%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL009-1 : 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 : 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 11:50:55 AM UTC 2026
% Result : Unsatisfiable 2.53s 1.31s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 17 unt; 2 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 41 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yql) ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ec_5) ).
fof(f4,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| is_a_theorem(equivalent(equivalent(X2,X1),equivalent(X0,X2))) ),
inference(resolution,[],[f2,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1))),equivalent(equivalent(X3,X2),X0))),
inference(resolution,[],[f4,f2]) ).
fof(f6,plain,
! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),X3)),equivalent(equivalent(X3,equivalent(equivalent(X4,X2),equivalent(X1,X4))),X0))),
inference(resolution,[],[f5,f4]) ).
fof(f7,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1))))
| is_a_theorem(equivalent(equivalent(X3,X2),X0)) ),
inference(resolution,[],[f5,f1]) ).
fof(f8,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X1))),
inference(resolution,[],[f7,f2]) ).
fof(f9,plain,
! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(equivalent(X3,X1),equivalent(X2,X3))))),
inference(resolution,[],[f7,f5]) ).
fof(f11,plain,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X1,X2),X0))),
inference(resolution,[],[f8,f4]) ).
fof(f15,plain,
! [X2,X3,X0,X1,X4] :
( is_a_theorem(equivalent(equivalent(X3,equivalent(equivalent(X4,X2),equivalent(X1,X4))),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),X3))) ),
inference(resolution,[],[f6,f1]) ).
fof(f16,plain,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X2,X1)))),
inference(resolution,[],[f11,f7]) ).
fof(f19,plain,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(equivalent(X2,X0),X1))),
inference(resolution,[],[f9,f7]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(equivalent(equivalent(X0,X2),equivalent(equivalent(X3,X1),equivalent(X2,X3))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[],[f9,f1]) ).
fof(f24,plain,
! [X2,X0,X1] :
( is_a_theorem(equivalent(equivalent(X2,X0),X1))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[],[f19,f1]) ).
fof(f28,plain,
! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X0),equivalent(X1,X1))),
inference(resolution,[],[f16,f7]) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4] :
( is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X3,equivalent(equivalent(X4,X2),equivalent(X1,X4))))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),X3))) ),
inference(resolution,[],[f15,f1]) ).
fof(f36,plain,
! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,X0))
| is_a_theorem(equivalent(X1,X1)) ),
inference(resolution,[],[f28,f1]) ).
fof(f38,definition,
( spl0_1
<=> ! [X1] : is_a_theorem(equivalent(X1,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f39,plain,
( ! [X1] : is_a_theorem(equivalent(X1,X1))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl0_2
<=> ! [X0] : ~ is_a_theorem(equivalent(X0,X0)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( ! [X0] : ~ is_a_theorem(equivalent(X0,X0))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f36,f41,f38]) ).
fof(f51,plain,
( ! [X2,X3,X0,X1] : ~ is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1))),equivalent(equivalent(X3,X2),X0)))
| ~ spl0_2 ),
inference(resolution,[],[f42,f15]) ).
fof(f56,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f51,f5]) ).
fof(f57,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(equivalent(equivalent(X3,X1),equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[],[f21,f1]) ).
fof(f61,plain,
( ! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X0)))
| ~ spl0_1 ),
inference(resolution,[],[f39,f4]) ).
fof(f69,plain,
( ! [X0,X1] :
( is_a_theorem(equivalent(X1,X0))
| ~ is_a_theorem(equivalent(X0,X1)) )
| ~ spl0_1 ),
inference(resolution,[],[f61,f1]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(X3,X2),X0)))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X1)))) ),
inference(resolution,[],[f32,f3]) ).
fof(f88,plain,
! [X0] : ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(X0,equivalent(b,c)),equivalent(a,X0)))),
inference(resolution,[],[f81,f11]) ).
fof(f166,plain,
! [X0] :
( ~ is_a_theorem(equivalent(X0,c))
| ~ is_a_theorem(equivalent(X0,equivalent(b,equivalent(b,c)))) ),
inference(resolution,[],[f60,f88]) ).
fof(f175,plain,
( ~ is_a_theorem(equivalent(c,equivalent(b,equivalent(b,c))))
| ~ spl0_1 ),
inference(resolution,[],[f166,f39]) ).
fof(f182,plain,
( ~ is_a_theorem(equivalent(equivalent(b,equivalent(b,c)),c))
| ~ spl0_1 ),
inference(resolution,[],[f175,f69]) ).
fof(f191,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(b,c),c),b))
| ~ spl0_1 ),
inference(resolution,[],[f182,f24]) ).
fof(f197,plain,
( ~ is_a_theorem(equivalent(equivalent(c,b),equivalent(b,c)))
| ~ spl0_1 ),
inference(resolution,[],[f191,f24]) ).
fof(f200,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f197,f61]) ).
fof(f201,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f200]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s6,plain,
~ spl0_2,
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
~ spl0_1,
inference(sat_conversion,[],[f201]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f202,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:17:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.53/1.31 % (1360941)Input is clausal, will run a generic CNF schedule.
% 2.53/1.31 % (1360951)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2989671877:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.31 % (1360951)First to succeed.
% 2.53/1.31 % (1360951)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1360941"
% 2.53/1.31 % (1360952)dis-21_1_sil=8000:lcm=predicate:random_seed=2106329308: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)
% 2.53/1.31 % (1360948)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=466875226:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.31 % (1360947)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=726676420:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.31 % (1360946)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=4254030334:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.31 % (1360949)lrs+10_1_sil=8000:sp=occurrence:random_seed=3569588996:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.31 % (1360950)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2341771634:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.31 % (1360949)Also succeeded, but the first one will report.
% 2.53/1.31 % (1360950)Instruction limit reached!
% 2.53/1.31 % (1360950)------------------------------
% 2.53/1.31 % (1360950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1360950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1360950)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1360950)Termination reason: Instruction limit
% 2.53/1.31 % (1360950)Termination phase: Saturation
% 2.53/1.31 % (1360950)Time elapsed: 0.070 s
% 2.53/1.31 % (1360950)Peak memory usage: 88 MB
% 2.53/1.31 % (1360950)Instructions burned: 115 (million)
% 2.53/1.31 % (1360952)Instruction limit reached!
% 2.53/1.31 % (1360952)------------------------------
% 2.53/1.31 % (1360952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1360952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1360952)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1360952)Termination reason: Instruction limit
% 2.53/1.31 % (1360952)Termination phase: Saturation
% 2.53/1.31 % (1360952)Time elapsed: 0.071 s
% 2.53/1.31 % (1360952)Peak memory usage: 88 MB
% 2.53/1.31 % (1360952)Instructions burned: 119 (million)
% 2.53/1.31 % (1360951)Refutation found. Thanks to Tanya!
% 2.53/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.31 % (1360951)------------------------------
% 2.53/1.31 % (1360951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1360951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1360951)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1360951)Termination reason: Refutation
% 2.53/1.31 % (1360951)Time elapsed: 0.004 s
% 2.53/1.31 % (1360951)Peak memory usage: 89 MB
% 2.53/1.31 % (1360951)Instructions burned: 10 (million)
% 2.53/1.31 % (1360951)------------------------------
% 2.53/1.31 % (1360951)------------------------------
% 2.53/1.31 % (1360941)Success in time 0.267 s
% 2.53/1.31 % Vampire exiting
%------------------------------------------------------------------------------