%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL156-1 : 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 : n012.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 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 77 ( 10 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_253,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_253]) ).
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]) ).
fof(prove_alternative_wajsberg_axiom,axiom,
and_star(x,truth) != x,
file('theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_25,plain,
and_star(x,truth) != x,
inference(clausify,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_254,plain,
not(implies(not(not(x)),not(truth))) != x,
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_255,plain,
not(implies(not(not(x)),falsehood)) != x,
inference(paramod,[status(thm)],[c_24,c_254]) ).
cnf(c_26,plain,
not(implies(not(falsehood),not(x))) != x,
inference(paramod,[status(thm)],[c_9,c_255]) ).
cnf(c_256,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_27,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_256]) ).
cnf(c_28,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_257,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_33,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_257]) ).
cnf(c_258,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_40,plain,
implies(implies(not(A),falsehood),A) = truth,
inference(paramod,[status(thm)],[c_24,c_258]) ).
cnf(c_57,plain,
implies(implies(not(A),B),A) = implies(implies(A,not(B)),not(B)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_63,plain,
implies(implies(A,not(falsehood)),not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_57,c_40]) ).
cnf(c_259,plain,
implies(falsehood,A) = implies(not(A),truth),
inference(paramod,[status(thm)],[c_24,c_9]) ).
cnf(c_108,plain,
implies(not(A),truth) = implies(falsehood,A),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_260,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_261,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_260]) ).
cnf(c_112,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_261]) ).
cnf(c_123,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_112,c_33]) ).
cnf(c_138,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_123,c_27]) ).
cnf(c_262,plain,
truth = implies(falsehood,A),
inference(paramod,[status(thm)],[c_138,c_108]) ).
cnf(c_139,plain,
implies(falsehood,A) = truth,
inference(copy,[status(thm)],[c_262]) ).
cnf(c_263,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_138,c_28]) ).
cnf(c_140,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_263]) ).
cnf(c_264,plain,
implies(truth,not(falsehood)) = implies(implies(not(falsehood),implies(A,not(falsehood))),implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_63,c_3]) ).
cnf(c_265,plain,
not(falsehood) = implies(implies(not(falsehood),implies(A,not(falsehood))),implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_1,c_264]) ).
cnf(c_266,plain,
not(falsehood) = implies(truth,implies(A,not(falsehood))),
inference(paramod,[status(thm)],[c_140,c_265]) ).
cnf(c_267,plain,
not(falsehood) = implies(A,not(falsehood)),
inference(paramod,[status(thm)],[c_1,c_266]) ).
cnf(c_200,plain,
implies(A,not(falsehood)) = not(falsehood),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_268,plain,
truth = implies(implies(not(falsehood),A),A),
inference(paramod,[status(thm)],[c_63,c_3]) ).
cnf(c_201,plain,
implies(implies(not(falsehood),A),A) = truth,
inference(copy,[status(thm)],[c_268]) ).
cnf(c_269,plain,
implies(implies(implies(not(falsehood),A),A),not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_3,c_63]) ).
cnf(c_270,plain,
implies(truth,not(falsehood)) = truth,
inference(paramod,[status(thm)],[c_201,c_269]) ).
cnf(c_202,plain,
not(falsehood) = truth,
inference(paramod,[status(thm)],[c_200,c_270]) ).
cnf(c_271,plain,
not(implies(truth,not(x))) != x,
inference(paramod,[status(thm)],[c_202,c_26]) ).
cnf(c_208,plain,
not(not(x)) != x,
inference(paramod,[status(thm)],[c_1,c_271]) ).
cnf(c_272,plain,
implies(truth,A) = implies(not(A),falsehood),
inference(paramod,[status(thm)],[c_202,c_9]) ).
cnf(c_273,plain,
A = implies(not(A),falsehood),
inference(paramod,[status(thm)],[c_1,c_272]) ).
cnf(c_246,plain,
implies(not(A),falsehood) = A,
inference(copy,[status(thm)],[c_273]) ).
cnf(c_274,plain,
implies(A,falsehood) = implies(implies(falsehood,not(A)),not(A)),
inference(paramod,[status(thm)],[c_246,c_3]) ).
cnf(c_275,plain,
implies(A,falsehood) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_139,c_274]) ).
cnf(c_250,plain,
implies(A,falsehood) = not(A),
inference(paramod,[status(thm)],[c_1,c_275]) ).
cnf(c_276,plain,
or(A,falsehood) = A,
inference(paramod,[status(thm)],[c_246,c_5]) ).
cnf(c_277,plain,
implies(not(A),falsehood) = A,
inference(paramod,[status(thm)],[c_5,c_276]) ).
cnf(c_251,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_250,c_277]) ).
cnf(c_252,plain,
$false,
inference(resolve,[status(thm)],[c_251,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Fri Sep 25 21:55:50 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3146912 was started by sandbox2 on n012,
% 0.03/0.31 % Fri Sep 25 21:55:50 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.11/0.35
% 0.11/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.35
% 0.11/0.35 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.35 % Length of proof is 32.
% 0.11/0.35 % Level of proof is 11.
% 0.11/0.35 % Maximum clause weight is 14.000.
% 0.11/0.35 % Given clauses 29.
% 0.11/0.35
% 0.11/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------