%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:58:00 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 8 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_1,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
fof(wajsberg_2,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))) = truth,
file('theBenchmark.p',wajsberg_2) ).
cnf(c_2,plain,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
inference(clausify,[status(thm)],[wajsberg_2]) ).
fof(wajsberg_3,axiom,
! [VAR_0,VAR_1] : implies(implies(VAR_0,VAR_1),VAR_1) = implies(implies(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',wajsberg_3) ).
cnf(c_3,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
fof(wajsberg_4,axiom,
! [VAR_0,VAR_1] : implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0)) = truth,
file('theBenchmark.p',wajsberg_4) ).
cnf(c_4,plain,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
inference(clausify,[status(thm)],[wajsberg_4]) ).
fof(prove_mv_24,axiom,
implies(not(not(x)),x) != truth,
file('theBenchmark.p',prove_mv_24) ).
cnf(c_5,plain,
implies(not(not(x)),x) != truth,
inference(clausify,[status(thm)],[prove_mv_24]) ).
cnf(c_175,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_175]) ).
cnf(c_7,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_176,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_12,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_177,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_178,plain,
implies(implies(implies(A,B),B),A) = implies(implies(implies(B,A),A),A),
inference(paramod,[status(thm)],[c_3,c_177]) ).
cnf(c_17,plain,
implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_18,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_179,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_180,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_179]) ).
cnf(c_27,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_180]) ).
cnf(c_35,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_27,c_12]) ).
cnf(c_41,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_35,c_6]) ).
cnf(c_181,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_41,c_7]) ).
cnf(c_42,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_181]) ).
cnf(c_182,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_43,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_182]) ).
cnf(c_183,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_42,c_3]) ).
cnf(c_184,plain,
implies(A,B) = implies(implies(implies(A,B),B),B),
inference(paramod,[status(thm)],[c_1,c_183]) ).
cnf(c_45,plain,
implies(implies(implies(A,B),B),B) = implies(A,B),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_185,plain,
implies(A,B) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_45,c_17]) ).
cnf(c_46,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_186,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_18,c_46]) ).
cnf(c_187,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_186]) ).
cnf(c_85,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_188,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_18,c_43]) ).
cnf(c_102,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_188]) ).
cnf(c_189,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_102,c_85]) ).
cnf(c_110,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_189]) ).
cnf(c_190,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_102,c_3]) ).
cnf(c_191,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_190]) ).
cnf(c_112,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_191]) ).
cnf(c_192,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_112,c_4]) ).
cnf(c_193,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_110,c_192]) ).
cnf(c_151,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_193]) ).
cnf(c_194,plain,
implies(truth,implies(A,implies(not(A),not(truth)))) = truth,
inference(paramod,[status(thm)],[c_151,c_4]) ).
cnf(c_162,plain,
implies(A,implies(not(A),not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_194]) ).
cnf(c_195,plain,
implies(truth,implies(not(A),not(truth))) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_162,c_3]) ).
cnf(c_196,plain,
implies(not(A),not(truth)) = implies(implies(implies(not(A),not(truth)),A),A),
inference(paramod,[status(thm)],[c_1,c_195]) ).
cnf(c_197,plain,
implies(not(A),not(truth)) = implies(truth,A),
inference(paramod,[status(thm)],[c_18,c_196]) ).
cnf(c_168,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_197]) ).
cnf(c_198,plain,
implies(implies(not(not(truth)),not(not(A))),A) = truth,
inference(paramod,[status(thm)],[c_168,c_4]) ).
cnf(c_199,plain,
implies(implies(truth,not(not(A))),A) = truth,
inference(paramod,[status(thm)],[c_110,c_198]) ).
cnf(c_173,plain,
implies(not(not(A)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_199]) ).
cnf(c_174,plain,
$false,
inference(resolve,[status(thm)],[c_173,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.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 21:54:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1192125 was started by sandbox2 on n003,
% 0.08/0.37 % Fri Sep 25 21:54:08 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 0.08/0.40
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.40 % Length of proof is 26.
% 0.08/0.40 % Level of proof is 14.
% 0.08/0.40 % Maximum clause weight is 55.000.
% 0.08/0.40 % Given clauses 25.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------