%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:57:48 AM UTC 2026
% Result : Unsatisfiable 18.09s 2.79s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 39 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 174 ( 38 sgn 10 !; 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_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',c0_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[c0_1]) ).
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_3,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[c0_2]) ).
fof(c0_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_0),VAR_0)),
file('theBenchmark.p',c0_3) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(clausify,[status(thm)],[c0_3]) ).
fof(c0_4,axiom,
! [VAR_0] : is_a_theorem(implies(falsehood,VAR_0)),
file('theBenchmark.p',c0_4) ).
cnf(c_5,plain,
is_a_theorem(implies(falsehood,A)),
inference(clausify,[status(thm)],[c0_4]) ).
fof(prove_c0_CAMeredith,axiom,
~ is_a_theorem(implies(implies(implies(implies(implies(a,b),implies(c,falsehood)),e),falsehood),implies(implies(falsehood,a),implies(c,a)))),
file('theBenchmark.p',prove_c0_CAMeredith) ).
cnf(c_6,plain,
~ is_a_theorem(implies(implies(implies(implies(implies(a,b),implies(c,falsehood)),e),falsehood),implies(implies(falsehood,a),implies(c,a)))),
inference(clausify,[status(thm)],[prove_c0_CAMeredith]) ).
cnf(c_7,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_9965,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_9965,c_2]) ).
cnf(c_9966,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_9966,c_3]) ).
cnf(c_9967,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_9967,c_3]) ).
cnf(c_9968,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_17,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_9968,c_5]) ).
cnf(c_19,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),implies(D,C))),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_27,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_9969,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_28,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_9969,c_8]) ).
cnf(c_9970,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_29,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_9970,c_4]) ).
cnf(c_37,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_11,c_1]) ).
cnf(c_68,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_29,c_1]) ).
cnf(c_9971,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_69,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_9971,c_29]) ).
cnf(c_9972,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_70,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),B)),
inference(resolve,[status(thm)],[c_9972,c_19]) ).
cnf(c_9973,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_77,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))),
inference(resolve,[status(thm)],[c_9973,c_70]) ).
cnf(c_80,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,falsehood),C))),
inference(resolve,[status(thm)],[c_77,c_7]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)),
inference(resolve,[status(thm)],[c_21,c_68]) ).
cnf(c_9974,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_226,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_9974,c_153]) ).
cnf(c_233,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_226,c_1]) ).
cnf(c_286,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_69,c_37]) ).
cnf(c_9975,plain,
( is_a_theorem(implies(implies(D,B),implies(A,implies(D,C))))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_416,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_9975,c_286]) ).
cnf(c_9976,plain,
( is_a_theorem(implies(implies(A,falsehood),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_80]) ).
cnf(c_562,plain,
is_a_theorem(implies(implies(implies(A,B),falsehood),A)),
inference(resolve,[status(thm)],[c_9976,c_4]) ).
cnf(c_572,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),falsehood),B))),
inference(resolve,[status(thm)],[c_562,c_7]) ).
cnf(c_849,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_416,c_1]) ).
cnf(c_9977,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_416]) ).
cnf(c_862,plain,
is_a_theorem(implies(A,implies(implies(A,falsehood),B))),
inference(resolve,[status(thm)],[c_9977,c_77]) ).
cnf(c_9978,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_416]) ).
cnf(c_868,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_9978,c_2]) ).
cnf(c_890,plain,
is_a_theorem(implies(implies(implies(implies(A,falsehood),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_862,c_7]) ).
cnf(c_9979,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_868]) ).
cnf(c_1462,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),falsehood)),implies(A,B))),
inference(resolve,[status(thm)],[c_9979,c_562]) ).
cnf(c_2740,plain,
( is_a_theorem(implies(implies(implies(A,C),falsehood),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_572,c_1]) ).
cnf(c_3587,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_890,c_1]) ).
cnf(c_3981,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,falsehood),A))),
inference(resolve,[status(thm)],[c_1462,c_27]) ).
cnf(c_4014,plain,
is_a_theorem(implies(implies(A,falsehood),implies(implies(implies(B,C),A),B))),
inference(resolve,[status(thm)],[c_3981,c_849]) ).
cnf(c_6854,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),implies(A,falsehood)),B))),
inference(resolve,[status(thm)],[c_4014,c_3587]) ).
cnf(c_8637,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(C,A))),
inference(resolve,[status(thm)],[c_6854,c_849]) ).
cnf(c_8879,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(D,implies(C,A)))),
inference(resolve,[status(thm)],[c_8637,c_233]) ).
cnf(c_9963,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),falsehood),implies(E,implies(C,A)))),
inference(resolve,[status(thm)],[c_8879,c_2740]) ).
cnf(c_9964,plain,
$false,
inference(resolve,[status(thm)],[c_9963,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 21:50:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 130763 was started by sandbox2 on n001,
% 0.09/0.37 % Fri Sep 25 21:50:40 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 18.09/2.79
% 18.09/2.79 % SZS status Unsatisfiable for theBenchmark
% 18.09/2.79
% 18.09/2.79 % Proof 1 at 1.63 (+ 0.75) seconds.
% 18.09/2.79 % Length of proof is 43.
% 18.09/2.79 % Level of proof is 14.
% 18.09/2.79 % Maximum clause weight is 90.000.
% 18.09/2.79 % Given clauses 460.
% 18.09/2.79
% 18.09/2.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------