%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:51:00 AM UTC 2026
% Result : Unsatisfiable 3.49s 1.21s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 15 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 34 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 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,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
fof(f3,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
fof(f4,axiom,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
fof(f5,axiom,
! [X0,X1] : is_a_theorem(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation1) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(necessary(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
fof(f7,axiom,
! [X0] :
( is_a_theorem(necessary(X0))
| ~ is_a_theorem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_of_necessitation) ).
fof(f8,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f10,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1,f2]) ).
fof(f11,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f4,f1]) ).
fof(f13,plain,
! [X0,X1] :
( is_a_theorem(implies(necessary(X0),necessary(X1)))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(resolution,[],[f5,f1]) ).
fof(f16,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f3,f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f16,f1]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f29,f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(not(X0),not(X1)),X1))
| is_a_theorem(implies(implies(not(X0),not(X1)),X0)) ),
inference(resolution,[],[f29,f4]) ).
fof(f49,definition,
( spl0_3
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f50,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f77,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessary(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f35,f6]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X2),not(X1))))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f35,f4]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f36,f10]) ).
fof(f122,plain,
! [X0,X1] :
( ~ is_a_theorem(necessary(implies(X0,X1)))
| is_a_theorem(implies(necessary(X0),X1)) ),
inference(resolution,[],[f77,f13]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(not(X2),not(X0))))
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f103,f35]) ).
fof(f316,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[],[f84,f2]) ).
fof(f538,plain,
! [X0,X1] :
( is_a_theorem(implies(necessary(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f122,f7]) ).
fof(f630,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f50,f2]) ).
fof(f684,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f1043,plain,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(resolution,[],[f538,f8]) ).
fof(f1567,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f166,f316]) ).
fof(f1588,definition,
( spl0_37
<=> ! [X0] : is_a_theorem(implies(not(not(X0)),X0)) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1589,plain,
( ! [X0] : is_a_theorem(implies(not(not(X0)),X0))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1588]) ).
fof(f1590,plain,
( spl0_3
| spl0_37 ),
inference(avatar_split_clause,[],[f1567,f1588,f49]) ).
fof(f1617,plain,
( ! [X0] : is_a_theorem(implies(not(not(necessary(X0))),X0))
| ~ spl0_37 ),
inference(resolution,[],[f1589,f77]) ).
fof(f1835,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessary(not(X0)))))
| ~ spl0_37 ),
inference(resolution,[],[f1617,f11]) ).
fof(f2023,plain,
( $false
| ~ spl0_37 ),
inference(resolution,[],[f1835,f1043]) ).
fof(f2024,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[],[f2023]) ).
cnf(s37,plain,
~ spl0_3,
inference(sat_conversion,[],[f684]) ).
cnf(s81,plain,
( spl0_3
| spl0_37 ),
inference(sat_conversion,[],[f1590]) ).
cnf(s93,plain,
~ spl0_37,
inference(sat_conversion,[],[f2024]) ).
cnf(s95,plain,
spl0_3,
inference(rat,[],[s81,s93]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s37,s95]) ).
fof(f2025,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 % Computer : n012.cluster.edu
% 0.04/0.33 % Model : x86_64 x86_64
% 0.04/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.33 % Memory : 8046.5625MB
% 0.04/0.33 % OS : Linux 6.8.0-71-generic
% 0.04/0.33 % CPULimit : 300
% 0.04/0.33 % WCLimit : 300
% 0.04/0.33 % DateTime : Sun Sep 27 15:18:05 UTC 2026
% 0.04/0.33 % CPUTime :
% 0.04/0.33 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 Running first-order theorem proving
% 0.09/0.36 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
% 3.49/1.21 % (2495695)Input is clausal, will run a generic CNF schedule.
% 3.49/1.21 % (2495704)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3244655125:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.21 % (2495701)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1465294713:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.21 % (2495706)dis-21_1_sil=8000:lcm=predicate:random_seed=1105613878: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)
% 3.49/1.21 % (2495703)lrs+10_1_sil=8000:sp=occurrence:random_seed=2973599659:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.21 % (2495704)Instruction limit reached!
% 3.49/1.21 % (2495704)------------------------------
% 3.49/1.21 % (2495704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495704)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495704)Termination reason: Instruction limit
% 3.49/1.21 % (2495704)Termination phase: Saturation
% 3.49/1.21 % (2495704)Time elapsed: 0.041 s
% 3.49/1.21 % (2495704)Peak memory usage: 88 MB
% 3.49/1.21 % (2495704)Instructions burned: 114 (million)
% 3.49/1.21 % (2495703)First to succeed.
% 3.49/1.21 % (2495703)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2495695"
% 3.49/1.21 % (2495702)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1985859021:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.21 % (2495705)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3368371892:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.21 % (2495700)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=3172914350:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.21 % (2495706)Instruction limit reached!
% 3.49/1.21 % (2495706)------------------------------
% 3.49/1.21 % (2495706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495706)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495706)Termination reason: Instruction limit
% 3.49/1.21 % (2495706)Termination phase: Saturation
% 3.49/1.21 % (2495706)Time elapsed: 0.054 s
% 3.49/1.21 % (2495706)Peak memory usage: 88 MB
% 3.49/1.21 % (2495706)Instructions burned: 117 (million)
% 3.49/1.21 % (2495705)Instruction limit reached!
% 3.49/1.21 % (2495705)------------------------------
% 3.49/1.21 % (2495705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495705)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495705)Termination reason: Instruction limit
% 3.49/1.21 % (2495705)Termination phase: Saturation
% 3.49/1.21 % (2495705)Time elapsed: 0.102 s
% 3.49/1.21 % (2495705)Peak memory usage: 89 MB
% 3.49/1.21 % (2495705)Instructions burned: 181 (million)
% 3.49/1.21 % (2495715)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2424861760:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.49/1.21 % (2495711)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=3979100375:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.49/1.21 % (2495711)Refutation not found, incomplete strategy
% 3.49/1.21 % (2495711)------------------------------
% 3.49/1.21 % (2495711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495711)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495711)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.21 % (2495711)Time elapsed: 0.001 s
% 3.49/1.21 % (2495711)Peak memory usage: 87 MB
% 3.49/1.21 % (2495715)Instruction limit reached!
% 3.49/1.21 % (2495715)------------------------------
% 3.49/1.21 % (2495715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495715)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495715)Termination reason: Instruction limit
% 3.49/1.21 % (2495715)Termination phase: Saturation
% 3.49/1.21 % (2495715)Time elapsed: 0.063 s
% 3.49/1.21 % (2495715)Peak memory usage: 90 MB
% 3.49/1.21 % (2495715)Instructions burned: 191 (million)
% 3.49/1.21 % (2495703)Refutation found. Thanks to Tanya!
% 3.49/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.21 % (2495703)------------------------------
% 3.49/1.21 % (2495703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.21 % (2495703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.21 % (2495703)CaDiCaL version: 2.1.3
% 3.49/1.21 % (2495703)Termination reason: Refutation
% 3.49/1.21 % (2495703)Time elapsed: 0.039 s
% 3.49/1.21 % (2495703)Peak memory usage: 90 MB
% 3.49/1.21 % (2495703)Instructions burned: 69 (million)
% 3.49/1.21 % (2495703)------------------------------
% 3.49/1.21 % (2495703)------------------------------
% 3.49/1.21 % (2495695)Success in time 0.452 s
% 3.49/1.21 % Vampire exiting
%------------------------------------------------------------------------------