%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL141-1 : 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 : n026.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 0.12s 10.53s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 11 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(not(x),not(y)) != implies(y,x),
file('theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c_5,plain,
implies(not(x),not(y)) != implies(y,x),
inference(clausify,[status(thm)],[prove_wajsberg_lemma]) ).
cnf(c_394,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_394]) ).
cnf(c_7,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_395,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_12,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_395]) ).
cnf(c_14,plain,
implies(implies(A,implies(B,C)),implies(implies(implies(C,B),B),implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_396,plain,
implies(truth,implies(implies(A,B),implies(C,B))) = implies(implies(implies(implies(A,B),implies(C,B)),implies(C,A)),implies(C,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_397,plain,
implies(implies(A,B),implies(C,B)) = implies(implies(implies(implies(A,B),implies(C,B)),implies(C,A)),implies(C,A)),
inference(paramod,[status(thm)],[c_1,c_396]) ).
cnf(c_16,plain,
implies(implies(implies(implies(A,B),implies(C,B)),implies(C,A)),implies(C,A)) = implies(implies(A,B),implies(C,B)),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_17,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_19,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_398,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_399,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_398]) ).
cnf(c_28,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_399]) ).
cnf(c_36,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_28,c_12]) ).
cnf(c_42,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_400,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_43,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_400]) ).
cnf(c_401,plain,
implies(implies(implies(A,B),B),A) = implies(truth,implies(B,A)),
inference(paramod,[status(thm)],[c_43,c_17]) ).
cnf(c_44,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_401]) ).
cnf(c_402,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_45,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_402]) ).
cnf(c_403,plain,
implies(truth,A) = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_404,plain,
A = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_1,c_403]) ).
cnf(c_66,plain,
implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))) = A,
inference(copy,[status(thm)],[c_404]) ).
cnf(c_405,plain,
implies(truth,not(not(truth))) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_19,c_44]) ).
cnf(c_406,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(paramod,[status(thm)],[c_1,c_405]) ).
cnf(c_78,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(copy,[status(thm)],[c_406]) ).
cnf(c_407,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_78,c_44]) ).
cnf(c_408,plain,
implies(truth,not(truth)) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_28,c_407]) ).
cnf(c_409,plain,
not(truth) = implies(not(not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_408]) ).
cnf(c_84,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(copy,[status(thm)],[c_409]) ).
cnf(c_410,plain,
implies(truth,implies(not(truth),A)) = truth,
inference(paramod,[status(thm)],[c_19,c_45]) ).
cnf(c_128,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_1,c_410]) ).
cnf(c_411,plain,
implies(implies(implies(A,not(not(truth))),not(truth)),not(truth)) = truth,
inference(paramod,[status(thm)],[c_84,c_45]) ).
cnf(c_412,plain,
implies(implies(not(truth),implies(A,not(not(truth)))),implies(A,not(not(truth)))) = truth,
inference(paramod,[status(thm)],[c_3,c_411]) ).
cnf(c_413,plain,
implies(truth,implies(A,not(not(truth)))) = truth,
inference(paramod,[status(thm)],[c_128,c_412]) ).
cnf(c_131,plain,
implies(A,not(not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_413]) ).
cnf(c_414,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_131,c_78]) ).
cnf(c_135,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_414]) ).
cnf(c_415,plain,
implies(truth,A) = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_128,c_3]) ).
cnf(c_416,plain,
A = implies(implies(A,not(truth)),not(truth)),
inference(paramod,[status(thm)],[c_1,c_415]) ).
cnf(c_137,plain,
implies(implies(A,not(truth)),not(truth)) = A,
inference(copy,[status(thm)],[c_416]) ).
cnf(c_417,plain,
implies(implies(not(not(truth)),not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_137,c_4]) ).
cnf(c_418,plain,
implies(implies(truth,not(implies(A,not(truth)))),A) = truth,
inference(paramod,[status(thm)],[c_135,c_417]) ).
cnf(c_176,plain,
implies(not(implies(A,not(truth))),A) = truth,
inference(paramod,[status(thm)],[c_1,c_418]) ).
cnf(c_419,plain,
implies(truth,implies(A,implies(not(A),not(truth)))) = truth,
inference(paramod,[status(thm)],[c_176,c_4]) ).
cnf(c_189,plain,
implies(A,implies(not(A),not(truth))) = truth,
inference(paramod,[status(thm)],[c_1,c_419]) ).
cnf(c_420,plain,
implies(truth,implies(not(A),not(truth))) = A,
inference(paramod,[status(thm)],[c_189,c_66]) ).
cnf(c_194,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_1,c_420]) ).
cnf(c_421,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_194,c_3]) ).
cnf(c_422,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_128,c_421]) ).
cnf(c_423,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_1,c_422]) ).
cnf(c_198,plain,
not(A) = implies(A,not(truth)),
inference(copy,[status(thm)],[c_423]) ).
cnf(c_424,plain,
implies(implies(not(A),implies(B,not(truth))),implies(implies(implies(not(truth),B),B),A)) = truth,
inference(paramod,[status(thm)],[c_194,c_14]) ).
cnf(c_425,plain,
implies(implies(not(A),implies(B,not(truth))),implies(implies(truth,B),A)) = truth,
inference(paramod,[status(thm)],[c_128,c_424]) ).
cnf(c_241,plain,
implies(implies(not(A),implies(B,not(truth))),implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_425]) ).
cnf(c_247,plain,
implies(implies(x,not(truth)),not(y)) != implies(y,x),
inference(paramod,[status(thm)],[c_198,c_5]) ).
cnf(c_318,plain,
implies(implies(x,not(truth)),implies(y,not(truth))) != implies(y,x),
inference(paramod,[status(thm)],[c_198,c_247]) ).
cnf(c_426,plain,
implies(implies(implies(not(A),implies(B,not(truth))),implies(B,A)),implies(B,A)) = implies(implies(A,not(truth)),implies(B,not(truth))),
inference(paramod,[status(thm)],[c_198,c_16]) ).
cnf(c_427,plain,
implies(truth,implies(B,A)) = implies(implies(A,not(truth)),implies(B,not(truth))),
inference(paramod,[status(thm)],[c_241,c_426]) ).
cnf(c_428,plain,
implies(B,A) = implies(implies(A,not(truth)),implies(B,not(truth))),
inference(paramod,[status(thm)],[c_1,c_427]) ).
cnf(c_392,plain,
implies(implies(A,not(truth)),implies(B,not(truth))) = implies(B,A),
inference(copy,[status(thm)],[c_428]) ).
cnf(c_393,plain,
$false,
inference(resolve,[status(thm)],[c_392,c_318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n026.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 21:57:35 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 3560957 was started by sandbox on n026,
% 0.09/10.38 % Fri Sep 25 21:57:35 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.38
% 0.09/10.38 % From the command line: assign(max_seconds, 300).
% 0.12/10.53
% 0.12/10.53 % SZS status Unsatisfiable for theBenchmark
% 0.12/10.53
% 0.12/10.53 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.12/10.53 % Length of proof is 34.
% 0.12/10.53 % Level of proof is 17.
% 0.12/10.53 % Maximum clause weight is 23.000.
% 0.12/10.53 % Given clauses 39.
% 0.12/10.53
% 0.12/10.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------