%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL157-1 : 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 : n015.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 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 2 sgn 14 !; 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_78,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_78]) ).
fof(and_star_definition,axiom,
! [VAR_0,VAR_1] : and_star(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_star_definition) ).
cnf(c_20,plain,
and_star(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_star_definition]) ).
cnf(c_21,plain,
and_star(A,B) = not(implies(not(not(A)),not(B))),
inference(paramod,[status(thm)],[c_5,c_20]) ).
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,
and_star(x,falsehood) != falsehood,
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_26,plain,
and_star(x,falsehood) != falsehood,
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_79,plain,
and_star(x,not(truth)) != falsehood,
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_80,plain,
not(implies(not(not(x)),not(not(truth)))) != falsehood,
inference(paramod,[status(thm)],[c_21,c_79]) ).
cnf(c_27,plain,
not(implies(not(not(x)),not(not(truth)))) != not(truth),
inference(paramod,[status(thm)],[c_25,c_80]) ).
cnf(c_81,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_81]) ).
cnf(c_82,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_35,plain,
implies(implies(not(A),B),A) = implies(implies(A,not(B)),not(B)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_36,plain,
implies(implies(not(not(A)),B),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_83,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_84,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_83]) ).
cnf(c_42,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_84]) ).
cnf(c_44,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_42,c_31]) ).
cnf(c_56,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_44,c_28]) ).
cnf(c_85,plain,
implies(truth,A) = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_42,c_35]) ).
cnf(c_86,plain,
A = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_1,c_85]) ).
cnf(c_70,plain,
implies(implies(A,not(not(A))),not(not(A))) = A,
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
implies(truth,implies(A,not(not(A)))) = truth,
inference(paramod,[status(thm)],[c_42,c_36]) ).
cnf(c_74,plain,
implies(A,not(not(A))) = truth,
inference(paramod,[status(thm)],[c_1,c_87]) ).
cnf(c_88,plain,
implies(truth,not(not(A))) = A,
inference(paramod,[status(thm)],[c_74,c_70]) ).
cnf(c_76,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_1,c_88]) ).
cnf(c_89,plain,
not(implies(x,not(not(truth)))) != not(truth),
inference(paramod,[status(thm)],[c_76,c_27]) ).
cnf(c_90,plain,
not(implies(x,truth)) != not(truth),
inference(paramod,[status(thm)],[c_76,c_89]) ).
cnf(c_91,plain,
not(truth) != not(truth),
inference(paramod,[status(thm)],[c_56,c_90]) ).
cnf(c_77,plain,
$false,
inference(copy,[status(thm)],[c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 21:59:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2364476 was started by sandbox on n015,
% 0.11/0.37 % Fri Sep 25 21:59:12 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 24.
% 0.11/0.41 % Level of proof is 5.
% 0.11/0.41 % Maximum clause weight is 29.000.
% 0.11/0.41 % Given clauses 24.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------