%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL371-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:58:42 AM UTC 2026
% Result : Unsatisfiable 53.56s 7.27s
% Output : CNFRefutation 53.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 37 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 34 ~; 32 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 186 ( 33 sgn 8 !; 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(cn_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',cn_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[cn_1]) ).
fof(cn_2,axiom,
! [VAR_0] : is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0)),
file('theBenchmark.p',cn_2) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(clausify,[status(thm)],[cn_2]) ).
fof(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))),
file('theBenchmark.p',cn_3) ).
cnf(c_4,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
fof(prove_cn_27,axiom,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
file('theBenchmark.p',prove_cn_27) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(clausify,[status(thm)],[prove_cn_27]) ).
cnf(c_17911,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_6,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_17911,c_2]) ).
cnf(c_17912,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_7,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_17912,c_3]) ).
cnf(c_17913,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_9,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_17913,c_4]) ).
cnf(c_17914,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_6]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_17914,c_6]) ).
cnf(c_17915,plain,
( is_a_theorem(implies(implies(not(A),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_17915,c_6]) ).
cnf(c_17916,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_6]) ).
cnf(c_29,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_17916,c_9]) ).
cnf(c_17917,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_34,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_17917,c_3]) ).
cnf(c_17918,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_36,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_17918,c_34]) ).
cnf(c_17919,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_43,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_17919,c_29]) ).
cnf(c_17920,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_44,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_17920,c_36]) ).
cnf(c_17921,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_12]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_17921,c_7]) ).
cnf(c_17922,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_184,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_17922,c_44]) ).
cnf(c_17923,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_184]) ).
cnf(c_205,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_17923,c_7]) ).
cnf(c_17924,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_12]) ).
cnf(c_415,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_17924,c_205]) ).
cnf(c_17925,plain,
( is_a_theorem(implies(implies(B,not(A)),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_907,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_17925,c_415]) ).
cnf(c_17926,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_939,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_17926,c_907]) ).
cnf(c_17927,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_980,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_17927,c_939]) ).
cnf(c_17928,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_980]) ).
cnf(c_1092,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_17928,c_907]) ).
cnf(c_17929,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_1111,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_17929,c_1092]) ).
cnf(c_17930,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_415]) ).
cnf(c_1207,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_17930,c_1111]) ).
cnf(c_17931,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1207]) ).
cnf(c_2831,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_17931,c_1207]) ).
cnf(c_17932,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D))) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_2849,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_17932,c_1207]) ).
cnf(c_17933,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_6]) ).
cnf(c_2932,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_17933,c_2849]) ).
cnf(c_17934,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_980]) ).
cnf(c_3026,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_17934,c_2932]) ).
cnf(c_17935,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_12]) ).
cnf(c_3100,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_17935,c_3026]) ).
cnf(c_17936,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3100]) ).
cnf(c_3390,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_17936,c_2]) ).
cnf(c_17937,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3390]) ).
cnf(c_3780,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_17937,c_2831]) ).
cnf(c_17938,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_6]) ).
cnf(c_17909,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_17938,c_3780]) ).
cnf(c_17910,plain,
$false,
inference(resolve,[status(thm)],[c_17909,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL371-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 22:25:29 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3452541 was started by sandbox on n016,
% 0.17/0.44 % Fri Sep 25 22:25:29 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 53.56/7.27
% 53.56/7.27 % SZS status Unsatisfiable for theBenchmark
% 53.56/7.27
% 53.56/7.27 % Proof 1 at 5.12 (+ 1.66) seconds.
% 53.56/7.27 % Length of proof is 34.
% 53.56/7.27 % Level of proof is 21.
% 53.56/7.27 % Maximum clause weight is 62.000.
% 53.56/7.27 % Given clauses 408.
% 53.56/7.27
% 53.56/7.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------