TSTP Solution File: HWV003-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Sat Jul 16 19:01:06 EDT 2022
% Result : Unsatisfiable 2.46s 2.72s
% Output : Refutation 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 06:20:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.46/2.72 ============================== Prover9 ===============================
% 2.46/2.72 Prover9 (32) version 2009-11A, November 2009.
% 2.46/2.72 Process 6238 was started by sandbox2 on n029.cluster.edu,
% 2.46/2.72 Fri Jun 17 06:20:43 2022
% 2.46/2.72 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6085_n029.cluster.edu".
% 2.46/2.72 ============================== end of head ===========================
% 2.46/2.72
% 2.46/2.72 ============================== INPUT =================================
% 2.46/2.72
% 2.46/2.72 % Reading from file /tmp/Prover9_6085_n029.cluster.edu
% 2.46/2.72
% 2.46/2.72 set(prolog_style_variables).
% 2.46/2.72 set(auto2).
% 2.46/2.72 % set(auto2) -> set(auto).
% 2.46/2.72 % set(auto) -> set(auto_inference).
% 2.46/2.72 % set(auto) -> set(auto_setup).
% 2.46/2.72 % set(auto_setup) -> set(predicate_elim).
% 2.46/2.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.46/2.72 % set(auto) -> set(auto_limits).
% 2.46/2.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.46/2.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.46/2.72 % set(auto) -> set(auto_denials).
% 2.46/2.72 % set(auto) -> set(auto_process).
% 2.46/2.72 % set(auto2) -> assign(new_constants, 1).
% 2.46/2.72 % set(auto2) -> assign(fold_denial_max, 3).
% 2.46/2.72 % set(auto2) -> assign(max_weight, "200.000").
% 2.46/2.72 % set(auto2) -> assign(max_hours, 1).
% 2.46/2.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.46/2.72 % set(auto2) -> assign(max_seconds, 0).
% 2.46/2.72 % set(auto2) -> assign(max_minutes, 5).
% 2.46/2.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.46/2.72 % set(auto2) -> set(sort_initial_sos).
% 2.46/2.72 % set(auto2) -> assign(sos_limit, -1).
% 2.46/2.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.46/2.72 % set(auto2) -> assign(max_megs, 400).
% 2.46/2.72 % set(auto2) -> assign(stats, some).
% 2.46/2.72 % set(auto2) -> clear(echo_input).
% 2.46/2.72 % set(auto2) -> set(quiet).
% 2.46/2.72 % set(auto2) -> clear(print_initial_clauses).
% 2.46/2.72 % set(auto2) -> clear(print_given).
% 2.46/2.72 assign(lrs_ticks,-1).
% 2.46/2.72 assign(sos_limit,10000).
% 2.46/2.72 assign(order,kbo).
% 2.46/2.72 set(lex_order_vars).
% 2.46/2.72 clear(print_given).
% 2.46/2.72
% 2.46/2.72 % formulas(sos). % not echoed (36 formulas)
% 2.46/2.72
% 2.46/2.72 ============================== end of input ==========================
% 2.46/2.72
% 2.46/2.72 % From the command line: assign(max_seconds, 300).
% 2.46/2.72
% 2.46/2.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.46/2.72
% 2.46/2.72 % Formulas that are not ordinary clauses:
% 2.46/2.72
% 2.46/2.72 ============================== end of process non-clausal formulas ===
% 2.46/2.72
% 2.46/2.72 ============================== PROCESS INITIAL CLAUSES ===============
% 2.46/2.72
% 2.46/2.72 ============================== PREDICATE ELIMINATION =================
% 2.46/2.72
% 2.46/2.72 ============================== end predicate elimination =============
% 2.46/2.72
% 2.46/2.72 Auto_denials:
% 2.46/2.72 % copying label prove_circuit to answer in negative clause
% 2.46/2.72
% 2.46/2.72 Term ordering decisions:
% 2.46/2.72
% 2.46/2.72 % Assigning unary symbol not kb_weight 0 and highest precedence (21).
% 2.46/2.72 Function symbol KB weights: ll0=1. ll1=1. a=1. b=1. cin=1. t1=1. t5=1. t4=1. t2=1. t3=1. t6=1. t7=1. carry=1. carry_def=1. sum=1. sum_def=1. and=1. or=1. xor=1. not=0.
% 2.46/2.72
% 2.46/2.72 ============================== end of process initial clauses ========
% 2.46/2.72
% 2.46/2.72 ============================== CLAUSES FOR SEARCH ====================
% 2.46/2.72
% 2.46/2.72 ============================== end of clauses for search =============
% 2.46/2.72
% 2.46/2.72 ============================== SEARCH ================================
% 2.46/2.72
% 2.46/2.72 % Starting search at 0.01 seconds.
% 2.46/2.72
% 2.46/2.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 1.58 sec).
% 2.46/2.72
% 2.46/2.72 ============================== PROOF =================================
% 2.46/2.72 % SZS status Unsatisfiable
% 2.46/2.72 % SZS output start Refutation
% 2.46/2.72
% 2.46/2.72 % Proof 1 at 1.72 (+ 0.03) seconds: prove_circuit.
% 2.46/2.72 % Length of proof is 156.
% 2.46/2.72 % Level of proof is 18.
% 2.46/2.72 % Maximum clause weight is 27.000.
% 2.46/2.72 % Given clauses 554.
% 2.46/2.72
% 2.46/2.72 2 not(ll1) = ll0 # label(ll1_inverse) # label(axiom). [assumption].
% 2.46/2.72 3 or(A,ll0) = A # label(or_identity) # label(axiom). [assumption].
% 2.46/2.72 4 and(A,ll1) = A # label(and_identity) # label(axiom). [assumption].
% 2.46/2.72 6 and(A,A) = A # label(and_idempotent) # label(axiom). [assumption].
% 2.46/2.72 7 not(not(A)) = A # label(not_involution) # label(axiom). [assumption].
% 2.46/2.72 8 or(A,ll1) = ll1 # label(or_boundedness) # label(axiom). [assumption].
% 2.46/2.72 9 and(A,ll0) = ll0 # label(and_boundedness) # label(axiom). [assumption].
% 2.46/2.72 10 or(A,not(A)) = ll1 # label(or_complement) # label(axiom). [assumption].
% 2.46/2.72 11 and(A,not(A)) = ll0 # label(and_complement) # label(axiom). [assumption].
% 2.46/2.72 12 not(and(a,b)) = t1 # label(t1) # label(negated_conjecture). [assumption].
% 2.46/2.72 13 not(and(a,t1)) = t2 # label(t2) # label(negated_conjecture). [assumption].
% 2.46/2.72 14 not(and(b,t1)) = t3 # label(t3) # label(negated_conjecture). [assumption].
% 2.46/2.72 15 not(and(t2,t3)) = t4 # label(t4) # label(negated_conjecture). [assumption].
% 2.46/2.72 16 not(and(t4,cin)) = t5 # label(t5) # label(negated_conjecture). [assumption].
% 2.46/2.72 17 not(and(t4,t5)) = t6 # label(t6) # label(negated_conjecture). [assumption].
% 2.46/2.72 18 not(and(t5,cin)) = t7 # label(t7) # label(negated_conjecture). [assumption].
% 2.46/2.72 19 not(and(t6,t7)) = sum # label(sum) # label(negated_conjecture). [assumption].
% 2.46/2.72 20 not(and(t1,t5)) = carry # label(carry) # label(negated_conjecture). [assumption].
% 2.46/2.72 21 or(A,B) = or(B,A) # label(or_commutative) # label(axiom). [assumption].
% 2.46/2.72 22 and(A,B) = and(B,A) # label(and_commutative) # label(axiom). [assumption].
% 2.46/2.72 23 or(A,and(A,B)) = A # label(or_absorption) # label(axiom). [assumption].
% 2.46/2.72 24 and(A,or(A,B)) = A # label(and_absorption) # label(axiom). [assumption].
% 2.46/2.72 25 xor(A,B) = xor(B,A) # label(xor_commutative) # label(axiom). [assumption].
% 2.46/2.72 26 xor(xor(a,b),cin) = sum_def # label(sum_def) # label(negated_conjecture). [assumption].
% 2.46/2.72 27 xor(cin,xor(a,b)) = sum_def. [copy(26),rewrite([25(5)])].
% 2.46/2.72 28 not(or(A,B)) = and(not(A),not(B)) # label(or_demorgan) # label(axiom). [assumption].
% 2.46/2.72 29 not(and(A,B)) = or(not(A),not(B)) # label(and_demorgan) # label(axiom). [assumption].
% 2.46/2.72 30 or(or(A,B),C) = or(A,or(B,C)) # label(or_associative) # label(axiom). [assumption].
% 2.46/2.72 31 or(A,or(B,C)) = or(C,or(A,B)). [copy(30),rewrite([21(2)]),flip(a)].
% 2.46/2.72 32 and(and(A,B),C) = and(A,and(B,C)) # label(and_associative) # label(axiom). [assumption].
% 2.46/2.72 33 and(A,and(B,C)) = and(C,and(A,B)). [copy(32),rewrite([22(2)]),flip(a)].
% 2.46/2.72 36 and(A,or(B,C)) = or(and(A,B),and(A,C)) # label(or_distributive) # label(axiom). [assumption].
% 2.46/2.72 37 or(and(A,B),and(A,C)) = and(A,or(B,C)). [copy(36),flip(a)].
% 2.46/2.72 38 or(A,and(B,C)) = and(or(A,B),or(A,C)) # label(and_distributive) # label(axiom). [assumption].
% 2.46/2.72 39 and(or(A,B),or(A,C)) = or(A,and(B,C)). [copy(38),flip(a)].
% 2.46/2.72 40 or(and(not(A),B),and(A,not(B))) = xor(A,B) # label(xor_definition) # label(axiom). [assumption].
% 2.46/2.72 41 xor(A,B) = or(and(A,not(B)),and(B,not(A))). [copy(40),rewrite([22(2),21(5)]),flip(a)].
% 2.46/2.72 42 or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def # label(carry_def) # label(negated_conjecture). [assumption].
% 2.46/2.72 43 or(and(a,and(b,not(cin))),and(cin,or(a,b))) = carry_def. [copy(42),rewrite([33(11),22(10),33(11,R),22(10),21(12)])].
% 2.46/2.72 44 sum != sum_def | carry != carry_def # label(prove_circuit) # label(negated_conjecture) # answer(prove_circuit). [assumption].
% 2.46/2.72 45 sum_def != sum | carry_def != carry # answer(prove_circuit). [copy(44),flip(a),flip(b)].
% 2.46/2.72 46 or(not(cin),not(t5)) = t7. [back_rewrite(18),rewrite([22(3),29(4)])].
% 2.46/2.72 47 or(not(t5),not(t4)) = t6. [back_rewrite(17),rewrite([22(3),29(4)])].
% 2.46/2.72 48 or(not(cin),not(t4)) = t5. [back_rewrite(16),rewrite([22(3),29(4)])].
% 2.46/2.72 49 or(not(t1),not(t5)) = carry. [back_rewrite(20),rewrite([29(4)])].
% 2.46/2.72 50 or(not(t6),not(t7)) = sum. [back_rewrite(19),rewrite([29(4)])].
% 2.46/2.72 51 or(not(t2),not(t3)) = t4. [back_rewrite(15),rewrite([29(4)])].
% 2.46/2.72 52 or(not(b),not(t1)) = t3. [back_rewrite(14),rewrite([29(4)])].
% 2.46/2.72 53 or(not(a),not(t1)) = t2. [back_rewrite(13),rewrite([29(4)])].
% 2.46/2.72 54 or(not(a),not(b)) = t1. [back_rewrite(12),rewrite([29(4)])].
% 2.46/2.72 55 or(and(cin,and(or(a,not(b)),or(b,not(a)))),and(not(cin),or(and(a,not(b)),and(b,not(a))))) = sum_def. [back_rewrite(27),rewrite([41(4),41(11),28(11),29(6),7(6),21(5),29(10),7(10),21(9),22(10),22(23)])].
% 2.46/2.72 63 or(ll0,not(A)) = not(A). [para(2(a,1),29(a,2,1)),rewrite([22(2),4(2)]),flip(a)].
% 2.46/2.72 64 or(not(A),or(not(B),and(A,B))) = ll1. [para(29(a,1),10(a,1,2)),rewrite([31(5),21(4),31(5,R),21(4)])].
% 2.46/2.72 68 or(A,or(B,not(A))) = ll1. [para(10(a,1),31(a,2,2)),rewrite([21(2),8(5)])].
% 2.46/2.72 70 and(A,and(A,B)) = and(A,B). [para(33(a,1),6(a,1)),rewrite([22(1),22(2),33(2,R),6(1),22(3)])].
% 2.46/2.72 73 or(ll0,and(A,B)) = and(A,B). [para(3(a,1),37(a,2,2)),rewrite([9(3),21(3)])].
% 2.46/2.72 75 and(A,or(B,not(A))) = and(A,B). [para(11(a,1),37(a,1,1)),rewrite([73(3),21(3)]),flip(a)].
% 2.46/2.72 76 or(and(A,B),and(B,C)) = and(B,or(A,C)). [para(22(a,1),37(a,1,1))].
% 2.46/2.72 79 and(ll1,or(A,B)) = or(A,B). [para(4(a,1),39(a,2,2)),rewrite([8(3),22(3)])].
% 2.46/2.72 81 or(A,and(B,not(A))) = or(A,B). [para(10(a,1),39(a,1,1)),rewrite([79(3),22(3)]),flip(a)].
% 2.46/2.72 82 and(or(A,B),or(B,C)) = or(B,and(A,C)). [para(21(a,1),39(a,1,1))].
% 2.46/2.72 87 or(A,and(B,or(A,C))) = or(A,and(C,B)). [para(39(a,1),37(a,2)),rewrite([22(2),24(2),22(2)])].
% 2.46/2.72 92 and(or(cin,t1),or(not(cin),and(not(a),not(b)))) = not(carry_def). [para(43(a,1),28(a,1,1)),rewrite([29(9),29(9),7(9),21(8),31(9,R),21(8),54(8),29(11),28(11)]),flip(a)].
% 2.46/2.72 96 and(cin,t5) = not(t7). [para(46(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 99 and(t5,t4) = not(t6). [para(47(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 100 or(not(t5),and(A,not(t4))) = and(t6,or(A,not(t5))). [para(47(a,1),39(a,1,1)),rewrite([21(4),22(10)]),flip(a)].
% 2.46/2.72 102 and(cin,t4) = not(t5). [para(48(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 105 and(t1,t5) = not(carry). [para(49(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 108 and(t6,t7) = not(sum). [para(50(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 111 and(t2,t3) = not(t4). [para(51(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 112 or(not(t2),and(A,not(t3))) = and(t4,or(A,not(t2))). [para(51(a,1),39(a,1,1)),rewrite([21(4),22(10)]),flip(a)].
% 2.46/2.72 114 and(b,t1) = not(t3). [para(52(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 115 or(not(b),and(A,not(t1))) = and(t3,or(A,not(b))). [para(52(a,1),39(a,1,1)),rewrite([21(4),22(10)]),flip(a)].
% 2.46/2.72 117 and(a,t1) = not(t2). [para(53(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 120 and(a,b) = not(t1). [para(54(a,1),28(a,1,1)),rewrite([7(5),7(6)]),flip(a)].
% 2.46/2.72 123 and(or(cin,and(or(a,not(b)),or(b,not(a)))),or(not(cin),or(and(a,not(b)),and(b,not(a))))) = not(sum_def). [para(55(a,1),28(a,1,1)),rewrite([29(14),29(14),28(9),7(9),22(8),28(13),7(13),22(12),21(13),29(27),7(17),28(25),29(20),7(20),21(19),29(24),7(24),21(23),22(24),22(26)]),flip(a)].
% 2.46/2.72 225 or(a,not(t2)) = a. [para(117(a,1),23(a,1,2))].
% 2.46/2.72 227 or(a,not(t1)) = a. [para(120(a,1),23(a,1,2))].
% 2.46/2.72 254 or(t6,not(cin)) = ll1. [para(102(a,1),64(a,1,2,2)),rewrite([21(7),47(7),21(4)])].
% 2.46/2.72 259 or(t3,not(a)) = ll1. [para(120(a,1),64(a,1,2,2)),rewrite([52(7),21(4)])].
% 2.46/2.72 276 and(cin,not(t6)) = ll0. [para(254(a,1),28(a,1,1)),rewrite([2(2),7(6),22(5)]),flip(a)].
% 2.46/2.72 282 and(ll1,t3) = t3. [para(259(a,1),24(a,1,2)),rewrite([22(3)])].
% 2.46/2.72 283 and(a,not(t3)) = ll0. [para(259(a,1),28(a,1,1)),rewrite([2(2),7(6),22(5)]),flip(a)].
% 2.46/2.72 301 and(cin,or(A,not(t6))) = and(A,cin). [para(276(a,1),37(a,1,1)),rewrite([22(3),73(4),21(6)]),flip(a)].
% 2.46/2.72 318 and(a,or(A,not(t3))) = and(A,a). [para(283(a,1),37(a,1,1)),rewrite([22(3),73(4),21(6)]),flip(a)].
% 2.46/2.72 325 or(t4,t6) = ll1. [para(47(a,1),68(a,1,2))].
% 2.46/2.72 326 or(t5,t4) = ll1. [para(48(a,1),68(a,1,2)),rewrite([21(3)])].
% 2.46/2.72 329 or(t4,t3) = ll1. [para(51(a,1),68(a,1,2)),rewrite([21(3)])].
% 2.46/2.72 341 or(a,t1) = ll1. [para(227(a,1),68(a,1,2)),rewrite([21(3)])].
% 2.46/2.72 357 and(ll1,t4) = t4. [para(325(a,1),24(a,1,2)),rewrite([22(3)])].
% 2.46/2.72 361 and(not(t5),not(t4)) = ll0. [para(326(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.46/2.72 404 and(not(t4),not(t3)) = ll0. [para(329(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.46/2.72 425 and(a,not(t1)) = not(t1). [para(120(a,1),70(a,1,2)),rewrite([120(7)])].
% 2.46/2.72 498 and(not(a),not(t1)) = ll0. [para(341(a,1),28(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.46/2.72 506 or(ll0,t3) = t3. [para(282(a,1),73(a,1,2)),rewrite([282(6)])].
% 2.46/2.72 509 or(ll0,t4) = t4. [para(357(a,1),73(a,1,2)),rewrite([357(6)])].
% 2.46/2.72 511 and(not(A),or(A,B)) = and(B,not(A)). [para(7(a,1),75(a,1,2,2)),rewrite([21(2),22(5)])].
% 2.46/2.72 518 and(t4,not(cin)) = not(t6). [para(48(a,1),75(a,1,2)),rewrite([22(3),99(3)]),flip(a)].
% 2.46/2.72 522 and(t1,not(b)) = and(t1,t3). [para(52(a,1),75(a,1,2)),flip(a)].
% 2.46/2.72 524 and(b,not(a)) = not(t3). [para(54(a,1),75(a,1,2)),rewrite([114(3)]),flip(a)].
% 2.46/2.72 530 and(or(not(cin),or(not(t3),and(a,not(b)))),or(cin,and(or(a,not(b)),or(b,not(a))))) = not(sum_def). [back_rewrite(123),rewrite([524(21),21(20),22(22)])].
% 2.46/2.72 536 or(A,and(B,A)) = A. [para(4(a,1),76(a,1,2)),rewrite([21(2),8(4),4(4)])].
% 2.46/2.72 541 and(and(A,B),or(C,D)) = and(A,and(B,or(C,D))). [para(33(a,1),76(a,1,1)),rewrite([22(3),22(4),33(4),22(3),33(4,R),22(3),37(5),76(3),22(4)]),flip(a)].
% 2.46/2.72 554 or(not(t3),and(A,t1)) = and(t1,or(A,b)). [para(114(a,1),76(a,1,1)),rewrite([22(4),21(8)])].
% 2.46/2.72 725 or(a,t3) = t3. [para(283(a,1),81(a,1,2)),rewrite([21(3),506(3),21(4)]),flip(a)].
% 2.46/2.72 1033 or(not(t2),and(A,t4)) = and(t4,or(A,not(t2))). [para(51(a,1),87(a,1,2,2)),rewrite([22(10),112(11)])].
% 2.46/2.72 1197 or(and(t1,not(cin)),and(not(a),and(not(b),or(cin,t1)))) = not(carry_def). [para(92(a,1),37(a,2)),rewrite([22(6),511(6),22(13),541(13)])].
% 2.46/2.72 1230 and(t6,or(t4,not(t5))) = not(t5). [para(11(a,1),100(a,1,2)),rewrite([21(4),63(4)]),flip(a)].
% 2.46/2.72 1305 or(t4,not(t5)) = t4. [para(361(a,1),81(a,1,2)),rewrite([21(3),509(3)]),flip(a)].
% 2.46/2.72 1307 and(t4,t6) = not(t5). [back_rewrite(1230),rewrite([1305(5),22(3)])].
% 2.46/2.72 1346 or(not(t4),not(t6)) = t5. [para(1307(a,1),29(a,1,1)),rewrite([7(3)]),flip(a)].
% 2.46/2.72 1375 and(t4,or(t3,not(t2))) = not(t2). [para(11(a,1),112(a,1,2)),rewrite([21(4),63(4)]),flip(a)].
% 2.46/2.72 1377 and(a,t4) = not(t2). [para(225(a,1),112(a,2,2)),rewrite([283(6),21(4),63(4),22(5)]),flip(a)].
% 2.46/2.72 1395 or(not(a),not(t4)) = t2. [para(1377(a,1),29(a,1,1)),rewrite([7(3)]),flip(a)].
% 2.46/2.72 1399 and(t4,or(A,not(t2))) = and(t4,or(A,a)). [para(1377(a,1),76(a,1,1)),rewrite([22(4),1033(5),21(8)])].
% 2.46/2.72 1408 and(t4,t3) = not(t2). [back_rewrite(1375),rewrite([1399(6),21(4),725(4)])].
% 2.46/2.72 1413 or(not(t4),not(t3)) = t2. [para(1408(a,1),29(a,1,1)),rewrite([7(3)]),flip(a)].
% 2.46/2.72 1437 and(t1,t3) = not(b). [para(54(a,1),115(a,2,2)),rewrite([498(7),21(4),63(4),22(5)]),flip(a)].
% 2.46/2.72 1446 and(t1,not(b)) = not(b). [back_rewrite(522),rewrite([1437(7)])].
% 2.46/2.72 1490 or(t3,not(t4)) = t3. [para(404(a,1),81(a,1,2)),rewrite([21(3),506(3)]),flip(a)].
% 2.46/2.72 1506 and(t4,not(t3)) = not(t3). [para(1490(a,1),28(a,1,1)),rewrite([7(7),22(6)]),flip(a)].
% 2.46/2.72 1944 and(a,t2) = not(t1). [para(425(a,1),75(a,2)),rewrite([21(6),53(6)])].
% 2.46/2.72 2127 or(cin,not(t4)) = t6. [para(518(a,1),29(a,1,1)),rewrite([7(3),7(6),21(5)]),flip(a)].
% 2.46/2.72 2617 or(a,not(b)) = t3. [para(524(a,1),29(a,1,1)),rewrite([7(3),7(6),21(5)]),flip(a)].
% 2.46/2.72 2625 or(a,not(t3)) = or(a,b). [para(524(a,1),81(a,1,2))].
% 2.46/2.72 2644 and(or(cin,and(t3,or(b,not(a)))),or(not(cin),or(not(t3),and(a,not(b))))) = not(sum_def). [back_rewrite(530),rewrite([2617(15),22(19)])].
% 2.46/2.72 2657 and(b,t3) = not(t1). [para(2617(a,1),75(a,1,2)),rewrite([22(6),120(6)])].
% 2.46/2.72 2675 or(not(b),not(t3)) = t1. [para(2657(a,1),29(a,1,1)),rewrite([7(3)]),flip(a)].
% 2.46/2.72 2752 or(t1,not(t3)) = t1. [para(114(a,1),536(a,1,2))].
% 2.46/2.72 2829 and(t1,or(A,not(t3))) = and(t1,or(A,b)). [para(2752(a,1),82(a,1,1)),rewrite([21(4),22(9),554(10)])].
% 2.46/2.72 3072 and(t4,not(a)) = and(t4,t2). [para(1395(a,1),75(a,1,2)),flip(a)].
% 2.46/2.72 3109 and(not(b),or(A,t1)) = not(b). [para(1446(a,1),76(a,1,1)),rewrite([22(5),536(6),21(6)]),flip(a)].
% 2.46/2.72 3114 or(and(t1,not(cin)),and(not(a),not(b))) = not(carry_def). [back_rewrite(1197),rewrite([3109(12)])].
% 2.46/2.72 3161 and(t4,t2) = not(t3). [para(1506(a,1),75(a,2)),rewrite([21(6),1413(6)])].
% 2.46/2.72 3167 and(t4,not(a)) = not(t3). [back_rewrite(3072),rewrite([3161(7)])].
% 2.46/2.72 3557 or(not(t3),and(A,not(b))) = and(t1,or(A,b)). [para(2675(a,1),82(a,1,1)),rewrite([21(4),2829(5),22(9)]),flip(a)].
% 2.46/2.72 3562 and(or(cin,and(t3,or(b,not(a)))),or(not(cin),and(t1,or(a,b)))) = not(sum_def). [back_rewrite(2644),rewrite([3557(17)])].
% 2.46/2.72 4078 or(a,t4) = or(a,b). [para(3167(a,1),81(a,1,2)),rewrite([2625(4)]),flip(a)].
% 2.46/2.72 4941 and(cin,not(t4)) = not(t7). [para(1346(a,1),301(a,1,2)),rewrite([96(3),22(6)]),flip(a)].
% 2.46/2.72 4959 or(t4,not(cin)) = t7. [para(4941(a,1),29(a,1,1)),rewrite([7(3),7(6),21(5)]),flip(a)].
% 2.46/2.72 5003 and(a,not(t4)) = not(t1). [para(1413(a,1),318(a,1,2)),rewrite([1944(3),22(6)]),flip(a)].
% 2.46/2.72 5004 and(a,not(b)) = not(t2). [para(2675(a,1),318(a,1,2)),rewrite([117(3),22(6)]),flip(a)].
% 2.46/2.72 5016 or(t4,not(a)) = t1. [para(5003(a,1),29(a,1,1)),rewrite([7(3),7(6),21(5)]),flip(a)].
% 2.46/2.72 5024 or(t4,not(t1)) = or(a,b). [para(5003(a,1),81(a,1,2)),rewrite([21(7),4078(7)])].
% 2.46/2.72 5031 and(t1,t4) = t4. [para(5016(a,1),24(a,1,2)),rewrite([22(3)])].
% 2.46/2.72 5048 and(t1,or(a,b)) = t4. [para(5031(a,1),75(a,2)),rewrite([5024(5)])].
% 2.46/2.72 5058 and(t7,or(cin,and(t3,or(b,not(a))))) = not(sum_def). [back_rewrite(3562),rewrite([5048(15),21(12),4959(12),22(10)])].
% 2.46/2.72 5095 or(b,not(a)) = t2. [para(5004(a,1),29(a,1,1)),rewrite([7(3),7(6),21(5)]),flip(a)].
% 2.46/2.72 5107 not(sum_def) = not(sum). [back_rewrite(5058),rewrite([5095(7),22(5),111(5),2127(5),22(3),108(3)]),flip(a)].
% 2.46/2.72 5129 sum_def = sum. [para(5107(a,1),7(a,1,1)),rewrite([7(3)]),flip(a)].
% 2.46/2.72 5151 carry_def != carry # answer(prove_circuit). [back_rewrite(45),rewrite([5129(1)]),xx(a)].
% 2.46/2.72 6094 and(not(a),not(b)) = and(t3,not(a)). [para(2625(a,1),28(a,1,1)),rewrite([28(4),7(10),22(9)])].
% 2.46/2.72 6114 or(and(t1,not(cin)),and(t3,not(a))) = not(carry_def). [back_rewrite(3114),rewrite([6094(9)])].
% 2.46/2.72 6837 and(t3,not(a)) = and(t1,not(t4)). [para(5024(a,1),28(a,1,1)),rewrite([28(4),6094(5),7(9),22(8)])].
% 2.46/2.72 6853 not(carry_def) = not(carry). [back_rewrite(6114),rewrite([6837(8),37(9),48(6),105(3)]),flip(a)].
% 2.46/2.72 6893 $F # answer(prove_circuit). [para(6853(a,1),7(a,1,1)),rewrite([7(3)]),flip(a),unit_del(a,5151)].
% 2.46/2.72
% 2.46/2.72 % SZS output end Refutation
% 2.46/2.72 ============================== end of proof ==========================
% 2.46/2.72
% 2.46/2.72 ============================== STATISTICS ============================
% 2.46/2.72
% 2.46/2.72 Given=554. Generated=37694. Kept=6883. proofs=1.
% 2.46/2.72 Usable=518. Sos=4105. Demods=4210. Limbo=0, Disabled=2296. Hints=0.
% 2.46/2.72 Megabytes=10.76.
% 2.46/2.72 User_CPU=1.72, System_CPU=0.03, Wall_clock=2.
% 2.46/2.72
% 2.46/2.72 ============================== end of statistics =====================
% 2.46/2.72
% 2.46/2.72 ============================== end of search =========================
% 2.46/2.72
% 2.46/2.72 THEOREM PROVED
% 2.46/2.72 % SZS status Unsatisfiable
% 2.46/2.72
% 2.46/2.72 Exiting with 1 proof.
% 2.46/2.72
% 2.46/2.72 Process 6238 exit (max_proofs) Fri Jun 17 06:20:45 2022
% 2.46/2.72 Prover9 interrupted
%------------------------------------------------------------------------------