%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL096-1 : 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 : n009.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 11:51:11 AM UTC 2026
% Result : Unsatisfiable 3.54s 1.46s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 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,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).
fof(f5,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
fof(f9,plain,
! [X2,X3,X0,X1,X4] :
( is_a_theorem(equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X3)) ),
inference(resolution,[],[f4,f1]) ).
fof(f19,plain,
! [X2,X3,X0,X1,X4] :
( is_a_theorem(equivalent(equivalent(X1,X4),X3))
| ~ is_a_theorem(equivalent(equivalent(X0,X4),X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X3)) ),
inference(resolution,[],[f9,f1]) ).
fof(f42,plain,
! [X0,X1] :
( ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(a,equivalent(equivalent(b,b),a))),X1),c))
| ~ is_a_theorem(equivalent(equivalent(X0,c),X1)) ),
inference(resolution,[],[f19,f5]) ).
fof(f48,plain,
! [X0] : ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,a),equivalent(X0,equivalent(equivalent(b,b),a))),c),c)),
inference(resolution,[],[f42,f2]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X2,a),equivalent(X2,equivalent(equivalent(b,b),a)))),X1),c))
| ~ is_a_theorem(equivalent(equivalent(X0,c),X1)) ),
inference(resolution,[],[f48,f19]) ).
fof(f66,plain,
! [X0,X1] : ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,a)),equivalent(X1,equivalent(equivalent(b,b),a))),c),c)),
inference(resolution,[],[f58,f3]) ).
fof(f79,plain,
$false,
inference(resolution,[],[f66,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:21:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.54/1.46 % (2162224)Input is clausal, will run a generic CNF schedule.
% 3.54/1.46 % (2162230)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3490142751:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.54/1.46 % (2162233)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1628219829:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.54/1.46 % (2162234)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=323064955:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.54/1.46 % (2162232)lrs+10_1_sil=8000:sp=occurrence:random_seed=254078645:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.54/1.46 % (2162229)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=1905590265:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.54/1.46 % (2162235)dis-21_1_sil=8000:lcm=predicate:random_seed=1089263042: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)
% 3.54/1.46 % (2162231)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2262474315:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.54/1.46 % (2162235)First to succeed.
% 3.54/1.46 % (2162235)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2162224"
% 3.54/1.46 % (2162234)Also succeeded, but the first one will report.
% 3.54/1.46 % (2162233)Also succeeded, but the first one will report.
% 3.54/1.46 % (2162232)Also succeeded, but the first one will report.
% 3.54/1.46 % (2162235)Refutation found. Thanks to Tanya!
% 3.54/1.46 % SZS status Unsatisfiable for theBenchmark
% 3.54/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.46 % (2162235)------------------------------
% 3.54/1.46 % (2162235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.46 % (2162235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.46 % (2162235)CaDiCaL version: 2.1.3
% 3.54/1.46 % (2162235)Termination reason: Refutation
% 3.54/1.46 % (2162235)Time elapsed: 0.004 s
% 3.54/1.46 % (2162235)Peak memory usage: 88 MB
% 3.54/1.46 % (2162235)Instructions burned: 3 (million)
% 3.54/1.46 % (2162235)------------------------------
% 3.54/1.46 % (2162235)------------------------------
% 3.54/1.46 % (2162224)Success in time 0.418 s
% 3.54/1.46 % Vampire exiting
%------------------------------------------------------------------------------