TSTP Solution File: KLE027+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 02:21:50 EDT 2022
% Result : Theorem 0.94s 1.23s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n013.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 : Thu Jun 16 09:25:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.06 ============================== Prover9 ===============================
% 0.43/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.06 Process 5165 was started by sandbox on n013.cluster.edu,
% 0.43/1.06 Thu Jun 16 09:25:59 2022
% 0.43/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5011_n013.cluster.edu".
% 0.43/1.06 ============================== end of head ===========================
% 0.43/1.06
% 0.43/1.06 ============================== INPUT =================================
% 0.43/1.06
% 0.43/1.06 % Reading from file /tmp/Prover9_5011_n013.cluster.edu
% 0.43/1.06
% 0.43/1.06 set(prolog_style_variables).
% 0.43/1.06 set(auto2).
% 0.43/1.06 % set(auto2) -> set(auto).
% 0.43/1.06 % set(auto) -> set(auto_inference).
% 0.43/1.06 % set(auto) -> set(auto_setup).
% 0.43/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.06 % set(auto) -> set(auto_limits).
% 0.43/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.06 % set(auto) -> set(auto_denials).
% 0.43/1.06 % set(auto) -> set(auto_process).
% 0.43/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.06 % set(auto2) -> assign(stats, some).
% 0.43/1.06 % set(auto2) -> clear(echo_input).
% 0.43/1.06 % set(auto2) -> set(quiet).
% 0.43/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.06 % set(auto2) -> clear(print_given).
% 0.43/1.06 assign(lrs_ticks,-1).
% 0.43/1.06 assign(sos_limit,10000).
% 0.43/1.06 assign(order,kbo).
% 0.43/1.06 set(lex_order_vars).
% 0.43/1.06 clear(print_given).
% 0.43/1.06
% 0.43/1.06 % formulas(sos). % not echoed (19 formulas)
% 0.43/1.06
% 0.43/1.06 ============================== end of input ==========================
% 0.43/1.06
% 0.43/1.06 % From the command line: assign(max_seconds, 300).
% 0.43/1.06
% 0.43/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.06
% 0.43/1.06 % Formulas that are not ordinary clauses:
% 0.43/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.06 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.94/1.23
% 0.94/1.23 ============================== end of process non-clausal formulas ===
% 0.94/1.23
% 0.94/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.23
% 0.94/1.23 ============================== PREDICATE ELIMINATION =================
% 0.94/1.23 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.94/1.23 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.94/1.23 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.94/1.23 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.94/1.23 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.94/1.23 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.94/1.23 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.94/1.23 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.94/1.23 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.94/1.23 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.94/1.23 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.94/1.23 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.94/1.23 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.94/1.23 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.94/1.23 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.94/1.23 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.94/1.23
% 0.94/1.23 ============================== end predicate elimination =============
% 0.94/1.23
% 0.94/1.23 Auto_denials: (non-Horn, no changes).
% 0.94/1.23
% 0.94/1.23 Term ordering decisions:
% 0.94/1.23 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
% 0.94/1.23
% 0.94/1.23 ============================== end of process initial clauses ========
% 0.94/1.23
% 0.94/1.23 ============================== CLAUSES FOR SEARCH ====================
% 0.94/1.23
% 0.94/1.23 ============================== end of clauses for search =============
% 0.94/1.23
% 0.94/1.23 ============================== SEARCH ================================
% 0.94/1.23
% 0.94/1.23 % Starting search at 0.02 seconds.
% 0.94/1.23
% 0.94/1.23 ============================== PROOF =================================
% 0.94/1.23 % SZS status Theorem
% 0.94/1.23 % SZS output start Refutation
% 0.94/1.23
% 0.94/1.23 % Proof 1 at 0.17 (+ 0.01) seconds.
% 0.94/1.23 % Length of proof is 73.
% 0.94/1.23 % Level of proof is 15.
% 0.94/1.23 % Maximum clause weight is 24.000.
% 0.94/1.23 % Given clauses 208.
% 0.94/1.23
% 0.94/1.23 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.23 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.94/1.23 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.94/1.23 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.94/1.23 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.94/1.23 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.94/1.23 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.94/1.23 30 test(c4) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.94/1.23 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.94/1.23 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.94/1.23 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.94/1.23 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.94/1.23 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.94/1.23 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.94/1.23 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.94/1.23 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.94/1.23 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.94/1.23 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 0.98/1.23 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.98/1.23 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 0.98/1.23 47 addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3)) != addition(multiplication(c4,c1),multiplication(c(c4),c3)) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.98/1.23 48 addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2)))) != addition(multiplication(c4,c1),multiplication(c(c4),c3)). [copy(47),rewrite([39(15)])].
% 0.98/1.23 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.98/1.23 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 0.98/1.23 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.98/1.23 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 0.98/1.23 53 multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.98/1.23 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.98/1.23 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.98/1.23 58 -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.98/1.23 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.98/1.23 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.98/1.23 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([33(5)])].
% 0.98/1.23 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),44(a,2,2)),rewrite([36(3),39(3)])].
% 0.98/1.23 88 multiplication(c4,f1(c4)) = zero. [resolve(53,b,30,a)].
% 0.98/1.23 94 addition(c4,f1(c4)) = one. [resolve(55,b,30,a)].
% 0.98/1.23 103 c(c4) != A | multiplication(c4,A) = zero. [resolve(58,a,30,a)].
% 0.98/1.23 110 test(one). [resolve(62,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 0.98/1.23 124 multiplication(c(c4),c(c4)) = c(c4). [resolve(64,a,30,a)].
% 0.98/1.23 135 addition(one,f1(one)) = one. [resolve(110,a,55,b)].
% 0.98/1.23 136 f1(one) = zero. [resolve(110,a,54,b),rewrite([34(4)])].
% 0.98/1.23 140 addition(zero,one) = one. [back_rewrite(135),rewrite([136(3),39(3)])].
% 0.98/1.23 141 -test(zero) | c(zero) = one. [para(136(a,1),61(a,1)),rewrite([136(4)]),unit_del(c,110)].
% 0.98/1.23 142 test(zero). [resolve(140,a,62,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 0.98/1.23 143 c(zero) = one. [back_unit_del(141),unit_del(a,142)].
% 0.98/1.23 146 -test(A) | addition(one,c(A)) = one. [resolve(142,a,52,b),rewrite([143(4),39(4),36(6),143(6)])].
% 0.98/1.23 165 multiplication(c4,addition(A,f1(c4))) = multiplication(c4,A). [para(88(a,1),44(a,1,1)),rewrite([69(4),39(6)]),flip(a)].
% 0.98/1.23 487 addition(one,c(c4)) = one. [resolve(146,a,30,a)].
% 0.98/1.23 499 addition(A,multiplication(c(c4),A)) = A. [para(487(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 0.98/1.23 895 multiplication(c4,c(c4)) = zero. [resolve(103,a,499,a(flip)),rewrite([124(8),33(6)])].
% 0.98/1.23 903 multiplication(c4,multiplication(c(c4),A)) = zero. [para(895(a,1),42(a,1,1)),rewrite([37(2)]),flip(a)].
% 0.98/1.23 908 multiplication(c4,addition(A,multiplication(c(c4),B))) = multiplication(c4,A). [para(903(a,1),44(a,1,1)),rewrite([69(4),39(7)]),flip(a)].
% 0.98/1.23 912 addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1))) != addition(multiplication(c4,c1),multiplication(c(c4),c3)). [back_rewrite(48),rewrite([908(14)])].
% 0.98/1.23 1396 multiplication(c4,c4) = c4. [para(94(a,1),165(a,1,2)),rewrite([34(3)]),flip(a)].
% 0.98/1.23 1419 multiplication(c4,multiplication(c4,A)) = multiplication(c4,A). [para(1396(a,1),42(a,1,1)),flip(a)].
% 0.98/1.23 1426 $F. [back_rewrite(912),rewrite([1419(9),39(8)]),xx(a)].
% 0.98/1.23
% 0.98/1.23 % SZS output end Refutation
% 0.98/1.23 ============================== end of proof ==========================
% 0.98/1.23
% 0.98/1.23 ============================== STATISTICS ============================
% 0.98/1.23
% 0.98/1.23 Given=208. Generated=4309. Kept=1389. proofs=1.
% 0.98/1.23 Usable=188. Sos=901. Demods=445. Limbo=7, Disabled=330. Hints=0.
% 0.98/1.23 Megabytes=1.42.
% 0.98/1.23 User_CPU=0.17, System_CPU=0.01, Wall_clock=0.
% 0.98/1.23
% 0.98/1.23 ============================== end of statistics =====================
% 0.98/1.23
% 0.98/1.23 ============================== end of search =========================
% 0.98/1.23
% 0.98/1.23 THEOREM PROVED
% 0.98/1.23 % SZS status Theorem
% 0.98/1.23
% 0.98/1.23 Exiting with 1 proof.
% 0.98/1.23
% 0.98/1.23 Process 5165 exit (max_proofs) Thu Jun 16 09:25:59 2022
% 0.98/1.23 Prover9 interrupted
%------------------------------------------------------------------------------