%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL080-2 : 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 : n018.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 07:57:55 AM UTC 2026
% Result : Unsatisfiable 5.34s 1.11s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 23 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 15 sgn 9 !; 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(ic_2,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',ic_2) ).
cnf(c_3,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[ic_2]) ).
fof(ic_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_0),VAR_0)),
file('theBenchmark.p',ic_3) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(clausify,[status(thm)],[ic_3]) ).
fof(ic_4,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',ic_4) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[ic_4]) ).
fof(prove_ic_JLukasiewicz,axiom,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
file('theBenchmark.p',prove_ic_JLukasiewicz) ).
cnf(c_6,plain,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(clausify,[status(thm)],[prove_ic_JLukasiewicz]) ).
cnf(c_5713,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_5713,c_3]) ).
cnf(c_5714,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_5714,c_5]) ).
cnf(c_5715,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_13,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_5715,c_3]) ).
cnf(c_5716,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_10]) ).
cnf(c_103,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_5716,c_4]) ).
cnf(c_5717,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_10]) ).
cnf(c_109,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_5717,c_103]) ).
cnf(c_5718,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_136,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_5718,c_109]) ).
cnf(c_5719,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_109]) ).
cnf(c_146,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)),
inference(resolve,[status(thm)],[c_5719,c_7]) ).
cnf(c_5720,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_154,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_5720,c_136]) ).
cnf(c_5721,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_10]) ).
cnf(c_199,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_5721,c_146]) ).
cnf(c_5722,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_154]) ).
cnf(c_630,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_5722,c_10]) ).
cnf(c_5723,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_630]) ).
cnf(c_688,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(A,implies(B,implies(D,C))))),
inference(resolve,[status(thm)],[c_5723,c_199]) ).
cnf(c_5724,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_630]) ).
cnf(c_714,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_5724,c_4]) ).
cnf(c_5725,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_10]) ).
cnf(c_1599,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_5725,c_714]) ).
cnf(c_5726,plain,
( is_a_theorem(implies(A,implies(B,implies(D,C))))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_688]) ).
cnf(c_5711,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),implies(D,A)))),
inference(resolve,[status(thm)],[c_5726,c_1599]) ).
cnf(c_5712,plain,
$false,
inference(resolve,[status(thm)],[c_5711,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n018.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 21:51:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2927030 was started by sandbox on n018,
% 0.11/0.36 % Fri Sep 25 21:51:51 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 5.34/1.11
% 5.34/1.11 % SZS status Unsatisfiable for theBenchmark
% 5.34/1.11
% 5.34/1.11 % Proof 1 at 0.47 (+ 0.20) seconds.
% 5.34/1.11 % Length of proof is 20.
% 5.34/1.11 % Level of proof is 10.
% 5.34/1.11 % Maximum clause weight is 53.000.
% 5.34/1.11 % Given clauses 167.
% 5.34/1.11
% 5.34/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------