%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL145-1 : 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 : n005.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 07:58:06 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_wajsberg_theorem,axiom,
not(big_V(x,y)) != big_hat(not(x),not(y)),
file('theBenchmark.p',prove_wajsberg_theorem) ).
cnf(c_3,plain,
not(big_V(x,y)) != big_hat(not(x),not(y)),
inference(clausify,[status(thm)],[prove_wajsberg_theorem]) ).
fof(big_hat_definition,axiom,
! [VAR_0,VAR_1] : big_hat(VAR_0,VAR_1) = not(big_V(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',big_hat_definition) ).
cnf(c_4,plain,
big_hat(A,B) = not(big_V(not(A),not(B))),
inference(clausify,[status(thm)],[big_hat_definition]) ).
fof(big_V_definition,axiom,
! [VAR_0,VAR_1] : big_V(VAR_0,VAR_1) = implies(implies(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',big_V_definition) ).
cnf(c_5,plain,
big_V(A,B) = implies(implies(A,B),B),
inference(clausify,[status(thm)],[big_V_definition]) ).
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_6,plain,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
inference(clausify,[status(thm)],[wajsberg_4]) ).
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_7,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
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_8,plain,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
inference(clausify,[status(thm)],[wajsberg_2]) ).
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_9,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
cnf(c_62,plain,
not(implies(implies(x,y),y)) != big_hat(not(x),not(y)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_63,plain,
not(implies(implies(x,y),y)) != not(big_V(not(not(x)),not(not(y)))),
inference(paramod,[status(thm)],[c_4,c_62]) ).
cnf(c_64,plain,
not(implies(implies(x,y),y)) != not(implies(implies(not(not(x)),not(not(y))),not(not(y)))),
inference(paramod,[status(thm)],[c_5,c_63]) ).
cnf(c_10,plain,
not(implies(implies(not(not(x)),not(not(y))),not(not(y)))) != not(implies(implies(x,y),y)),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_15,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_65,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_16,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_66,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_17,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_9,c_66]) ).
cnf(c_18,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_67,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference(paramod,[status(thm)],[c_15,c_5]) ).
cnf(c_68,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(paramod,[status(thm)],[c_5,c_67]) ).
cnf(c_28,plain,
implies(implies(not(truth),not(not(truth))),not(not(truth))) = truth,
inference(paramod,[status(thm)],[c_7,c_68]) ).
cnf(c_69,plain,
implies(implies(A,implies(not(B),not(truth))),implies(truth,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_30,plain,
implies(implies(A,implies(not(B),not(truth))),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_9,c_69]) ).
cnf(c_70,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_17,c_9]) ).
cnf(c_71,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_9,c_70]) ).
cnf(c_35,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,plain,
implies(A,implies(A,A)) = truth,
inference(paramod,[status(thm)],[c_16,c_17]) ).
cnf(c_36,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_35,c_72]) ).
cnf(c_73,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_37,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_9,c_73]) ).
cnf(c_74,plain,
implies(truth,not(not(truth))) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))),
inference(paramod,[status(thm)],[c_28,c_7]) ).
cnf(c_75,plain,
not(not(truth)) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))),
inference(paramod,[status(thm)],[c_9,c_74]) ).
cnf(c_76,plain,
not(not(truth)) = implies(truth,implies(not(truth),not(not(truth)))),
inference(paramod,[status(thm)],[c_37,c_75]) ).
cnf(c_77,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_9,c_76]) ).
cnf(c_38,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_78,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_37,c_8]) ).
cnf(c_41,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_9,c_78]) ).
cnf(c_79,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_15,c_41]) ).
cnf(c_46,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_9,c_79]) ).
cnf(c_80,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_46,c_38]) ).
cnf(c_49,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_80]) ).
cnf(c_81,plain,
implies(truth,implies(implies(not(not(truth)),not(not(A))),A)) = truth,
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_82,plain,
implies(truth,implies(implies(truth,not(not(A))),A)) = truth,
inference(paramod,[status(thm)],[c_49,c_81]) ).
cnf(c_83,plain,
implies(truth,implies(not(not(A)),A)) = truth,
inference(paramod,[status(thm)],[c_9,c_82]) ).
cnf(c_50,plain,
implies(not(not(A)),A) = truth,
inference(paramod,[status(thm)],[c_9,c_83]) ).
cnf(c_84,plain,
implies(truth,implies(A,not(not(A)))) = truth,
inference(paramod,[status(thm)],[c_50,c_6]) ).
cnf(c_59,plain,
implies(A,not(not(A))) = truth,
inference(paramod,[status(thm)],[c_9,c_84]) ).
cnf(c_85,plain,
implies(truth,A) = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_50,c_7]) ).
cnf(c_86,plain,
A = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_9,c_85]) ).
cnf(c_87,plain,
A = implies(truth,not(not(A))),
inference(paramod,[status(thm)],[c_59,c_86]) ).
cnf(c_88,plain,
A = not(not(A)),
inference(paramod,[status(thm)],[c_9,c_87]) ).
cnf(c_60,plain,
not(not(A)) = A,
inference(copy,[status(thm)],[c_88]) ).
cnf(c_89,plain,
not(implies(implies(x,not(not(y))),not(not(y)))) != not(implies(implies(x,y),y)),
inference(paramod,[status(thm)],[c_60,c_10]) ).
cnf(c_90,plain,
not(implies(implies(x,y),not(not(y)))) != not(implies(implies(x,y),y)),
inference(paramod,[status(thm)],[c_60,c_89]) ).
cnf(c_91,plain,
not(implies(implies(x,y),y)) != not(implies(implies(x,y),y)),
inference(paramod,[status(thm)],[c_60,c_90]) ).
cnf(c_61,plain,
$false,
inference(copy,[status(thm)],[c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n005.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Fri Sep 25 21:55:46 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.36 % Process 343136 was started by sandbox on n005,
% 0.06/0.36 % Fri Sep 25 21:55:46 2026
% 0.06/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.37
% 0.06/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 25.
% 0.09/0.43 % Level of proof is 11.
% 0.09/0.43 % Maximum clause weight is 41.000.
% 0.09/0.43 % Given clauses 27.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------