TSTP Solution File: LCL109-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL109-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:44:05 EDT 2022
% Result : Unsatisfiable 5.44s 5.72s
% Output : Refutation 5.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL109-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 21:23:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.89/4.18 ============================== Prover9 ===============================
% 3.89/4.18 Prover9 (32) version 2009-11A, November 2009.
% 3.89/4.18 Process 29489 was started by sandbox on n017.cluster.edu,
% 3.89/4.18 Mon Jul 4 21:23:28 2022
% 3.89/4.18 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29335_n017.cluster.edu".
% 3.89/4.18 ============================== end of head ===========================
% 3.89/4.18
% 3.89/4.18 ============================== INPUT =================================
% 3.89/4.18
% 3.89/4.18 % Reading from file /tmp/Prover9_29335_n017.cluster.edu
% 3.89/4.18
% 3.89/4.18 set(prolog_style_variables).
% 3.89/4.18 set(auto2).
% 3.89/4.18 % set(auto2) -> set(auto).
% 3.89/4.18 % set(auto) -> set(auto_inference).
% 3.89/4.18 % set(auto) -> set(auto_setup).
% 3.89/4.18 % set(auto_setup) -> set(predicate_elim).
% 3.89/4.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.89/4.18 % set(auto) -> set(auto_limits).
% 3.89/4.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.89/4.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.89/4.18 % set(auto) -> set(auto_denials).
% 3.89/4.18 % set(auto) -> set(auto_process).
% 3.89/4.18 % set(auto2) -> assign(new_constants, 1).
% 3.89/4.18 % set(auto2) -> assign(fold_denial_max, 3).
% 3.89/4.18 % set(auto2) -> assign(max_weight, "200.000").
% 3.89/4.18 % set(auto2) -> assign(max_hours, 1).
% 3.89/4.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.89/4.18 % set(auto2) -> assign(max_seconds, 0).
% 3.89/4.18 % set(auto2) -> assign(max_minutes, 5).
% 3.89/4.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.89/4.18 % set(auto2) -> set(sort_initial_sos).
% 3.89/4.18 % set(auto2) -> assign(sos_limit, -1).
% 3.89/4.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.89/4.18 % set(auto2) -> assign(max_megs, 400).
% 3.89/4.18 % set(auto2) -> assign(stats, some).
% 3.89/4.18 % set(auto2) -> clear(echo_input).
% 3.89/4.18 % set(auto2) -> set(quiet).
% 3.89/4.18 % set(auto2) -> clear(print_initial_clauses).
% 3.89/4.18 % set(auto2) -> clear(print_given).
% 3.89/4.18 assign(lrs_ticks,-1).
% 3.89/4.18 assign(sos_limit,10000).
% 3.89/4.18 assign(order,kbo).
% 3.89/4.18 set(lex_order_vars).
% 3.89/4.18 clear(print_given).
% 3.89/4.18
% 3.89/4.18 % formulas(sos). % not echoed (9 formulas)
% 3.89/4.18
% 3.89/4.18 ============================== end of input ==========================
% 3.89/4.18
% 3.89/4.18 % From the command line: assign(max_seconds, 300).
% 3.89/4.18
% 3.89/4.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.89/4.18
% 3.89/4.18 % Formulas that are not ordinary clauses:
% 3.89/4.18
% 3.89/4.18 ============================== end of process non-clausal formulas ===
% 3.89/4.18
% 3.89/4.18 ============================== PROCESS INITIAL CLAUSES ===============
% 3.89/4.18
% 3.89/4.18 ============================== PREDICATE ELIMINATION =================
% 3.89/4.18 1 implies(A,B) != truth | ordered(A,B) # label(partial_order_definition2) # label(axiom). [assumption].
% 3.89/4.18 2 -ordered(A,B) | implies(A,B) = truth # label(partial_order_definition1) # label(axiom). [assumption].
% 3.89/4.18
% 3.89/4.18 ============================== end predicate elimination =============
% 3.89/4.18
% 3.89/4.18 Auto_denials:
% 3.89/4.18 % copying label prove_mv_4 to answer in negative clause
% 3.89/4.18
% 3.89/4.18 Term ordering decisions:
% 3.89/4.18
% 3.89/4.18 % Assigning unary symbol not kb_weight 0 and highest precedence (8).
% 3.89/4.18 Function symbol KB weights: truth=1. x=1. y=1. implies=1. big_V=1. big_hat=1. not=0.
% 3.89/4.18
% 3.89/4.18 ============================== end of process initial clauses ========
% 3.89/4.18
% 3.89/4.18 ============================== CLAUSES FOR SEARCH ====================
% 3.89/4.18
% 3.89/4.18 ============================== end of clauses for search =============
% 3.89/4.18
% 3.89/4.18 ============================== SEARCH ================================
% 3.89/4.18
% 3.89/4.18 % Starting search at 0.01 seconds.
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=55.000, iters=3355
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=52.000, iters=3336
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=50.000, iters=3369
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=47.000, iters=3342
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=46.000, iters=3367
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=44.000, iters=3339
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=43.000, iters=3365
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=41.000, iters=3386
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=40.000, iters=3335
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=39.000, iters=3358
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=37.000, iters=3345
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=36.000, iters=3341
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=35.000, iters=3336
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=34.000, iters=3335
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=33.000, iters=3342
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=32.000, iters=3346
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=31.000, iters=3345
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=30.000, iters=3355
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=29.000, iters=3340
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=28.000, iters=3411
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=27.000, iters=3379
% 3.89/4.18
% 3.89/4.18 Low Water (keep): wt=26.000, iters=3373
% 5.44/5.72
% 5.44/5.72 Low Water (keep): wt=25.000, iters=3433
% 5.44/5.72
% 5.44/5.72 Low Water (keep): wt=24.000, iters=3366
% 5.44/5.72
% 5.44/5.72 Low Water (keep): wt=19.000, iters=3588
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=7325, wt=113.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=3507, wt=107.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=3647, wt=100.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=12813, wt=20.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=12981, wt=19.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=13041, wt=16.000
% 5.44/5.72
% 5.44/5.72 Low Water (displace): id=13307, wt=15.000
% 5.44/5.72
% 5.44/5.72 ============================== PROOF =================================
% 5.44/5.72 % SZS status Unsatisfiable
% 5.44/5.72 % SZS output start Refutation
% 5.44/5.72
% 5.44/5.72 % Proof 1 at 4.63 (+ 0.12) seconds: prove_mv_4.
% 5.44/5.72 % Length of proof is 72.
% 5.44/5.72 % Level of proof is 22.
% 5.44/5.72 % Maximum clause weight is 47.000.
% 5.44/5.72 % Given clauses 319.
% 5.44/5.72
% 5.44/5.72 3 implies(truth,A) = A # label(wajsberg_1) # label(axiom). [assumption].
% 5.44/5.72 4 big_V(A,B) = implies(implies(A,B),B) # label(big_V_definition) # label(axiom). [assumption].
% 5.44/5.72 5 big_hat(A,B) = not(big_V(not(A),not(B))) # label(big_hat_definition) # label(axiom). [assumption].
% 5.44/5.72 6 big_hat(A,B) = not(implies(implies(not(A),not(B)),not(B))). [copy(5),rewrite([4(4)])].
% 5.44/5.72 7 implies(implies(A,B),B) = implies(implies(B,A),A) # label(wajsberg_3) # label(axiom). [assumption].
% 5.44/5.72 8 implies(implies(not(A),not(B)),implies(B,A)) = truth # label(wajsberg_4) # label(axiom). [assumption].
% 5.44/5.72 9 implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth # label(wajsberg_2) # label(axiom). [assumption].
% 5.44/5.72 10 big_V(implies(x,y),implies(y,x)) != truth # label(prove_mv_4) # label(negated_conjecture) # answer(prove_mv_4). [assumption].
% 5.44/5.72 11 implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth # answer(prove_mv_4). [copy(10),rewrite([4(7)])].
% 5.44/5.72 12 implies(implies(A,truth),truth) = implies(A,A). [para(3(a,1),7(a,1,1)),flip(a)].
% 5.44/5.72 13 implies(implies(implies(A,B),B),B) = implies(implies(implies(B,A),A),B). [para(7(a,1),4(a,2,1)),rewrite([4(2)])].
% 5.44/5.72 14 not(implies(implies(not(A),not(B)),not(B))) = not(implies(implies(not(B),not(A)),not(A))). [para(7(a,1),6(a,2,1)),rewrite([6(1)])].
% 5.44/5.72 15 implies(implies(not(A),not(truth)),A) = truth. [para(3(a,1),8(a,1,2))].
% 5.44/5.72 16 implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B). [para(8(a,1),7(a,1,1)),rewrite([3(3)]),flip(a)].
% 5.44/5.72 19 implies(A,implies(implies(A,B),B)) = truth. [para(3(a,1),9(a,1,1)),rewrite([3(3)])].
% 5.44/5.72 20 implies(implies(A,truth),implies(B,implies(A,B))) = truth. [para(3(a,1),9(a,1,2,1))].
% 5.44/5.72 22 implies(implies(implies(A,B),B),implies(implies(A,C),implies(implies(B,A),C))) = truth. [para(7(a,1),9(a,1,1))].
% 5.44/5.72 31 implies(implies(A,implies(B,C)),implies(A,implies(implies(C,D),implies(B,D)))) = truth. [para(9(a,1),9(a,1,2,1)),rewrite([3(8)])].
% 5.44/5.72 55 implies(A,A) = truth. [para(19(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 5.44/5.72 64 implies(A,truth) = truth. [para(12(a,1),19(a,1,2)),rewrite([55(1)])].
% 5.44/5.72 65 implies(A,implies(B,A)) = truth. [back_rewrite(20),rewrite([64(2),3(4)])].
% 5.44/5.72 67 implies(implies(implies(A,B),B),A) = implies(B,A). [para(13(a,1),7(a,1)),rewrite([65(5),3(6)])].
% 5.44/5.72 83 implies(implies(implies(A,B),C),implies(B,C)) = truth. [para(65(a,1),9(a,1,1)),rewrite([3(6)])].
% 5.44/5.72 85 implies(not(truth),not(not(truth))) = not(not(truth)). [para(15(a,1),67(a,1,1)),rewrite([3(5)]),flip(a)].
% 5.44/5.72 99 not(implies(implies(not(implies(implies(not(A),not(B)),not(B))),not(C)),not(C))) = not(implies(implies(not(C),not(implies(implies(not(B),not(A)),not(A)))),not(implies(implies(not(B),not(A)),not(A))))). [para(14(a,1),14(a,1,1,1,1))].
% 5.44/5.72 101 not(implies(implies(not(implies(implies(not(A),not(B)),not(B))),not(C)),not(C))) = not(implies(implies(not(C),not(implies(implies(not(A),not(B)),not(B)))),not(implies(implies(not(B),not(A)),not(A))))). [para(14(a,1),14(a,1,1,2)),flip(a)].
% 5.44/5.72 103 implies(not(A),implies(A,B)) = truth. [para(8(a,1),83(a,1,1)),rewrite([3(5)])].
% 5.44/5.72 107 implies(not(truth),A) = truth. [para(15(a,1),83(a,1,1)),rewrite([3(5)])].
% 5.44/5.72 115 not(not(truth)) = truth. [back_rewrite(85),rewrite([107(6)]),flip(a)].
% 5.44/5.72 116 implies(implies(A,not(truth)),not(truth)) = A. [para(107(a,1),7(a,1,1)),rewrite([3(2)]),flip(a)].
% 5.44/5.72 118 implies(implies(implies(implies(A,B),B),implies(not(A),not(implies(B,A)))),implies(not(A),not(implies(B,A)))) = implies(implies(B,A),A). [para(7(a,1),16(a,1,1,1))].
% 5.44/5.72 124 implies(implies(implies(implies(implies(not(A),not(B)),not(B)),C),implies(not(C),not(implies(implies(not(B),not(A)),not(A))))),implies(not(C),not(implies(implies(not(A),not(B)),not(B))))) = implies(implies(implies(not(A),not(B)),not(B)),C). [para(14(a,1),16(a,1,1,2,2))].
% 5.44/5.72 125 implies(implies(implies(A,implies(implies(not(B),not(C)),not(C))),implies(not(implies(implies(not(B),not(C)),not(C))),not(A))),implies(not(implies(implies(not(C),not(B)),not(B))),not(A))) = implies(A,implies(implies(not(B),not(C)),not(C))). [para(14(a,1),16(a,1,2,1))].
% 5.44/5.72 129 implies(implies(implies(A,B),not(A)),not(A)) = implies(A,B). [para(103(a,1),7(a,1,1)),rewrite([3(3)]),flip(a)].
% 5.44/5.72 143 implies(not(implies(A,not(truth))),A) = truth. [para(116(a,1),8(a,1,2)),rewrite([115(3),3(6)])].
% 5.44/5.72 148 implies(A,implies(not(A),not(truth))) = truth. [para(143(a,1),8(a,1,1)),rewrite([3(7)])].
% 5.44/5.72 162 implies(not(A),not(truth)) = A. [para(148(a,1),7(a,1,1)),rewrite([3(6),15(9),3(6)])].
% 5.44/5.72 163 implies(A,not(truth)) = not(A). [para(162(a,1),7(a,1,1)),rewrite([107(7),3(6)])].
% 5.44/5.72 166 implies(implies(A,not(B)),implies(B,not(A))) = truth. [para(162(a,1),9(a,1,2,1)),rewrite([163(5)])].
% 5.44/5.72 167 implies(implies(not(A),B),implies(not(B),A)) = truth. [para(162(a,1),9(a,1,2,2)),rewrite([163(5)])].
% 5.44/5.72 168 not(not(A)) = A. [para(162(a,1),67(a,2)),rewrite([107(4),3(3),163(4)])].
% 5.44/5.72 172 implies(A,not(B)) = implies(B,not(A)). [para(168(a,1),16(a,1,1,2,1)),rewrite([166(5),168(3),3(4)])].
% 5.44/5.72 173 implies(not(A),B) = implies(not(B),A). [para(168(a,1),16(a,1,1,2,2)),rewrite([167(5),168(4),3(4)])].
% 5.44/5.72 179 implies(A,not(implies(A,not(implies(A,B))))) = implies(A,B). [back_rewrite(129),rewrite([172(3),172(5)])].
% 5.44/5.72 181 implies(A,implies(B,not(implies(B,C)))) = implies(A,implies(C,not(implies(C,B)))). [back_rewrite(125),rewrite([172(3),168(2),172(3),172(7),168(6),172(7),172(10),168(9),55(9),172(4),168(3),172(4),172(7),168(6),3(6),172(7),168(6),172(7)])].
% 5.44/5.72 182 implies(implies(implies(implies(A,not(implies(A,B))),C),implies(not(C),not(implies(B,not(implies(B,A)))))),implies(not(C),not(implies(A,not(implies(A,B)))))) = implies(implies(A,not(implies(A,B))),C). [back_rewrite(124),rewrite([172(3),168(2),172(3),172(8),168(7),172(8),172(15),168(14),172(15),172(21),168(20),172(21)])].
% 5.44/5.72 184 not(implies(implies(not(A),not(implies(B,not(implies(B,C))))),not(implies(C,not(implies(C,B)))))) = not(implies(A,not(implies(A,implies(B,not(implies(B,C))))))). [back_rewrite(101),rewrite([172(3),168(2),172(3),172(6),168(5),172(6),172(11),168(10),172(11),172(16),168(15),172(16)]),flip(a)].
% 5.44/5.72 186 not(implies(implies(A,not(implies(A,B))),not(implies(not(C),not(implies(A,not(implies(A,B)))))))) = not(implies(C,not(implies(C,implies(B,not(implies(B,A))))))). [back_rewrite(99),rewrite([172(3),168(2),172(3),172(6),168(5),172(6),172(11),168(10),172(11),172(16),168(15),172(16),172(18)]),flip(a)].
% 5.44/5.72 227 implies(A,implies(B,not(implies(A,not(B))))) = truth. [para(172(a,1),19(a,1,2,1)),rewrite([172(2),172(4)])].
% 5.44/5.72 241 implies(implies(A,not(implies(B,not(A)))),B) = implies(not(B),A). [para(173(a,1),67(a,2)),rewrite([172(4)])].
% 5.44/5.72 264 implies(implies(implies(A,B),B),implies(not(A),not(implies(B,A)))) = truth. [para(163(a,1),22(a,1,2,1)),rewrite([172(7),3(7)])].
% 5.44/5.72 269 implies(implies(implies(A,B),B),implies(implies(A,not(C)),implies(C,not(implies(B,A))))) = truth. [para(172(a,1),22(a,1,2,1)),rewrite([172(4),172(7)])].
% 5.44/5.72 274 implies(implies(A,B),B) = implies(not(B),not(implies(A,B))). [back_rewrite(118),rewrite([264(7),3(6)]),flip(a)].
% 5.44/5.72 277 implies(implies(not(A),not(implies(B,A))),implies(implies(B,not(C)),implies(C,not(implies(A,B))))) = truth. [back_rewrite(269),rewrite([274(2)])].
% 5.44/5.72 351 implies(not(implies(y,x)),not(implies(implies(x,y),implies(y,x)))) != truth # answer(prove_mv_4). [back_rewrite(11),rewrite([274(11)])].
% 5.44/5.72 352 implies(not(A),not(implies(B,A))) = implies(not(B),not(implies(A,B))). [back_rewrite(7),rewrite([274(2),274(6)])].
% 5.44/5.72 353 big_V(A,B) = implies(not(B),not(implies(A,B))). [back_rewrite(4),rewrite([274(3)])].
% 5.44/5.72 406 implies(not(A),implies(B,not(implies(B,A)))) = truth. [para(227(a,1),173(a,1)),rewrite([172(4),168(3),173(6)]),flip(a)].
% 5.44/5.72 434 implies(A,implies(implies(not(B),implies(A,not(C))),implies(C,B))) = truth. [para(227(a,1),31(a,1,1)),rewrite([173(5),3(9)])].
% 5.44/5.72 1257 implies(A,not(implies(A,B))) = implies(B,not(implies(B,A))). [para(181(a,1),3(a,1)),rewrite([3(5)])].
% 5.44/5.72 1268 implies(A,implies(implies(B,C),not(implies(B,not(implies(B,C)))))) = implies(A,B). [para(103(a,1),181(a,1,2,2,1)),rewrite([163(4),168(2),172(5)]),flip(a)].
% 5.44/5.72 1298 implies(A,implies(implies(B,not(implies(B,C))),not(implies(C,not(implies(B,not(implies(B,C)))))))) = implies(A,C). [para(406(a,1),181(a,1,2,2,1)),rewrite([163(4),168(2),172(9)]),flip(a)].
% 5.44/5.72 1576 implies(implies(implies(implies(A,B),not(implies(A,not(implies(A,B))))),implies(implies(A,B),not(implies(B,not(implies(B,A)))))),A) = implies(implies(A,B),not(implies(A,not(implies(A,B))))). [para(274(a,1),182(a,1,1,1)),rewrite([168(3),168(9),168(16),1268(20),172(20)])].
% 5.44/5.72 1729 not(implies(implies(A,B),not(implies(B,not(implies(B,A)))))) = not(A). [para(103(a,1),184(a,2,1,2,1)),rewrite([168(2),179(5),163(11),168(9)])].
% 5.44/5.72 2402 not(implies(A,not(implies(B,not(implies(B,A)))))) = not(implies(A,B)). [para(65(a,1),186(a,2,1,2,1)),rewrite([168(6),1729(10),172(5),172(11),168(10),3(9)])].
% 5.44/5.72 2615 implies(A,implies(implies(B,C),not(implies(C,not(implies(C,B)))))) = implies(A,B). [back_rewrite(1298),rewrite([2402(9),172(6)])].
% 5.44/5.72 2622 implies(implies(A,B),not(implies(A,not(implies(A,B))))) = A. [back_rewrite(1576),rewrite([2615(13),241(7),103(3),3(2)]),flip(a)].
% 5.44/5.72 3082 implies(implies(A,B),not(implies(B,not(implies(B,A))))) = A. [para(1257(a,1),353(a,2,2,1)),rewrite([353(3),168(3),2622(6),168(3)]),flip(a)].
% 5.44/5.72 8049 implies(A,implies(implies(implies(B,A),implies(A,B)),B)) = truth. [para(3082(a,1),277(a,1,2,2)),rewrite([173(4),103(4),163(4),168(2),172(5),168(4)])].
% 5.44/5.72 11705 implies(not(implies(x,y)),not(implies(implies(y,x),implies(x,y)))) != truth # answer(prove_mv_4). [para(352(a,1),351(a,1))].
% 5.44/5.72 14012 implies(not(implies(A,B)),not(implies(implies(B,A),implies(A,B)))) = truth. [para(8049(a,1),434(a,1,2,1)),rewrite([172(3),168(2),172(4),168(3),3(6),274(5)])].
% 5.44/5.72 14013 $F # answer(prove_mv_4). [resolve(14012,a,11705,a)].
% 5.44/5.72
% 5.44/5.72 % SZS output end Refutation
% 5.44/5.72 ============================== end of proof ==========================
% 5.44/5.72
% 5.44/5.72 ============================== STATISTICS ============================
% 5.44/5.72
% 5.44/5.72 Given=319. Generated=217887. Kept=14008. proofs=1.
% 5.44/5.72 Usable=286. Sos=9999. Demods=10171. Limbo=27, Disabled=3704. Hints=0.
% 5.44/5.72 Megabytes=16.30.
% 5.44/5.72 User_CPU=4.63, System_CPU=0.12, Wall_clock=5.
% 5.44/5.72
% 5.44/5.72 ============================== end of statistics =====================
% 5.44/5.72
% 5.44/5.72 ============================== end of search =========================
% 5.44/5.72
% 5.44/5.72 THEOREM PROVED
% 5.44/5.72 % SZS status Unsatisfiable
% 5.44/5.72
% 5.44/5.72 Exiting with 1 proof.
% 5.44/5.72
% 5.44/5.72 Process 29489 exit (max_proofs) Mon Jul 4 21:23:33 2022
% 5.44/5.72 Prover9 interrupted
%------------------------------------------------------------------------------