%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL139-1 : 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 07:58:05 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 64 ( 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_wajsberg_lemma,axiom,
implies(x,not(truth)) != not(x),
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c_5,plain,
implies(x,not(truth)) != not(x),
inference(clausify,[status(thm)],[prove_wajsberg_lemma]) ).
cnf(c_6,plain,
not(x) != implies(x,not(truth)),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_65,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_65]) ).
cnf(c_8,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_66,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_11,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_67,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_68,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_67]) ).
cnf(c_14,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_68]) ).
cnf(c_17,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_24,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_17,c_7]) ).
cnf(c_69,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_24,c_8]) ).
cnf(c_25,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_69]) ).
cnf(c_70,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_26,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_70]) ).
cnf(c_71,plain,
implies(truth,implies(implies(A,B),implies(implies(not(A),not(truth)),B))) = truth,
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_28,plain,
implies(implies(A,B),implies(implies(not(A),not(truth)),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_71]) ).
cnf(c_72,plain,
truth = implies(implies(not(truth),not(not(truth))),not(not(truth))),
inference(paramod,[status(thm)],[c_11,c_3]) ).
cnf(c_30,plain,
implies(implies(not(truth),not(not(truth))),not(not(truth))) = truth,
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_11,c_26]) ).
cnf(c_35,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_73]) ).
cnf(c_74,plain,
implies(truth,not(not(truth))) = truth,
inference(paramod,[status(thm)],[c_35,c_30]) ).
cnf(c_36,plain,
not(not(truth)) = truth,
inference(paramod,[status(thm)],[c_1,c_74]) ).
cnf(c_75,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_35,c_3]) ).
cnf(c_76,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_75]) ).
cnf(c_42,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_76]) ).
cnf(c_77,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_42,c_4]) ).
cnf(c_78,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_36,c_77]) ).
cnf(c_49,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_78]) ).
cnf(c_79,plain,
implies(truth,A) = implies(implies(A,not(implies(A,not(truth)))),not(implies(A,not(truth)))),
inference(paramod,[status(thm)],[c_49,c_3]) ).
cnf(c_80,plain,
A = implies(implies(A,not(implies(A,not(truth)))),not(implies(A,not(truth)))),
inference(paramod,[status(thm)],[c_1,c_79]) ).
cnf(c_52,plain,
implies(implies(A,not(implies(A,not(truth)))),not(implies(A,not(truth)))) = A,
inference(copy,[status(thm)],[c_80]) ).
cnf(c_81,plain,
implies(A,implies(implies(not(implies(A,not(truth))),not(truth)),not(truth))) = truth,
inference(paramod,[status(thm)],[c_42,c_28]) ).
cnf(c_82,plain,
implies(A,implies(implies(not(truth),not(implies(A,not(truth)))),not(implies(A,not(truth))))) = truth,
inference(paramod,[status(thm)],[c_3,c_81]) ).
cnf(c_83,plain,
implies(A,implies(truth,not(implies(A,not(truth))))) = truth,
inference(paramod,[status(thm)],[c_35,c_82]) ).
cnf(c_59,plain,
implies(A,not(implies(A,not(truth)))) = truth,
inference(paramod,[status(thm)],[c_1,c_83]) ).
cnf(c_84,plain,
implies(truth,not(implies(A,not(truth)))) = A,
inference(paramod,[status(thm)],[c_59,c_52]) ).
cnf(c_60,plain,
not(implies(A,not(truth))) = A,
inference(paramod,[status(thm)],[c_1,c_84]) ).
cnf(c_85,plain,
not(implies(implies(not(truth),A),A)) = implies(A,not(truth)),
inference(paramod,[status(thm)],[c_3,c_60]) ).
cnf(c_86,plain,
not(implies(truth,A)) = implies(A,not(truth)),
inference(paramod,[status(thm)],[c_35,c_85]) ).
cnf(c_63,plain,
not(A) = implies(A,not(truth)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_64,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL139-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 21:54:32 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 340521 was started by sandbox on n005,
% 0.11/0.37 % Fri Sep 25 21:54:32 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).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.40 % Length of proof is 26.
% 0.11/0.40 % Level of proof is 13.
% 0.11/0.40 % Maximum clause weight is 29.000.
% 0.11/0.40 % Given clauses 22.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------