%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL109-3 : 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 : 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 07:58:00 AM UTC 2026
% Result : Unsatisfiable 10.12s 1.90s
% Output : CNFRefutation 10.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 89 ( 86 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 15 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 9 ( 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 : 140 ( 9 sgn 17 !; 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_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(lemma_1,axiom,
! [VAR_0] : implies(VAR_0,VAR_0) = truth,
file('theBenchmark.p',lemma_1) ).
cnf(c_5,plain,
implies(A,A) = truth,
inference(clausify,[status(thm)],[lemma_1]) ).
fof(lemma_3,axiom,
! [VAR_0] : implies(VAR_0,truth) = truth,
file('theBenchmark.p',lemma_3) ).
cnf(c_7,plain,
implies(A,truth) = truth,
inference(clausify,[status(thm)],[lemma_3]) ).
fof(lemma_4,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,implies(VAR_1,VAR_0)) = truth,
file('theBenchmark.p',lemma_4) ).
cnf(c_8,plain,
implies(A,implies(B,A)) = truth,
inference(clausify,[status(thm)],[lemma_4]) ).
fof(lemma_5,axiom,
! [VAR_0,VAR_1,VAR_2] :
( implies(VAR_0,VAR_2) = truth
| implies(VAR_0,VAR_1) != implies(VAR_1,VAR_2) ),
file('theBenchmark.p',lemma_5) ).
cnf(c_9,plain,
( implies(A,C) = truth
| implies(A,B) != implies(B,C) ),
inference(clausify,[status(thm)],[lemma_5]) ).
cnf(c_10,plain,
( implies(C,B) = truth
| implies(A,B) != implies(C,A) ),
inference(copy,[status(thm)],[c_9]) ).
fof(lemma_7,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(VAR_0,implies(VAR_1,VAR_2)) = implies(VAR_1,implies(VAR_0,VAR_2)),
file('theBenchmark.p',lemma_7) ).
cnf(c_12,plain,
implies(A,implies(B,C)) = implies(B,implies(A,C)),
inference(clausify,[status(thm)],[lemma_7]) ).
fof(lemma_8,axiom,
! [VAR_0] : implies(VAR_0,not(truth)) = not(VAR_0),
file('theBenchmark.p',lemma_8) ).
cnf(c_13,plain,
implies(A,not(truth)) = not(A),
inference(clausify,[status(thm)],[lemma_8]) ).
fof(lemma_9,axiom,
! [VAR_0] : not(not(VAR_0)) = VAR_0,
file('theBenchmark.p',lemma_9) ).
cnf(c_14,plain,
not(not(A)) = A,
inference(clausify,[status(thm)],[lemma_9]) ).
fof(lemma_10,axiom,
! [VAR_0,VAR_1] : implies(not(VAR_0),not(VAR_1)) = implies(VAR_1,VAR_0),
file('theBenchmark.p',lemma_10) ).
cnf(c_15,plain,
implies(not(A),not(B)) = implies(B,A),
inference(clausify,[status(thm)],[lemma_10]) ).
fof(prove_wajsberg_mv_4,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_16,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_2945,plain,
implies(implies(b,implies(implies(a,b),a)),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_17,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(paramod,[status(thm)],[c_12,c_2945]) ).
cnf(c_2946,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_2947,plain,
implies(implies(implies(A,B),B),A) = implies(truth,implies(B,A)),
inference(paramod,[status(thm)],[c_8,c_2946]) ).
cnf(c_27,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(paramod,[status(thm)],[c_1,c_2947]) ).
cnf(c_44,plain,
implies(not(truth),not(A)) = truth,
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_2948,plain,
implies(A,not(B)) = implies(B,implies(A,not(truth))),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_45,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_13,c_2948]) ).
cnf(c_2949,plain,
implies(implies(A,B),not(A)) = implies(implies(not(A),not(B)),not(B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_2950,plain,
implies(A,not(implies(A,B))) = implies(implies(not(A),not(B)),not(B)),
inference(paramod,[status(thm)],[c_45,c_2949]) ).
cnf(c_2951,plain,
implies(A,not(implies(A,B))) = implies(B,not(implies(not(A),not(B)))),
inference(paramod,[status(thm)],[c_45,c_2950]) ).
cnf(c_54,plain,
implies(A,not(implies(not(B),not(A)))) = implies(B,not(implies(B,A))),
inference(copy,[status(thm)],[c_2951]) ).
cnf(c_56,plain,
implies(not(A),not(implies(B,A))) = implies(implies(A,B),B),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_61,plain,
implies(not(A),B) = implies(not(B),A),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_62,plain,
implies(A,implies(implies(b,implies(implies(a,b),a)),a)) != implies(b,A),
inference(resolve,[status(thm)],[c_10,c_17]) ).
cnf(c_117,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_14,c_44]) ).
cnf(c_136,plain,
implies(not(implies(A,B)),C) = implies(A,implies(not(C),B)),
inference(paramod,[status(thm)],[c_61,c_12]) ).
cnf(c_238,plain,
implies(implies(not(A),not(implies(B,A))),B) = implies(A,B),
inference(paramod,[status(thm)],[c_15,c_27]) ).
cnf(c_350,plain,
implies(implies(A,not(A)),not(implies(not(A),A))) = truth,
inference(resolve,[status(thm)],[c_10,c_56]) ).
cnf(c_2952,plain,
implies(not(A),not(implies(B,A))) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_56,c_3]) ).
cnf(c_358,plain,
implies(implies(A,B),B) = implies(not(B),not(implies(A,B))),
inference(copy,[status(thm)],[c_2952]) ).
cnf(c_2953,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_56,c_15]) ).
cnf(c_2954,plain,
implies(not(B),not(implies(A,B))) = implies(implies(B,A),A),
inference(paramod,[status(thm)],[c_358,c_2953]) ).
cnf(c_366,plain,
implies(not(A),not(implies(B,A))) = implies(not(B),not(implies(A,B))),
inference(paramod,[status(thm)],[c_358,c_2954]) ).
cnf(c_2955,plain,
implies(A,implies(not(implies(B,not(implies(A,C)))),C)) = truth,
inference(paramod,[status(thm)],[c_136,c_8]) ).
cnf(c_484,plain,
implies(A,implies(not(B),implies(C,not(implies(A,B))))) = truth,
inference(paramod,[status(thm)],[c_61,c_2955]) ).
cnf(c_2956,plain,
implies(not(implies(not(A),not(implies(B,A)))),C) = implies(implies(B,A),implies(not(C),A)),
inference(paramod,[status(thm)],[c_358,c_136]) ).
cnf(c_2957,plain,
implies(not(A),implies(not(C),not(implies(B,A)))) = implies(implies(B,A),implies(not(C),A)),
inference(paramod,[status(thm)],[c_136,c_2956]) ).
cnf(c_520,plain,
implies(implies(A,B),implies(not(C),B)) = implies(not(B),implies(not(C),not(implies(A,B)))),
inference(copy,[status(thm)],[c_2957]) ).
cnf(c_2958,plain,
implies(not(not(implies(not(A),A))),not(truth)) = implies(not(implies(A,not(A))),not(implies(not(implies(not(A),A)),implies(A,not(A))))),
inference(paramod,[status(thm)],[c_350,c_366]) ).
cnf(c_2959,plain,
implies(implies(not(A),A),not(truth)) = implies(not(implies(A,not(A))),not(implies(not(implies(not(A),A)),implies(A,not(A))))),
inference(paramod,[status(thm)],[c_14,c_2958]) ).
cnf(c_2960,plain,
implies(truth,not(implies(not(A),A))) = implies(not(implies(A,not(A))),not(implies(not(implies(not(A),A)),implies(A,not(A))))),
inference(paramod,[status(thm)],[c_45,c_2959]) ).
cnf(c_2961,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(implies(not(implies(not(A),A)),implies(A,not(A))))),
inference(paramod,[status(thm)],[c_1,c_2960]) ).
cnf(c_2962,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(implies(A,implies(not(implies(not(A),A)),not(A))))),
inference(paramod,[status(thm)],[c_12,c_2961]) ).
cnf(c_2963,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(implies(A,implies(A,not(not(implies(not(A),A))))))),
inference(paramod,[status(thm)],[c_45,c_2962]) ).
cnf(c_2964,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(implies(A,implies(A,implies(not(A),A))))),
inference(paramod,[status(thm)],[c_14,c_2963]) ).
cnf(c_2965,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(implies(A,truth))),
inference(paramod,[status(thm)],[c_8,c_2964]) ).
cnf(c_2966,plain,
not(implies(not(A),A)) = implies(not(implies(A,not(A))),not(truth)),
inference(paramod,[status(thm)],[c_7,c_2965]) ).
cnf(c_2967,plain,
not(implies(not(A),A)) = implies(truth,not(not(implies(A,not(A))))),
inference(paramod,[status(thm)],[c_45,c_2966]) ).
cnf(c_2968,plain,
not(implies(not(A),A)) = implies(truth,implies(A,not(A))),
inference(paramod,[status(thm)],[c_14,c_2967]) ).
cnf(c_1678,plain,
not(implies(not(A),A)) = implies(A,not(A)),
inference(paramod,[status(thm)],[c_1,c_2968]) ).
cnf(c_1873,plain,
not(implies(A,not(A))) = implies(not(A),A),
inference(paramod,[status(thm)],[c_1678,c_14]) ).
cnf(c_2310,plain,
implies(A,not(implies(A,B))) = implies(B,not(implies(B,A))),
inference(paramod,[status(thm)],[c_15,c_54]) ).
cnf(c_2969,plain,
implies(not(implies(b,A)),implies(implies(b,implies(implies(a,b),a)),a)) != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_2310,c_62]) ).
cnf(c_2970,plain,
implies(b,implies(not(implies(implies(b,implies(implies(a,b),a)),a)),A)) != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_136,c_2969]) ).
cnf(c_2496,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),implies(not(A),a))) != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_136,c_2970]) ).
cnf(c_2971,plain,
implies(implies(not(not(A)),implies(not(A),A)),A) = implies(not(A),A),
inference(paramod,[status(thm)],[c_1873,c_238]) ).
cnf(c_2972,plain,
implies(implies(A,implies(not(A),A)),A) = implies(not(A),A),
inference(paramod,[status(thm)],[c_14,c_2971]) ).
cnf(c_2973,plain,
implies(truth,A) = implies(not(A),A),
inference(paramod,[status(thm)],[c_8,c_2972]) ).
cnf(c_2974,plain,
A = implies(not(A),A),
inference(paramod,[status(thm)],[c_1,c_2973]) ).
cnf(c_2768,plain,
implies(not(A),A) = A,
inference(copy,[status(thm)],[c_2974]) ).
cnf(c_2975,plain,
implies(A,B) = implies(not(B),implies(A,B)),
inference(paramod,[status(thm)],[c_2768,c_12]) ).
cnf(c_2853,plain,
implies(not(A),implies(B,A)) = implies(B,A),
inference(copy,[status(thm)],[c_2975]) ).
cnf(c_2976,plain,
implies(A,B) = implies(A,implies(not(implies(A,B)),B)),
inference(paramod,[status(thm)],[c_2768,c_12]) ).
cnf(c_2977,plain,
implies(A,B) = implies(A,implies(not(B),implies(A,B))),
inference(paramod,[status(thm)],[c_61,c_2976]) ).
cnf(c_2978,plain,
implies(A,B) = implies(A,implies(A,B)),
inference(paramod,[status(thm)],[c_2853,c_2977]) ).
cnf(c_2854,plain,
implies(A,implies(A,B)) = implies(A,B),
inference(copy,[status(thm)],[c_2978]) ).
cnf(c_2979,plain,
implies(implies(not(implies(A,B)),not(implies(A,B))),A) = implies(implies(A,B),A),
inference(paramod,[status(thm)],[c_2854,c_238]) ).
cnf(c_2980,plain,
implies(truth,A) = implies(implies(A,B),A),
inference(paramod,[status(thm)],[c_5,c_2979]) ).
cnf(c_2981,plain,
A = implies(implies(A,B),A),
inference(paramod,[status(thm)],[c_1,c_2980]) ).
cnf(c_2935,plain,
implies(implies(A,B),A) = A,
inference(copy,[status(thm)],[c_2981]) ).
cnf(c_2982,plain,
implies(b,implies(implies(b,a),implies(not(A),a))) != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_2935,c_2496]) ).
cnf(c_2983,plain,
implies(b,implies(not(a),implies(not(A),not(implies(b,a))))) != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_520,c_2982]) ).
cnf(c_2984,plain,
truth != implies(A,not(implies(A,b))),
inference(paramod,[status(thm)],[c_484,c_2983]) ).
cnf(c_2943,plain,
implies(A,not(implies(A,b))) != truth,
inference(copy,[status(thm)],[c_2984]) ).
cnf(c_2944,plain,
$false,
inference(resolve,[status(thm)],[c_2943,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 21:54:42 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2353205 was started by sandbox2 on n015,
% 0.17/0.45 % Fri Sep 25 21:54:42 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 10.12/1.90
% 10.12/1.90 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 10.12/1.90
% 10.12/1.90 % SZS status Unsatisfiable for theBenchmark
% 10.12/1.90
% 10.12/1.90 % Proof 1 at 1.16 (+ 0.27) seconds.
% 10.12/1.90 % Length of proof is 38.
% 10.12/1.90 % Level of proof is 11.
% 10.12/1.90 % Maximum clause weight is 61.000.
% 10.12/1.90 % Given clauses 123.
% 10.12/1.90
% 10.12/1.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------