%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL036-1 : 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 07:57:48 AM UTC 2026
% Result : Unsatisfiable 0.16s 10.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 157 ( 73 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_CAMeredith,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,falsehood)),VAR_3),VAR_4),implies(implies(VAR_4,VAR_0),implies(VAR_2,VAR_0)))),
file('theBenchmark.p',c0_CAMeredith) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E),implies(implies(E,A),implies(C,A)))),
inference(clausify,[status(thm)],[c0_CAMeredith]) ).
fof(prove_c0_5,axiom,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
file('theBenchmark.p',prove_c0_5) ).
cnf(c_3,plain,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
inference(clausify,[status(thm)],[prove_c0_5]) ).
cnf(c_321,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
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_321,c_2]) ).
cnf(c_322,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,implies(falsehood,B)),C),implies(D,C))),
inference(resolve,[status(thm)],[c_322,c_4]) ).
cnf(c_323,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(A,implies(falsehood,B)),C)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(B,implies(falsehood,C)))),
inference(resolve,[status(thm)],[c_323,c_6]) ).
cnf(c_324,plain,
( is_a_theorem(implies(B,implies(falsehood,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_324,c_14]) ).
cnf(c_325,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_325,c_18]) ).
cnf(c_326,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_28,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_326,c_21]) ).
cnf(c_327,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_29,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_327,c_28]) ).
cnf(c_328,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_33,plain,
is_a_theorem(implies(implies(implies(A,implies(implies(implies(B,C),implies(D,falsehood)),E)),B),implies(D,B))),
inference(resolve,[status(thm)],[c_328,c_29]) ).
cnf(c_329,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_67,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(B,D),implies(A,falsehood)),C))),
inference(resolve,[status(thm)],[c_329,c_33]) ).
cnf(c_330,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_75,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(D,implies(C,A)))),
inference(resolve,[status(thm)],[c_330,c_29]) ).
cnf(c_331,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_76,plain,
is_a_theorem(implies(implies(implies(A,B),implies(implies(falsehood,C),falsehood)),implies(D,A))),
inference(resolve,[status(thm)],[c_331,c_21]) ).
cnf(c_332,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_88,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),B),implies(D,B))),
inference(resolve,[status(thm)],[c_332,c_76]) ).
cnf(c_333,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_93,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_333,c_88]) ).
cnf(c_334,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_98,plain,
is_a_theorem(implies(implies(implies(implies(A,falsehood),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_334,c_93]) ).
cnf(c_335,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_98]) ).
cnf(c_190,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))),
inference(resolve,[status(thm)],[c_335,c_98]) ).
cnf(c_336,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,falsehood),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_98]) ).
cnf(c_205,plain,
is_a_theorem(implies(A,implies(implies(A,falsehood),B))),
inference(resolve,[status(thm)],[c_336,c_190]) ).
cnf(c_337,plain,
( is_a_theorem(implies(D,implies(C,A)))
| ~ is_a_theorem(implies(implies(A,B),implies(C,falsehood))) ),
inference(resolve,[status(thm)],[c_1,c_75]) ).
cnf(c_206,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_337,c_190]) ).
cnf(c_338,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_206]) ).
cnf(c_210,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_338,c_206]) ).
cnf(c_339,plain,
( is_a_theorem(implies(implies(implies(B,D),implies(A,falsehood)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_67]) ).
cnf(c_216,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,falsehood)),implies(C,A))),
inference(resolve,[status(thm)],[c_339,c_210]) ).
cnf(c_340,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),implies(C,falsehood))) ),
inference(resolve,[status(thm)],[c_1,c_216]) ).
cnf(c_319,plain,
is_a_theorem(implies(implies(implies(A,B),falsehood),A)),
inference(resolve,[status(thm)],[c_340,c_205]) ).
cnf(c_320,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.43 % Computer : n018.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Fri Sep 25 21:47:47 UTC 2026
% 0.16/10.43 % CPUTime :
% 0.16/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.43 % Process 2918965 was started by sandbox on n018,
% 0.16/10.43 % Fri Sep 25 21:47:47 2026
% 0.16/10.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/10.43
% 0.16/10.43 % From the command line: assign(max_seconds, 300).
% 0.16/10.48
% 0.16/10.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.48
% 0.16/10.48 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.16/10.48 % Length of proof is 24.
% 0.16/10.48 % Level of proof is 19.
% 0.16/10.48 % Maximum clause weight is 67.000.
% 0.16/10.48 % Given clauses 55.
% 0.16/10.48
% 0.16/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------