%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL082-1 : 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 : 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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 39 sgn 6 !; 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_JLukasiewicz,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(implies(VAR_2,VAR_0),implies(VAR_3,VAR_0)))),
file('theBenchmark.p',ic_JLukasiewicz) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),implies(D,A)))),
inference(clausify,[status(thm)],[ic_JLukasiewicz]) ).
fof(prove_ic_2,axiom,
~ is_a_theorem(implies(a,implies(b,a))),
file('theBenchmark.p',prove_ic_2) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(clausify,[status(thm)],[prove_ic_2]) ).
cnf(c_46,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_46,c_2]) ).
cnf(c_47,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(B,C))))),
inference(resolve,[status(thm)],[c_47,c_4]) ).
cnf(c_48,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(E,B))),implies(F,implies(implies(D,B),implies(E,B))))),
inference(resolve,[status(thm)],[c_48,c_4]) ).
cnf(c_49,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(A,B)))),
inference(resolve,[status(thm)],[c_49,c_5]) ).
cnf(c_50,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),B),implies(C,B))),
inference(resolve,[status(thm)],[c_50,c_7]) ).
cnf(c_51,plain,
( is_a_theorem(implies(F,implies(implies(D,B),implies(E,B))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(E,B)))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_24,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,C)))),
inference(resolve,[status(thm)],[c_51,c_9]) ).
cnf(c_52,plain,
( is_a_theorem(implies(implies(B,C),implies(C,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_26,plain,
is_a_theorem(implies(implies(A,B),implies(B,B))),
inference(resolve,[status(thm)],[c_52,c_24]) ).
cnf(c_53,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_30,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_53,c_26]) ).
cnf(c_54,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_37,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_54,c_30]) ).
cnf(c_55,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_37]) ).
cnf(c_44,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_55,c_37]) ).
cnf(c_45,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 21:52:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2928149 was started by sandbox on n018,
% 0.13/0.36 % Fri Sep 25 21:52:20 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 14.
% 0.13/0.38 % Level of proof is 10.
% 0.13/0.38 % Maximum clause weight is 24.000.
% 0.13/0.38 % Given clauses 18.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------