%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL088-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 11:57:37 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.58s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 14 unt; 7 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 61 ~; 66 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] : is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),implies(X2,X0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz_4) ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_3) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3)))
| is_a_theorem(implies(X4,implies(implies(X3,X0),implies(X2,X0)))) ),
inference(resolution,[],[f2,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1,X4,X5] : is_a_theorem(implies(X0,implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4))))),
inference(resolution,[],[f4,f2]) ).
fof(f9,definition,
( spl0_1
<=> ! [X3,X4,X5,X2,X1] : is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( ! [X2,X3,X1,X4,X5] : is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4))))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,definition,
( spl0_2
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f18,plain,
( $false
| ~ spl0_2 ),
inference(backward_subsumption_resolution,[],[f5,f13]) ).
fof(f20,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f18]) ).
fof(f24,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))) ),
inference(resolution,[],[f5,f1]) ).
fof(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f24,f12,f9]) ).
fof(f26,plain,
( ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),implies(implies(X3,X1),implies(X4,X1))),implies(X5,implies(implies(X3,X1),implies(X4,X1))))))
| ~ spl0_1 ),
inference(resolution,[],[f10,f4]) ).
fof(f27,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))) )
| ~ spl0_1 ),
inference(resolution,[],[f10,f1]) ).
fof(f34,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(implies(X1,X2),implies(X3,X2)))))
| ~ spl0_1 ),
inference(resolution,[],[f27,f2]) ).
fof(f42,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X3,X1),implies(X4,X1))),implies(X5,implies(implies(X3,X1),implies(X4,X1))))) )
| ~ spl0_1 ),
inference(resolution,[],[f26,f1]) ).
fof(f44,definition,
( spl0_4
<=> ! [X2,X3,X4,X5,X1] : is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X3,X1),implies(X4,X1))),implies(X5,implies(implies(X3,X1),implies(X4,X1))))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f45,plain,
( ! [X2,X3,X1,X4,X5] : is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X3,X1),implies(X4,X1))),implies(X5,implies(implies(X3,X1),implies(X4,X1)))))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( spl0_4
| spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f42,f9,f12,f44]) ).
fof(f56,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))) )
| ~ spl0_1 ),
inference(resolution,[],[f34,f1]) ).
fof(f58,definition,
( spl0_6
<=> ! [X2,X1,X3] : is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f59,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2))))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( spl0_6
| spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f56,f9,f12,f58]) ).
fof(f61,plain,
( ! [X2,X3,X0,X1,X4] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X3),implies(implies(implies(X3,X4),X2),X3))))
| ~ spl0_6 ),
inference(resolution,[],[f59,f4]) ).
fof(f94,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X3,X0))))
| is_a_theorem(implies(X4,implies(implies(X2,X0),implies(X3,X0)))) )
| ~ spl0_4 ),
inference(resolution,[],[f45,f1]) ).
fof(f177,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1))))
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f94,f59]) ).
fof(f311,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) )
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f177,f1]) ).
fof(f313,definition,
( spl0_18
<=> ! [X2,X1,X3] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f314,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1)))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f315,plain,
( spl0_18
| spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f311,f58,f44,f12,f313]) ).
fof(f334,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X3,X4),X2),X3))) )
| ~ spl0_6 ),
inference(resolution,[],[f61,f1]) ).
fof(f336,definition,
( spl0_19
<=> ! [X2,X4,X1,X3] : is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X3,X4),X2),X3))) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f337,plain,
( ! [X2,X3,X1,X4] : is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X3,X4),X2),X3)))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f338,plain,
( spl0_19
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f334,f58,f12,f336]) ).
fof(f344,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(X2,X0)) )
| ~ spl0_18 ),
inference(resolution,[],[f314,f1]) ).
fof(f1371,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),X1)))
| ~ spl0_18
| ~ spl0_19 ),
inference(resolution,[],[f337,f344]) ).
fof(f1396,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) )
| ~ spl0_18
| ~ spl0_19 ),
inference(resolution,[],[f1371,f1]) ).
fof(f1398,definition,
( spl0_72
<=> ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f1399,plain,
( ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),X1))
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1400,plain,
( spl0_72
| spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1396,f336,f313,f12,f1398]) ).
fof(f1406,plain,
( $false
| ~ spl0_72 ),
inference(backward_subsumption_resolution,[],[f3,f1399]) ).
fof(f1418,plain,
~ spl0_72,
inference(avatar_contradiction_clause,[],[f1406]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f20]) ).
cnf(s4,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f46]) ).
cnf(s8,plain,
( ~ spl0_1
| spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f60]) ).
cnf(s20,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f315]) ).
cnf(s21,plain,
( spl0_2
| ~ spl0_6
| spl0_19 ),
inference(sat_conversion,[],[f338]) ).
cnf(s112,plain,
( spl0_2
| ~ spl0_18
| ~ spl0_19
| spl0_72 ),
inference(sat_conversion,[],[f1400]) ).
cnf(s115,plain,
~ spl0_72,
inference(sat_conversion,[],[f1418]) ).
cnf(s116,plain,
( spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s112,s115]) ).
cnf(s122,plain,
spl0_1,
inference(rat,[],[s4,s3]) ).
cnf(s135,plain,
spl0_6,
inference(rat,[],[s8,s3,s122]) ).
cnf(s136,plain,
spl0_4,
inference(rat,[],[s6,s3,s122]) ).
cnf(s152,plain,
spl0_19,
inference(rat,[],[s21,s3,s135]) ).
cnf(s172,plain,
spl0_18,
inference(rat,[],[s20,s135,s3,s136]) ).
cnf(s179,plain,
$false,
inference(rat,[],[s116,s3,s152,s172]) ).
fof(f1419,plain,
$false,
inference(avatar_sat_refutation,[],[s179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL088-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 15:21:54 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 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
% 0.30/0.58 % (1367312)Will run a generic schedule for satisfiability detection.
% 0.30/0.58 % (1367318)% WARNING: option uhcvi not known.
% 0.30/0.58 % (1367321)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2476908173:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.30/0.58 % (1367318)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4127268884:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.30/0.58 % (1367320)dis+10_1_sil=32000:sp=arity:random_seed=2344989978:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.30/0.58 % (1367317)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=38821550_3000 on theBenchmark for (3000ds/0Mi)
% 0.30/0.58 % (1367322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2819114418:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.30/0.58 % (1367323)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2107588687:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.30/0.58 % TRYING [1]
% 0.30/0.58 % TRYING [2]
% 0.30/0.58 % TRYING [3]
% 0.30/0.58 % (1367319)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=233705525:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.30/0.58 % TRYING [4]
% 0.30/0.58 % (1367323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1367312-1367323"...
% 0.30/0.58 % (1367318) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1367312-1367318"...
% 0.30/0.58 % (1367323)...printing done.
% 0.30/0.58 % (1367318)...printing done.
% 0.30/0.58 % (1367318)Refutation found. Thanks to Tanya!
% 0.30/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.30/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.58 % (1367318)------------------------------
% 0.30/0.58 % (1367318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.58 % (1367318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.58 % (1367318)CaDiCaL version: 2.1.3
% 0.30/0.58 % (1367318)Termination reason: Refutation
% 0.30/0.58 % (1367318)Time elapsed: 0.051 s
% 0.30/0.58 % (1367318)Peak memory usage: 12 MB
% 0.30/0.58 % (1367318)Instructions burned: 49 (million)
% 0.30/0.58 % (1367312)Success in time 0.079 s
% 0.30/0.58 % Vampire exiting
%------------------------------------------------------------------------------