%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL152-1 : 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 : 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 07:58:06 AM UTC 2026
% Result : Unsatisfiable 4.96s 1.20s
% Output : CNFRefutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 106 ( 106 unt; 0 def)
% Number of atoms : 106 ( 105 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 169 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_wajsberg_theorem,axiom,
implies(big_hat(x,y),z) != implies(implies(x,y),implies(x,z)),
file('theBenchmark.p',prove_wajsberg_theorem) ).
cnf(c_3,plain,
implies(big_hat(x,y),z) != implies(implies(x,y),implies(x,z)),
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_2611,plain,
implies(not(big_V(not(x),not(y))),z) != implies(implies(x,y),implies(x,z)),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_10,plain,
implies(not(implies(implies(not(x),not(y)),not(y))),z) != implies(implies(x,y),implies(x,z)),
inference(paramod,[status(thm)],[c_5,c_2611]) ).
cnf(c_2612,plain,
big_V(implies(A,B),B) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_2613,plain,
implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_5,c_2612]) ).
cnf(c_2614,plain,
implies(implies(B,implies(A,B)),implies(A,B)) = implies(implies(implies(B,A),A),B),
inference(paramod,[status(thm)],[c_7,c_2613]) ).
cnf(c_13,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(copy,[status(thm)],[c_2614]) ).
cnf(c_2615,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_2616,plain,
implies(A,B) = implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))),
inference(paramod,[status(thm)],[c_9,c_2615]) ).
cnf(c_15,plain,
implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(copy,[status(thm)],[c_2616]) ).
cnf(c_2617,plain,
implies(truth,implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C))) = truth,
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_17,plain,
implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C)) = truth,
inference(paramod,[status(thm)],[c_9,c_2617]) ).
cnf(c_2618,plain,
implies(implies(A,implies(not(B),not(C))),implies(truth,implies(A,implies(C,B)))) = truth,
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_18,plain,
implies(implies(A,implies(not(B),not(C))),implies(A,implies(C,B))) = truth,
inference(paramod,[status(thm)],[c_9,c_2618]) ).
cnf(c_2619,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_8,c_7]) ).
cnf(c_2620,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_9,c_2619]) ).
cnf(c_21,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_2620]) ).
cnf(c_2621,plain,
implies(truth,implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))) = truth,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_25,plain,
implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D)) = truth,
inference(paramod,[status(thm)],[c_9,c_2621]) ).
cnf(c_29,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_2622,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_30,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_2622]) ).
cnf(c_2623,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_31,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_9,c_2623]) ).
cnf(c_32,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_2624,plain,
implies(truth,A) = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_29,c_7]) ).
cnf(c_2625,plain,
A = implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))),
inference(paramod,[status(thm)],[c_9,c_2624]) ).
cnf(c_70,plain,
implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))) = A,
inference(copy,[status(thm)],[c_2625]) ).
cnf(c_2626,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_29,c_13]) ).
cnf(c_2627,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_2626]) ).
cnf(c_77,plain,
implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(copy,[status(thm)],[c_2627]) ).
cnf(c_2628,plain,
implies(truth,implies(implies(implies(implies(A,B),B),C),implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_31,c_8]) ).
cnf(c_84,plain,
implies(implies(implies(implies(A,B),B),C),implies(A,C)) = truth,
inference(paramod,[status(thm)],[c_9,c_2628]) ).
cnf(c_2629,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_31,c_9]) ).
cnf(c_2630,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_9,c_2629]) ).
cnf(c_87,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_2630]) ).
cnf(c_2631,plain,
implies(A,implies(A,A)) = truth,
inference(paramod,[status(thm)],[c_30,c_31]) ).
cnf(c_91,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_87,c_2631]) ).
cnf(c_2632,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_91,c_32]) ).
cnf(c_92,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_9,c_2632]) ).
cnf(c_2633,plain,
implies(truth,implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(paramod,[status(thm)],[c_92,c_77]) ).
cnf(c_93,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(paramod,[status(thm)],[c_9,c_2633]) ).
cnf(c_2634,plain,
implies(truth,implies(implies(not(not(truth)),not(not(A))),A)) = truth,
inference(paramod,[status(thm)],[c_29,c_17]) ).
cnf(c_113,plain,
implies(implies(not(not(truth)),not(not(A))),A) = truth,
inference(paramod,[status(thm)],[c_9,c_2634]) ).
cnf(c_2635,plain,
implies(truth,implies(not(A),implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_92,c_18]) ).
cnf(c_125,plain,
implies(not(A),implies(A,B)) = truth,
inference(paramod,[status(thm)],[c_9,c_2635]) ).
cnf(c_2636,plain,
implies(truth,implies(A,B)) = implies(implies(implies(A,B),not(A)),not(A)),
inference(paramod,[status(thm)],[c_125,c_7]) ).
cnf(c_2637,plain,
implies(A,B) = implies(implies(implies(A,B),not(A)),not(A)),
inference(paramod,[status(thm)],[c_9,c_2636]) ).
cnf(c_129,plain,
implies(implies(implies(A,B),not(A)),not(A)) = implies(A,B),
inference(copy,[status(thm)],[c_2637]) ).
cnf(c_133,plain,
implies(not(truth),A) = truth,
inference(paramod,[status(thm)],[c_9,c_125]) ).
cnf(c_2638,plain,
truth = not(not(truth)),
inference(paramod,[status(thm)],[c_133,c_93]) ).
cnf(c_137,plain,
not(not(truth)) = truth,
inference(copy,[status(thm)],[c_2638]) ).
cnf(c_2639,plain,
implies(implies(truth,not(not(A))),A) = truth,
inference(paramod,[status(thm)],[c_137,c_113]) ).
cnf(c_138,plain,
implies(not(not(A)),A) = truth,
inference(paramod,[status(thm)],[c_9,c_2639]) ).
cnf(c_2640,plain,
implies(truth,implies(A,not(not(A)))) = truth,
inference(paramod,[status(thm)],[c_138,c_6]) ).
cnf(c_142,plain,
implies(A,not(not(A))) = truth,
inference(paramod,[status(thm)],[c_9,c_2640]) ).
cnf(c_2641,plain,
implies(truth,A) = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_138,c_7]) ).
cnf(c_2642,plain,
A = implies(implies(A,not(not(A))),not(not(A))),
inference(paramod,[status(thm)],[c_9,c_2641]) ).
cnf(c_2643,plain,
A = implies(truth,not(not(A))),
inference(paramod,[status(thm)],[c_142,c_2642]) ).
cnf(c_2644,plain,
A = not(not(A)),
inference(paramod,[status(thm)],[c_9,c_2643]) ).
cnf(c_143,plain,
not(not(A)) = A,
inference(copy,[status(thm)],[c_2644]) ).
cnf(c_147,plain,
implies(implies(not(A),B),implies(not(B),A)) = truth,
inference(paramod,[status(thm)],[c_143,c_6]) ).
cnf(c_2645,plain,
implies(implies(implies(not(A),B),implies(not(B),A)),implies(not(B),not(not(A)))) = implies(not(A),B),
inference(paramod,[status(thm)],[c_143,c_15]) ).
cnf(c_2646,plain,
implies(truth,implies(not(B),not(not(A)))) = implies(not(A),B),
inference(paramod,[status(thm)],[c_147,c_2645]) ).
cnf(c_2647,plain,
implies(truth,implies(not(B),A)) = implies(not(A),B),
inference(paramod,[status(thm)],[c_143,c_2646]) ).
cnf(c_151,plain,
implies(not(A),B) = implies(not(B),A),
inference(paramod,[status(thm)],[c_9,c_2647]) ).
cnf(c_156,plain,
implies(A,implies(not(A),B)) = truth,
inference(paramod,[status(thm)],[c_143,c_125]) ).
cnf(c_157,plain,
implies(not(z),implies(implies(not(x),not(y)),not(y))) != implies(implies(x,y),implies(x,z)),
inference(paramod,[status(thm)],[c_151,c_10]) ).
cnf(c_2648,plain,
implies(truth,implies(not(A),not(truth))) = A,
inference(paramod,[status(thm)],[c_156,c_70]) ).
cnf(c_158,plain,
implies(not(A),not(truth)) = A,
inference(paramod,[status(thm)],[c_9,c_2648]) ).
cnf(c_2649,plain,
implies(A,not(truth)) = implies(implies(not(truth),not(A)),not(A)),
inference(paramod,[status(thm)],[c_158,c_7]) ).
cnf(c_2650,plain,
implies(A,not(truth)) = implies(truth,not(A)),
inference(paramod,[status(thm)],[c_133,c_2649]) ).
cnf(c_2651,plain,
implies(A,not(truth)) = not(A),
inference(paramod,[status(thm)],[c_9,c_2650]) ).
cnf(c_159,plain,
not(A) = implies(A,not(truth)),
inference(copy,[status(thm)],[c_2651]) ).
cnf(c_201,plain,
implies(implies(A,B),implies(implies(B,not(truth)),not(A))) = truth,
inference(paramod,[status(thm)],[c_159,c_8]) ).
cnf(c_2652,plain,
implies(implies(implies(A,B),implies(implies(B,not(truth)),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(paramod,[status(thm)],[c_159,c_15]) ).
cnf(c_2653,plain,
implies(truth,implies(not(B),not(A))) = implies(A,B),
inference(paramod,[status(thm)],[c_201,c_2652]) ).
cnf(c_207,plain,
implies(not(A),not(B)) = implies(B,A),
inference(paramod,[status(thm)],[c_9,c_2653]) ).
cnf(c_224,plain,
implies(implies(z,not(truth)),implies(implies(not(x),not(y)),not(y))) != implies(implies(x,y),implies(x,z)),
inference(paramod,[status(thm)],[c_159,c_157]) ).
cnf(c_2654,plain,
implies(implies(A,B),not(A)) = implies(implies(not(A),not(B)),not(B)),
inference(paramod,[status(thm)],[c_207,c_7]) ).
cnf(c_282,plain,
implies(implies(not(A),not(B)),not(B)) = implies(implies(A,B),not(A)),
inference(copy,[status(thm)],[c_2654]) ).
cnf(c_329,plain,
implies(implies(A,not(truth)),not(B)) = implies(B,A),
inference(paramod,[status(thm)],[c_159,c_207]) ).
cnf(c_332,plain,
implies(implies(z,not(truth)),implies(implies(x,y),not(x))) != implies(implies(x,y),implies(x,z)),
inference(paramod,[status(thm)],[c_282,c_224]) ).
cnf(c_2655,plain,
implies(truth,implies(implies(A,implies(B,C)),implies(B,implies(A,C)))) = truth,
inference(paramod,[status(thm)],[c_84,c_25]) ).
cnf(c_760,plain,
implies(implies(A,implies(B,C)),implies(B,implies(A,C))) = truth,
inference(paramod,[status(thm)],[c_9,c_2655]) ).
cnf(c_2543,plain,
implies(implies(z,not(truth)),implies(implies(x,y),not(x))) != implies(implies(x,y),implies(implies(z,not(truth)),not(x))),
inference(paramod,[status(thm)],[c_329,c_332]) ).
cnf(c_2656,plain,
implies(implies(implies(implies(A,B),implies(C,not(A))),implies(C,implies(implies(A,B),not(A)))),implies(C,implies(implies(A,B),not(A)))) = implies(implies(implies(implies(A,B),not(A)),not(A)),implies(C,not(A))),
inference(paramod,[status(thm)],[c_129,c_21]) ).
cnf(c_2657,plain,
implies(truth,implies(C,implies(implies(A,B),not(A)))) = implies(implies(implies(implies(A,B),not(A)),not(A)),implies(C,not(A))),
inference(paramod,[status(thm)],[c_760,c_2656]) ).
cnf(c_2658,plain,
implies(C,implies(implies(A,B),not(A))) = implies(implies(implies(implies(A,B),not(A)),not(A)),implies(C,not(A))),
inference(paramod,[status(thm)],[c_9,c_2657]) ).
cnf(c_2659,plain,
implies(C,implies(implies(A,B),not(A))) = implies(implies(A,B),implies(C,not(A))),
inference(paramod,[status(thm)],[c_129,c_2658]) ).
cnf(c_2609,plain,
implies(implies(A,B),implies(C,not(A))) = implies(C,implies(implies(A,B),not(A))),
inference(copy,[status(thm)],[c_2659]) ).
cnf(c_2660,plain,
implies(implies(x,y),implies(implies(z,not(truth)),not(x))) != implies(implies(z,not(truth)),implies(implies(x,y),not(x))),
inference(copy,[status(thm)],[c_2543]) ).
cnf(c_2610,plain,
$false,
inference(resolve,[status(thm)],[c_2609,c_2660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL152-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 21:58:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2363004 was started by sandbox on n015,
% 0.08/0.37 % Fri Sep 25 21:58:12 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 4.96/1.20
% 4.96/1.20 % SZS status Unsatisfiable for theBenchmark
% 4.96/1.20
% 4.96/1.20 % Proof 1 at 0.64 (+ 0.18) seconds.
% 4.96/1.20 % Length of proof is 49.
% 4.96/1.20 % Level of proof is 19.
% 4.96/1.20 % Maximum clause weight is 88.000.
% 4.96/1.20 % Given clauses 113.
% 4.96/1.20
% 4.96/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------