%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 11:51:08 AM UTC 2026
% Result : Unsatisfiable 3.48s 1.39s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 12 unt; 5 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 87 ( 42 ~; 40 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),implies(X3,X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_JLukasiewicz) ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(a,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ic_1) ).
fof(f4,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(X2,X0),implies(X3,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[],[f2,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(implies(X3,X0)) ),
inference(resolution,[],[f4,f1]) ).
fof(f6,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3)))
| is_a_theorem(implies(X4,implies(X1,X3))) ),
inference(resolution,[],[f5,f2]) ).
fof(f7,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X1,X4),X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[],[f5,f4]) ).
fof(f10,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(factoring,[],[f7]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1)))),
inference(resolution,[],[f10,f2]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
inference(resolution,[],[f11,f1]) ).
fof(f20,definition,
( spl0_1
<=> ! [X2,X1,X3] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f21,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,definition,
( spl0_2
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f24,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f23,f20]) ).
fof(f29,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f24,f2]) ).
fof(f33,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f38,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1))))
| ~ spl0_1 ),
inference(resolution,[],[f21,f6]) ).
fof(f48,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(X2,X1))) )
| ~ spl0_1 ),
inference(resolution,[],[f38,f1]) ).
fof(f56,definition,
( spl0_3
<=> ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f57,plain,
( ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X1)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( spl0_3
| spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f48,f20,f23,f56]) ).
fof(f75,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2))))
| ~ spl0_3 ),
inference(resolution,[],[f57,f10]) ).
fof(f103,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(X2,X2))) )
| ~ spl0_3 ),
inference(resolution,[],[f75,f1]) ).
fof(f113,definition,
( spl0_6
<=> ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X2))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f114,plain,
( ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X2)))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl0_6
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f103,f56,f23,f113]) ).
fof(f116,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X1)) )
| ~ spl0_6 ),
inference(resolution,[],[f114,f1]) ).
fof(f126,definition,
( spl0_7
<=> ! [X1] : is_a_theorem(implies(X1,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f127,plain,
( ! [X1] : is_a_theorem(implies(X1,X1))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( spl0_7
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f116,f113,f23,f126]) ).
fof(f129,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f127,f3]) ).
fof(f137,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f129]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
( spl0_2
| ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f115]) ).
cnf(s8,plain,
( spl0_2
| ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f128]) ).
cnf(s9,plain,
~ spl0_7,
inference(sat_conversion,[],[f137]) ).
cnf(s11,plain,
( spl0_2
| ~ spl0_6 ),
inference(rat,[],[s8,s9]) ).
cnf(s12,plain,
~ spl0_6,
inference(rat,[],[s11,s3]) ).
cnf(s13,plain,
~ spl0_3,
inference(rat,[],[s7,s12,s3]) ).
cnf(s16,plain,
~ spl0_1,
inference(rat,[],[s4,s13,s3]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s3,s16]) ).
fof(f139,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:21:06 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.38 % (3655359)Input is clausal, will run a generic CNF schedule.
% 3.48/1.38 % (3655467)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3411860736:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.48/1.38 % (3655471)dis-21_1_sil=8000:lcm=predicate:random_seed=119995504:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.48/1.38 % (3655466)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2192361743:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.48/1.38 % (3655465)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=650861067:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.48/1.38 % (3655469)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1856528941:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.48/1.38 % (3655470)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1660378190:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.48/1.39 % (3655469)First to succeed.
% 3.48/1.39 % (3655470)Also succeeded, but the first one will report.
% 3.48/1.39 % (3655469)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3655359"
% 3.48/1.39 % (3655468)lrs+10_1_sil=8000:sp=occurrence:random_seed=3744172869:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.48/1.39 % (3655468)Also succeeded, but the first one will report.
% 3.48/1.39 % (3655471)Also succeeded, but the first one will report.
% 3.48/1.39 % (3655469)Refutation found. Thanks to Tanya!
% 3.48/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.48/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.39 % (3655469)------------------------------
% 3.48/1.39 % (3655469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.39 % (3655469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.39 % (3655469)CaDiCaL version: 2.1.3
% 3.48/1.39 % (3655469)Termination reason: Refutation
% 3.48/1.39 % (3655469)Time elapsed: 0.006 s
% 3.48/1.39 % (3655469)Peak memory usage: 89 MB
% 3.48/1.39 % (3655469)Instructions burned: 4 (million)
% 3.48/1.39 % (3655469)------------------------------
% 3.48/1.39 % (3655469)------------------------------
% 3.48/1.39 % (3655359)Success in time 0.425 s
% 3.48/1.39 % Vampire exiting
%------------------------------------------------------------------------------