%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:57:47 AM UTC 2026
% Result : Unsatisfiable 2.59s 0.77s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 36 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 33 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 144 ( 33 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(c0_2,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',c0_2) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[c0_2]) ).
fof(c0_5,axiom,
! [VAR_0] : is_a_theorem(implies(implies(implies(VAR_0,falsehood),falsehood),VAR_0)),
file('theBenchmark.p',c0_5) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(implies(A,falsehood),falsehood),A)),
inference(clausify,[status(thm)],[c0_5]) ).
fof(c0_6,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',c0_6) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(clausify,[status(thm)],[c0_6]) ).
fof(prove_c0_3,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('theBenchmark.p',prove_c0_3) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(clausify,[status(thm)],[prove_c0_3]) ).
cnf(c_1369,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_1369,c_2]) ).
cnf(c_1370,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(implies(A,falsehood),falsehood)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_7,plain,
is_a_theorem(implies(falsehood,falsehood)),
inference(resolve,[status(thm)],[c_1370,c_3]) ).
cnf(c_1371,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(A,implies(implies(implies(B,falsehood),falsehood),B))),
inference(resolve,[status(thm)],[c_1371,c_3]) ).
cnf(c_1372,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))),
inference(resolve,[status(thm)],[c_1372,c_4]) ).
cnf(c_1373,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))),
inference(resolve,[status(thm)],[c_1373,c_4]) ).
cnf(c_1374,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_1374,c_2]) ).
cnf(c_1375,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_1375,c_6]) ).
cnf(c_1376,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_15,plain,
is_a_theorem(implies(A,implies(falsehood,falsehood))),
inference(resolve,[status(thm)],[c_1376,c_7]) ).
cnf(c_1377,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_1377,c_15]) ).
cnf(c_1378,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_1378,c_20]) ).
cnf(c_1379,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_22,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_1379,c_20]) ).
cnf(c_1380,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_25,plain,
is_a_theorem(implies(implies(A,implies(implies(B,falsehood),falsehood)),implies(A,B))),
inference(resolve,[status(thm)],[c_1380,c_8]) ).
cnf(c_1381,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_51,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)),
inference(resolve,[status(thm)],[c_1381,c_6]) ).
cnf(c_1382,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_64,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_1382,c_22]) ).
cnf(c_1383,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_66,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_1383,c_6]) ).
cnf(c_1384,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_68,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_1384,c_64]) ).
cnf(c_1385,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_1,c_51]) ).
cnf(c_153,plain,
is_a_theorem(implies(falsehood,A)),
inference(resolve,[status(thm)],[c_1385,c_25]) ).
cnf(c_1386,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(implies(B,falsehood),falsehood))) ),
inference(resolve,[status(thm)],[c_1,c_25]) ).
cnf(c_165,plain,
is_a_theorem(implies(implies(implies(A,falsehood),A),A)),
inference(resolve,[status(thm)],[c_1386,c_21]) ).
cnf(c_1387,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_68]) ).
cnf(c_168,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_1387,c_153]) ).
cnf(c_1388,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_175,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))),
inference(resolve,[status(thm)],[c_1388,c_168]) ).
cnf(c_1389,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_180,plain,
is_a_theorem(implies(A,implies(implies(B,falsehood),implies(B,C)))),
inference(resolve,[status(thm)],[c_1389,c_175]) ).
cnf(c_1390,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_191,plain,
is_a_theorem(implies(A,implies(implies(implies(B,falsehood),B),B))),
inference(resolve,[status(thm)],[c_1390,c_165]) ).
cnf(c_1391,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_366,plain,
is_a_theorem(implies(implies(A,implies(implies(B,falsehood),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_1391,c_191]) ).
cnf(c_1392,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_66]) ).
cnf(c_448,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_1392,c_10]) ).
cnf(c_1393,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_461,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_1393,c_448]) ).
cnf(c_1394,plain,
( is_a_theorem(implies(implies(A,B),implies(C,B)))
| ~ is_a_theorem(implies(implies(A,B),implies(C,A))) ),
inference(resolve,[status(thm)],[c_1,c_461]) ).
cnf(c_996,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,falsehood),C))),
inference(resolve,[status(thm)],[c_1394,c_180]) ).
cnf(c_1395,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(implies(B,falsehood),B))) ),
inference(resolve,[status(thm)],[c_1,c_366]) ).
cnf(c_1367,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_1395,c_996]) ).
cnf(c_1368,plain,
$false,
inference(resolve,[status(thm)],[c_1367,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.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 : Fri Sep 25 21:46:22 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1166637 was started by sandbox on n003,
% 0.08/0.35 % Fri Sep 25 21:46:22 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 2.59/0.77
% 2.59/0.77 % SZS status Unsatisfiable for theBenchmark
% 2.59/0.77
% 2.59/0.77 % Proof 1 at 0.23 (+ 0.12) seconds.
% 2.59/0.77 % Length of proof is 33.
% 2.59/0.77 % Level of proof is 12.
% 2.59/0.77 % Maximum clause weight is 61.000.
% 2.59/0.77 % Given clauses 129.
% 2.59/0.77
% 2.59/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------