%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL086-1 : 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 : n016.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 11:51:09 AM UTC 2026
% Result : Unsatisfiable 2.05s 1.95s
% Output : Refutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 15 unt; 8 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 154 ( 70 ~; 76 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 9 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 108 !; 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,X4] : is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),implies(X2,X0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_JLukasiewicz_4) ).
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,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(f6,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(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(f14,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f6,f12,f9]) ).
fof(f15,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f13,f2]) ).
fof(f18,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f15]) ).
fof(f20,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(f29,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X2,implies(X1,X2)))))
| ~ spl0_1 ),
inference(resolution,[],[f20,f10]) ).
fof(f59,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2)))) )
| ~ spl0_1 ),
inference(resolution,[],[f29,f1]) ).
fof(f63,definition,
( spl0_7
<=> ! [X2,X1] : is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2)))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f64,plain,
( ! [X2,X1] : is_a_theorem(implies(implies(X1,X2),implies(X2,implies(X1,X2))))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl0_7
| spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f59,f9,f12,f63]) ).
fof(f66,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X2,X1))))
| ~ spl0_7 ),
inference(resolution,[],[f64,f4]) ).
fof(f107,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1))) )
| ~ spl0_7 ),
inference(resolution,[],[f66,f1]) ).
fof(f112,definition,
( spl0_8
<=> ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f113,plain,
( ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X2,X1)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( spl0_8
| spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f107,f63,f12,f112]) ).
fof(f120,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1))))
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f113,f20]) ).
fof(f135,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(X2,X1))) )
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f120,f1]) ).
fof(f136,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X3),implies(X2,X3))))
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f120,f4]) ).
fof(f140,definition,
( spl0_10
<=> ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f141,plain,
( ! [X2,X1] : is_a_theorem(implies(X1,implies(X2,X1)))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f142,plain,
( spl0_10
| spl0_2
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f135,f112,f9,f12,f140]) ).
fof(f154,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1))))
| ~ spl0_10 ),
inference(resolution,[],[f141,f4]) ).
fof(f821,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) )
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f136,f1]) ).
fof(f830,definition,
( spl0_50
<=> ! [X2,X1,X3] : is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f831,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3)))
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f832,plain,
( spl0_50
| spl0_2
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f821,f112,f9,f12,f830]) ).
fof(f1022,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) )
| ~ spl0_10 ),
inference(resolution,[],[f154,f1]) ).
fof(f1033,definition,
( spl0_51
<=> ! [X2,X1,X3] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f1034,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1)))
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f1035,plain,
( spl0_51
| spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1022,f140,f12,f1033]) ).
fof(f1062,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(X2,X0)) )
| ~ spl0_51 ),
inference(resolution,[],[f1034,f1]) ).
fof(f1128,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1)))
| ~ spl0_50
| ~ spl0_51 ),
inference(resolution,[],[f1062,f831]) ).
fof(f1194,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X1)) )
| ~ spl0_50
| ~ spl0_51 ),
inference(resolution,[],[f1128,f1]) ).
fof(f1207,definition,
( spl0_52
<=> ! [X1] : is_a_theorem(implies(X1,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1208,plain,
( ! [X1] : is_a_theorem(implies(X1,X1))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1209,plain,
( spl0_52
| spl0_2
| ~ spl0_50
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1194,f1033,f830,f12,f1207]) ).
fof(f1225,plain,
( $false
| ~ spl0_52 ),
inference(resolution,[],[f1208,f3]) ).
fof(f1237,plain,
~ spl0_52,
inference(avatar_contradiction_clause,[],[f1225]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f14]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f18]) ).
cnf(s8,plain,
( ~ spl0_1
| spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f65]) ).
cnf(s9,plain,
( spl0_2
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f114]) ).
cnf(s11,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f142]) ).
cnf(s54,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_8
| spl0_50 ),
inference(sat_conversion,[],[f832]) ).
cnf(s55,plain,
( spl0_2
| ~ spl0_10
| spl0_51 ),
inference(sat_conversion,[],[f1035]) ).
cnf(s56,plain,
( spl0_2
| ~ spl0_50
| ~ spl0_51
| spl0_52 ),
inference(sat_conversion,[],[f1209]) ).
cnf(s57,plain,
~ spl0_52,
inference(sat_conversion,[],[f1237]) ).
cnf(s58,plain,
( spl0_2
| ~ spl0_50
| ~ spl0_51 ),
inference(rat,[],[s56,s57]) ).
cnf(s64,plain,
spl0_1,
inference(rat,[],[s1,s3]) ).
cnf(s71,plain,
spl0_7,
inference(rat,[],[s8,s3,s64]) ).
cnf(s74,plain,
spl0_8,
inference(rat,[],[s9,s3,s71]) ).
cnf(s98,plain,
spl0_50,
inference(rat,[],[s54,s64,s3,s74]) ).
cnf(s99,plain,
spl0_10,
inference(rat,[],[s11,s64,s3,s74]) ).
cnf(s101,plain,
~ spl0_51,
inference(rat,[],[s58,s3,s98]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s55,s3,s101,s99]) ).
fof(f1238,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL086-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 15:26:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.05/1.95 % (2775546)Input is clausal, will run a generic CNF schedule.
% 2.05/1.95 % (2775556)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3077129038:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.05/1.95 % (2775552)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=1180979307:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.05/1.95 % (2775556)Instruction limit reached!
% 2.05/1.95 % (2775556)------------------------------
% 2.05/1.95 % (2775556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.95 % (2775556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.95 % (2775556)CaDiCaL version: 2.1.3
% 2.05/1.95 % (2775556)Termination reason: Instruction limit
% 2.05/1.95 % (2775556)Termination phase: Saturation
% 2.05/1.95 % (2775556)Time elapsed: 0.079 s
% 2.05/1.95 % (2775556)Peak memory usage: 88 MB
% 2.05/1.95 % (2775556)Instructions burned: 114 (million)
% 2.05/1.95 % (2775558)dis-21_1_sil=8000:lcm=predicate:random_seed=3825504256: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)
% 2.05/1.95 % (2775555)lrs+10_1_sil=8000:sp=occurrence:random_seed=3178330333:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.05/1.95 % (2775557)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=691622321:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.05/1.95 % (2775554)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3059055584:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.05/1.95 % (2775553)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1825990658:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.05/1.95 % (2775555)First to succeed.
% 2.05/1.95 % (2775555)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2775546"
% 2.05/1.95 % (2775558)Instruction limit reached!
% 2.05/1.95 % (2775558)------------------------------
% 2.05/1.95 % (2775558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.95 % (2775558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.95 % (2775558)CaDiCaL version: 2.1.3
% 2.05/1.95 % (2775558)Termination reason: Instruction limit
% 2.05/1.95 % (2775558)Termination phase: Saturation
% 2.05/1.95 % (2775558)Time elapsed: 0.105 s
% 2.05/1.95 % (2775558)Peak memory usage: 88 MB
% 2.05/1.95 % (2775558)Instructions burned: 117 (million)
% 2.05/1.95 % (2775566)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4042375918:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.05/1.95 % (2775566)Refutation not found, incomplete strategy
% 2.05/1.95 % (2775566)------------------------------
% 2.05/1.95 % (2775566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.95 % (2775566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.95 % (2775566)CaDiCaL version: 2.1.3
% 2.05/1.95 % (2775566)Termination reason: Refutation not found, incomplete strategy
% 2.05/1.95 % (2775566)Time elapsed: 0.001 s
% 2.05/1.95 % (2775566)Peak memory usage: 87 MB
% 2.05/1.95 % (2775557)Instruction limit reached!
% 2.05/1.95 % (2775557)------------------------------
% 2.05/1.95 % (2775557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/1.95 % (2775557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/1.95 % (2775557)CaDiCaL version: 2.1.3
% 2.05/1.95 % (2775557)Termination reason: Instruction limit
% 2.05/1.95 % (2775557)Termination phase: Saturation
% 2.05/1.95 % (2775557)Time elapsed: 0.187 s
% 2.05/1.95 % (2775557)Peak memory usage: 89 MB
% 2.05/1.95 % (2775557)Instructions burned: 181 (million)
% 2.05/1.95 % (2775567)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1996564102:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 2.05/1.95 % (2775555)Refutation found. Thanks to Tanya!
% 2.05/1.95 % SZS status Unsatisfiable for theBenchmark
% 2.05/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 6.23/2.15 % (2775555)------------------------------
% 6.23/2.15 % (2775555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.23/2.15 % (2775555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.23/2.15 % (2775555)CaDiCaL version: 2.1.3
% 6.23/2.15 % (2775555)Termination reason: Refutation
% 6.23/2.15 % (2775555)Time elapsed: 0.043 s
% 6.23/2.15 % (2775555)Peak memory usage: 89 MB
% 6.23/2.15 % (2775555)Instructions burned: 37 (million)
% 6.23/2.15 % (2775555)------------------------------
% 6.23/2.15 % (2775555)------------------------------
% 6.23/2.15 % (2775546)Success in time 0.762 s
% 6.23/2.15 % Vampire exiting
%------------------------------------------------------------------------------