%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL025-1 : 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 : n020.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 1.09s 0.85s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 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 : 61 ( 10 sgn 7 !; 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_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_1,axiom,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('theBenchmark.p',prove_c0_1) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(clausify,[status(thm)],[prove_c0_1]) ).
cnf(c_585,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_585,c_2]) ).
cnf(c_586,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_586,c_4]) ).
cnf(c_587,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_587,c_4]) ).
cnf(c_588,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_39,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_588,c_6]) ).
cnf(c_589,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_39]) ).
cnf(c_406,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_589,c_10]) ).
cnf(c_590,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_425,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_590,c_406]) ).
cnf(c_591,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_425]) ).
cnf(c_572,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_591,c_6]) ).
cnf(c_592,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_572]) ).
cnf(c_583,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_592,c_425]) ).
cnf(c_584,plain,
$false,
inference(resolve,[status(thm)],[c_583,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL025-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % Computer : n020.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8046.5625MB
% 0.11/0.45 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Fri Sep 25 21:45:20 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.45 % Process 3853710 was started by sandbox on n020,
% 0.11/0.45 % Fri Sep 25 21:45:20 2026
% 0.11/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.46
% 0.11/0.46 % From the command line: assign(max_seconds, 300).
% 1.09/0.85
% 1.09/0.85 % SZS status Unsatisfiable for theBenchmark
% 1.09/0.85
% 1.09/0.85 % Proof 1 at 0.09 (+ 0.05) seconds.
% 1.09/0.85 % Length of proof is 13.
% 1.09/0.85 % Level of proof is 7.
% 1.09/0.85 % Maximum clause weight is 45.000.
% 1.09/0.85 % Given clauses 83.
% 1.09/0.85
% 1.09/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------