ).
fof(f414,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,X0))),
inference(resolution,[],[f378,f119]) ).
fof(f424,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[],[f414,f98]) ).
fof(f441,plain,
$false,
inference(resolution,[],[f424,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:51:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.30/0.46 % (2207669)Will run a generic schedule for satisfiability detection.
% 0.30/0.46 % (2207678)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2607287298:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.30/0.46 % (2207675)% WARNING: option uhcvi not known.
% 0.30/0.46 % (2207678) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2207669-2207678"...
% 0.30/0.46 % (2207674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1444605942_2999 on theBenchmark for (2999ds/0Mi)
% 0.30/0.46 % (2207675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3418836340:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.30/0.46 % (2207676)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=134656243:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.30/0.46 % (2207678)...printing done.
% 0.30/0.46 % (2207677)dis+10_1_sil=32000:sp=arity:random_seed=1892685139:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.30/0.46 % (2207680)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2129945512:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.30/0.46 % (2207679)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=630392644:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.30/0.46 % (2207678)Refutation found. Thanks to Tanya!
% 0.30/0.46 % SZS status Theorem for theBenchmark
% 0.30/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.46 % (2207678)------------------------------
% 0.30/0.46 % (2207678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (2207678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (2207678)CaDiCaL version: 2.1.3
% 0.30/0.46 % (2207678)Termination reason: Refutation
% 0.30/0.46 % (2207678)Time elapsed: 0.006 s
% 0.30/0.46 % (2207678)Peak memory usage: 12 MB
% 0.30/0.46 % (2207678)Instructions burned: 14 (million)
% 0.30/0.46 % (2207669)Success in time 0.033 s
% 0.30/0.46 % Vampire exiting
%------------------------------------------------------------------------------