%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 5.36s 1.76s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 13 unt; 5 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 93 ( 45 ~; 43 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 90 !; 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] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),implies(X3,X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz) ).
fof(f3,axiom,
! [X0] : is_a_theorem(implies(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_1) ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_3) ).
fof(f6,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(f7,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,[],[f6,f1]) ).
fof(f9,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,[],[f7,f6]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(factoring,[],[f9]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1)))),
inference(resolution,[],[f15,f2]) ).
fof(f47,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(implies(implies(X0,X1),X0),implies(X2,X0)),X3))
| is_a_theorem(implies(X4,X3)) ),
inference(resolution,[],[f16,f7]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
inference(resolution,[],[f16,f1]) ).
fof(f50,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(f51,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_2
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f54,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f48,f53,f50]) ).
fof(f62,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f54,f3]) ).
fof(f72,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f147,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X3,implies(X2,X4)),implies(X1,X2)))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl0_1 ),
inference(resolution,[],[f51,f9]) ).
fof(f238,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ is_a_theorem(implies(implies(implies(X2,X3),X4),implies(implies(X3,X5),X3)))
| is_a_theorem(implies(X0,implies(X1,implies(X2,X3)))) ),
inference(resolution,[],[f47,f6]) ).
fof(f599,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2))))
| ~ spl0_1 ),
inference(resolution,[],[f147,f2]) ).
fof(f1510,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2))) )
| ~ spl0_1 ),
inference(resolution,[],[f599,f1]) ).
fof(f1512,definition,
( spl0_12
<=> ! [X2,X1,X3] : is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f1513,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f1514,plain,
( spl0_12
| spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1510,f50,f53,f1512]) ).
fof(f1518,plain,
( ! [X2,X3,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(implies(implies(X2,X3),X2),X2))))
| ~ spl0_12 ),
inference(resolution,[],[f1513,f238]) ).
fof(f1743,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))) )
| ~ spl0_12 ),
inference(resolution,[],[f1518,f1]) ).
fof(f1745,definition,
( spl0_13
<=> ! [X2,X1,X3] : is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f1746,plain,
( ! [X2,X3,X1] : is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2)))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f1747,plain,
( spl0_13
| spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f1743,f1512,f53,f1745]) ).
fof(f1779,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) )
| ~ spl0_13 ),
inference(resolution,[],[f1746,f1]) ).
fof(f1781,definition,
( spl0_14
<=> ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f1782,plain,
( ! [X2,X1] : is_a_theorem(implies(implies(implies(X1,X2),X1),X1))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f1783,plain,
( spl0_14
| spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1779,f1745,f53,f1781]) ).
fof(f1841,plain,
( $false
| ~ spl0_14 ),
inference(resolution,[],[f1782,f4]) ).
fof(f1844,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f1841]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s6,plain,
~ spl0_2,
inference(sat_conversion,[],[f72]) ).
cnf(s16,plain,
( ~ spl0_1
| spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f1514]) ).
cnf(s17,plain,
( spl0_2
| ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f1747]) ).
cnf(s18,plain,
( spl0_2
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f1783]) ).
cnf(s19,plain,
~ spl0_14,
inference(sat_conversion,[],[f1844]) ).
cnf(s20,plain,
( spl0_2
| ~ spl0_13 ),
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
~ spl0_13,
inference(rat,[],[s20,s6]) ).
cnf(s22,plain,
~ spl0_12,
inference(rat,[],[s17,s21,s6]) ).
cnf(s23,plain,
~ spl0_1,
inference(rat,[],[s16,s22,s6]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s6,s23]) ).
fof(f1845,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:20:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.36/1.76 % (341066)Input is clausal, will run a generic CNF schedule.
% 5.36/1.76 % (341086)dis-21_1_sil=8000:lcm=predicate:random_seed=1956140821:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 5.36/1.76 % (341086)Instruction limit reached!
% 5.36/1.76 % (341086)------------------------------
% 5.36/1.76 % (341086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.76 % (341086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.76 % (341086)CaDiCaL version: 2.1.3
% 5.36/1.76 % (341086)Termination reason: Instruction limit
% 5.36/1.76 % (341086)Termination phase: Saturation
% 5.36/1.76 % (341086)Time elapsed: 0.039 s
% 5.36/1.76 % (341086)Peak memory usage: 88 MB
% 5.36/1.76 % (341086)Instructions burned: 120 (million)
% 5.36/1.76 % (341080)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=4234551026:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 5.36/1.76 % (341081)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4174256291:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 5.36/1.76 % (341082)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1162322394:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 5.36/1.76 % (341084)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=497983014:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 5.36/1.76 % (341083)lrs+10_1_sil=8000:sp=occurrence:random_seed=28024379:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 5.36/1.76 % (341085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3734247593:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 5.36/1.76 % (341084)First to succeed.
% 5.36/1.76 % (341084)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-341066"
% 5.36/1.76 % (341085)Also succeeded, but the first one will report.
% 5.36/1.76 % (341083)Also succeeded, but the first one will report.
% 5.36/1.76 % (341090)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=997228667:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.36/1.76 % (341090)Refutation not found, incomplete strategy
% 5.36/1.76 % (341090)------------------------------
% 5.36/1.76 % (341090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.76 % (341090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.76 % (341090)CaDiCaL version: 2.1.3
% 5.36/1.76 % (341090)Termination reason: Refutation not found, incomplete strategy
% 5.36/1.76 % (341090)Time elapsed: 0.001 s
% 5.36/1.76 % (341090)Peak memory usage: 87 MB
% 5.36/1.76 % (341090)------------------------------
% 5.36/1.76 % (341090)------------------------------
% 5.36/1.76 % (341084)Refutation found. Thanks to Tanya!
% 5.36/1.76 % SZS status Unsatisfiable for theBenchmark
% 5.36/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/1.76 % (341084)------------------------------
% 5.36/1.76 % (341084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.76 % (341084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.76 % (341084)CaDiCaL version: 2.1.3
% 5.36/1.76 % (341084)Termination reason: Refutation
% 5.36/1.76 % (341084)Time elapsed: 0.051 s
% 5.36/1.76 % (341084)Peak memory usage: 89 MB
% 5.36/1.76 % (341084)Instructions burned: 50 (million)
% 5.36/1.76 % (341084)------------------------------
% 5.36/1.76 % (341084)------------------------------
% 5.36/1.76 % (341066)Success in time 0.663 s
% 5.36/1.76 % Vampire exiting
%------------------------------------------------------------------------------