%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL490+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 : n018.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 11:58:48 AM UTC 2026
% Result : Theorem 0.38s 0.56s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 33 unt; 0 def)
% Number of atoms : 112 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 32 ~; 28 |; 2 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 96 !; 2 ?)
% 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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
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(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
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(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_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f45,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f46,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ or_1,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
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,
( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f61,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f64,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f48]) ).
fof(f65,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f67,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f78,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f65]) ).
fof(f81,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f97,plain,
~ or_1,
inference(cnf_transformation,[],[f47]) ).
fof(f99,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f82,f84]) ).
fof(f100,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f81,f95]) ).
fof(f102,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f79,f94]) ).
fof(f103,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
inference(forward_subsumption_resolution,[],[f78,f92]) ).
fof(f105,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f76,f90]) ).
fof(f106,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f75,f89]) ).
fof(f108,plain,
~ is_a_theorem(implies(sK0,or(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f73,f97]) ).
fof(f110,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f71,f87]) ).
fof(f112,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f102,f100]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(or(X1,X2),or(X2,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f110,f105]) ).
fof(f123,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[],[f106,f112]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X1,or(X2,not(X1))),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f123,f110]) ).
fof(f265,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X0,or(X2,X1)))),
inference(resolution,[],[f120,f103]) ).
fof(f2252,plain,
! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(resolution,[],[f265,f124]) ).
fof(f2272,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(forward_demodulation,[],[f2252,f99]) ).
fof(f2279,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(superposition,[],[f2272,f99]) ).
fof(f2284,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f2279,f112]) ).
fof(f2312,plain,
$false,
inference(resolution,[],[f2284,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:52:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.38/0.56 % (2543043)Will run a generic schedule for satisfiability detection.
% 0.38/0.56 % (2543053)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2685939347:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.56 % (2543049)% WARNING: option uhcvi not known.
% 0.38/0.56 % (2543048)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3312605308_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.56 % (2543051)dis+10_1_sil=32000:sp=arity:random_seed=677178575:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.56 % (2543050)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3380270481:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.56 % (2543052)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2634555108:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.56 % (2543054)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2980172063:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.56 % (2543049)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=544111547:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.56 % TRYING [1]
% 0.38/0.56 % TRYING [2]
% 0.38/0.56 % TRYING [3]
% 0.38/0.56 % TRYING [4]
% 0.38/0.56 % (2543053)Instruction limit reached!
% 0.38/0.56 % (2543053)------------------------------
% 0.38/0.56 % (2543053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.56 % (2543053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.56 % (2543053)CaDiCaL version: 2.1.3
% 0.38/0.56 % (2543053)Termination reason: Instruction limit
% 0.38/0.56 % (2543053)Termination phase: Saturation
% 0.38/0.56 % (2543053)Time elapsed: 0.048 s
% 0.38/0.56 % (2543053)Peak memory usage: 14 MB
% 0.38/0.56 % (2543053)Instructions burned: 132 (million)
% 0.38/0.56 % (2543062)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1848420982:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.38/0.56 % TRYING [1]
% 0.38/0.56 % TRYING [2]
% 0.38/0.56 % TRYING [3]
% 0.38/0.56 % (2543051)Instruction limit reached!
% 0.38/0.56 % (2543051)------------------------------
% 0.38/0.56 % (2543051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.56 % (2543051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.56 % (2543051)CaDiCaL version: 2.1.3
% 0.38/0.56 % (2543051)Termination reason: Instruction limit
% 0.38/0.56 % (2543051)Termination phase: Saturation
% 0.38/0.56 % (2543051)Time elapsed: 0.068 s
% 0.38/0.56 % (2543051)Peak memory usage: 13 MB
% 0.38/0.56 % (2543051)Instructions burned: 104 (million)
% 0.38/0.56 % TRYING [4]
% 0.38/0.56 % (2543052)Instruction limit reached!
% 0.38/0.56 % (2543052)------------------------------
% 0.38/0.56 % (2543052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.56 % (2543052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.56 % (2543052)CaDiCaL version: 2.1.3
% 0.38/0.56 % (2543052)Termination reason: Instruction limit
% 0.38/0.56 % (2543052)Termination phase: Saturation
% 0.38/0.56 % (2543052)Time elapsed: 0.077 s
% 0.38/0.56 % (2543052)Peak memory usage: 13 MB
% 0.38/0.56 % (2543052)Instructions burned: 116 (million)
% 0.38/0.56 % (2543064)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1548020717:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.56 % (2543065)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=741475924:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.38/0.56 % TRYING [5]
% 0.38/0.56 % (2543054)Instruction limit reached!
% 0.38/0.56 % (2543054)------------------------------
% 0.38/0.56 % (2543054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.56 % (2543054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.56 % (2543054)CaDiCaL version: 2.1.3
% 0.38/0.56 % (2543054)Termination reason: Instruction limit
% 0.38/0.56 % (2543054)Termination phase: Saturation
% 0.38/0.56 % (2543054)Time elapsed: 0.112 s
% 0.38/0.56 % (2543054)Peak memory usage: 14 MB
% 0.38/0.56 % (2543054)Instructions burned: 159 (million)
% 0.38/0.56 % (2543064) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2543043-2543064"...
% 0.38/0.56 % (2543064)...printing done.
% 0.38/0.56 % (2543064)Refutation found. Thanks to Tanya!
% 0.38/0.56 % SZS status Theorem for theBenchmark
% 0.38/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.56 % (2543064)------------------------------
% 0.38/0.56 % (2543064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.56 % (2543064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.56 % (2543064)CaDiCaL version: 2.1.3
% 0.38/0.56 % (2543064)Termination reason: Refutation
% 0.38/0.56 % (2543064)Time elapsed: 0.035 s
% 0.38/0.56 % (2543064)Peak memory usage: 14 MB
% 0.38/0.56 % (2543064)Instructions burned: 94 (million)
% 0.38/0.56 % (2543043)Success in time 0.149 s
% 0.38/0.56 % Vampire exiting
%------------------------------------------------------------------------------