%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL154-1 : 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 : n004.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 07:58:07 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 7 sgn 16 !; 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(or_definition,axiom,
! [VAR_0,VAR_1] : or(VAR_0,VAR_1) = implies(not(VAR_0),VAR_1),
file('theBenchmark.p',or_definition) ).
cnf(c_5,plain,
or(A,B) = implies(not(A),B),
inference(clausify,[status(thm)],[or_definition]) ).
fof(or_commutativity,axiom,
! [VAR_0,VAR_1] : or(VAR_0,VAR_1) = or(VAR_1,VAR_0),
file('theBenchmark.p',or_commutativity) ).
cnf(c_8,plain,
or(A,B) = or(B,A),
inference(clausify,[status(thm)],[or_commutativity]) ).
cnf(c_157,plain,
implies(not(A),B) = or(B,A),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_9,plain,
implies(not(A),B) = implies(not(B),A),
inference(paramod,[status(thm)],[c_5,c_157]) ).
fof(and_definition,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_definition) ).
cnf(c_10,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_definition]) ).
cnf(c_11,plain,
and(A,B) = not(implies(not(not(A)),not(B))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
fof(xor_definition,axiom,
! [VAR_0,VAR_1] : xor(VAR_0,VAR_1) = or(and(VAR_0,not(VAR_1)),and(not(VAR_0),VAR_1)),
file('theBenchmark.p',xor_definition) ).
cnf(c_16,plain,
xor(A,B) = or(and(A,not(B)),and(not(A),B)),
inference(clausify,[status(thm)],[xor_definition]) ).
cnf(c_158,plain,
xor(A,B) = or(not(implies(not(not(A)),not(not(B)))),and(not(A),B)),
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_159,plain,
xor(A,B) = or(not(implies(not(not(A)),not(not(B)))),not(implies(not(not(not(A))),not(B)))),
inference(paramod,[status(thm)],[c_11,c_158]) ).
cnf(c_17,plain,
xor(A,B) = implies(not(not(implies(not(not(A)),not(not(B))))),not(implies(not(not(not(A))),not(B)))),
inference(paramod,[status(thm)],[c_5,c_159]) ).
fof(false_definition,axiom,
not(truth) = falsehood,
file('theBenchmark.p',false_definition) ).
cnf(c_24,plain,
not(truth) = falsehood,
inference(clausify,[status(thm)],[false_definition]) ).
cnf(c_25,plain,
falsehood = not(truth),
inference(copy,[status(thm)],[c_24]) ).
fof(prove_alternative_wajsberg_axiom,axiom,
xor(x,falsehood) != x,
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_26,plain,
xor(x,falsehood) != x,
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_160,plain,
xor(x,not(truth)) != x,
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_161,plain,
implies(not(not(implies(not(not(x)),not(not(not(truth)))))),not(implies(not(not(not(x))),not(not(truth))))) != x,
inference(paramod,[status(thm)],[c_17,c_160]) ).
cnf(c_27,plain,
implies(not(not(implies(not(not(x)),not(not(not(truth)))))),not(implies(not(not(not(truth))),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_9,c_161]) ).
cnf(c_162,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_28,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_162]) ).
cnf(c_29,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_163,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_34,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_40,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_164,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_165,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_164]) ).
cnf(c_73,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_165]) ).
cnf(c_84,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_73,c_34]) ).
cnf(c_98,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_84,c_28]) ).
cnf(c_166,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_98,c_29]) ).
cnf(c_100,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_166]) ).
cnf(c_167,plain,
truth = implies(not(truth),A),
inference(paramod,[status(thm)],[c_98,c_9]) ).
cnf(c_102,plain,
implies(not(truth),A) = truth,
inference(copy,[status(thm)],[c_167]) ).
cnf(c_114,plain,
implies(A,implies(not(A),B)) = truth,
inference(paramod,[status(thm)],[c_9,c_100]) ).
cnf(c_168,plain,
implies(truth,A) = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_40,c_3]) ).
cnf(c_169,plain,
A = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_1,c_168]) ).
cnf(c_170,plain,
A = implies(truth,implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_114,c_169]) ).
cnf(c_171,plain,
A = implies(not(A),not(truth)),
inference(paramod,[status(thm)],[c_1,c_170]) ).
cnf(c_146,plain,
implies(not(A),not(truth)) = A,
inference(copy,[status(thm)],[c_171]) ).
cnf(c_172,plain,
truth = implies(implies(not(truth),not(not(truth))),not(not(truth))),
inference(paramod,[status(thm)],[c_40,c_3]) ).
cnf(c_173,plain,
truth = implies(truth,not(not(truth))),
inference(paramod,[status(thm)],[c_102,c_172]) ).
cnf(c_174,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_1,c_173]) ).
cnf(c_147,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_174]) ).
cnf(c_175,plain,
implies(not(not(implies(not(not(x)),not(truth)))),not(implies(not(not(not(truth))),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_147,c_27]) ).
cnf(c_176,plain,
implies(not(not(implies(not(not(truth)),not(x)))),not(implies(not(not(not(truth))),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_9,c_175]) ).
cnf(c_177,plain,
implies(not(not(implies(truth,not(x)))),not(implies(not(not(not(truth))),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_147,c_176]) ).
cnf(c_178,plain,
implies(not(not(not(x))),not(implies(not(not(not(truth))),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_1,c_177]) ).
cnf(c_179,plain,
implies(not(not(not(x))),not(implies(not(truth),not(not(x))))) != x,
inference(paramod,[status(thm)],[c_147,c_178]) ).
cnf(c_180,plain,
implies(not(not(not(x))),not(truth)) != x,
inference(paramod,[status(thm)],[c_102,c_179]) ).
cnf(c_181,plain,
implies(not(not(truth)),not(not(x))) != x,
inference(paramod,[status(thm)],[c_9,c_180]) ).
cnf(c_182,plain,
implies(truth,not(not(x))) != x,
inference(paramod,[status(thm)],[c_147,c_181]) ).
cnf(c_151,plain,
not(not(x)) != x,
inference(paramod,[status(thm)],[c_1,c_182]) ).
cnf(c_183,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_146,c_3]) ).
cnf(c_184,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_102,c_183]) ).
cnf(c_154,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_184]) ).
cnf(c_185,plain,
or(A,not(truth)) = A,
inference(paramod,[status(thm)],[c_146,c_5]) ).
cnf(c_186,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_5,c_185]) ).
cnf(c_155,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_154,c_186]) ).
cnf(c_156,plain,
$false,
inference(resolve,[status(thm)],[c_155,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 21:56:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 56461 was started by sandbox2 on n004,
% 0.12/0.37 % Fri Sep 25 21:56:06 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % Assigning unary symbol not kb_weight 0 and highest precedence (10).
% 0.12/0.42
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.42 % Length of proof is 31.
% 0.12/0.42 % Level of proof is 10.
% 0.12/0.42 % Maximum clause weight is 97.000.
% 0.12/0.42 % Given clauses 25.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------