%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 : 300s
% DateTime : Wed Jul 27 13:00:31 EDT 2022
% Result : Theorem 27.10s 27.27s
% Output : Refutation 27.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of clauses : 72 ( 50 unt; 2 nHn; 49 RR)
% Number of literals : 101 ( 56 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE024+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE024+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE024+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ complement(A,B)
| multiplication(B,A) = zero ),
file('KLE024+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE024+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE024+1.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE024+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE024+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ test(A)
| c(A) = B
| ~ complement(A,B) ),
file('KLE024+1.p',unknown),
[] ).
cnf(11,axiom,
multiplication(multiplication(dollar_c2,dollar_c3),c(dollar_c1)) != zero,
file('KLE024+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('KLE024+1.p',unknown),
[] ).
cnf(14,axiom,
addition(A,B) = addition(B,A),
file('KLE024+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE024+1.p',unknown),
[] ).
cnf(16,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
addition(A,zero) = A,
file('KLE024+1.p',unknown),
[] ).
cnf(20,axiom,
addition(A,A) = A,
file('KLE024+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE024+1.p',unknown),
[] ).
cnf(24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(26,axiom,
multiplication(A,one) = A,
file('KLE024+1.p',unknown),
[] ).
cnf(28,axiom,
multiplication(one,A) = A,
file('KLE024+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE024+1.p',unknown),
[] ).
cnf(34,axiom,
multiplication(A,zero) = zero,
file('KLE024+1.p',unknown),
[] ).
cnf(36,axiom,
multiplication(zero,A) = zero,
file('KLE024+1.p',unknown),
[] ).
cnf(37,axiom,
( test(A)
| c(A) = zero ),
file('KLE024+1.p',unknown),
[] ).
cnf(38,axiom,
test(dollar_c2),
file('KLE024+1.p',unknown),
[] ).
cnf(39,axiom,
test(dollar_c1),
file('KLE024+1.p',unknown),
[] ).
cnf(40,axiom,
addition(multiplication(dollar_c3,c(dollar_c1)),multiplication(c(dollar_c2),dollar_c3)) = multiplication(c(dollar_c2),dollar_c3),
file('KLE024+1.p',unknown),
[] ).
cnf(43,plain,
multiplication(dollar_c2,multiplication(dollar_c3,c(dollar_c1))) != zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),24]),
[iquote('back_demod,11,demod,24')] ).
cnf(44,plain,
complement(dollar_c2,c(dollar_c2)),
inference(hyper,[status(thm)],[38,9,13]),
[iquote('hyper,38,9,13')] ).
cnf(45,plain,
complement(dollar_f1(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[38,3]),
[iquote('hyper,38,3')] ).
cnf(47,plain,
complement(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[39,3]),
[iquote('hyper,39,3')] ).
cnf(50,plain,
multiplication(dollar_c2,c(dollar_c2)) = zero,
inference(hyper,[status(thm)],[44,6]),
[iquote('hyper,44,6')] ).
cnf(57,plain,
( addition(A,B) = one
| ~ complement(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,7])]),
[iquote('para_into,14.1.1,7.2.1,flip.1')] ).
cnf(58,plain,
( addition(A,B) = A
| ~ le_q(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,1])]),
[iquote('para_into,14.1.1,1.2.1,flip.1')] ).
cnf(61,plain,
addition(dollar_c2,dollar_f1(dollar_c2)) = one,
inference(hyper,[status(thm)],[45,7]),
[iquote('hyper,45,7')] ).
cnf(63,plain,
multiplication(dollar_f1(dollar_c2),dollar_c2) = zero,
inference(hyper,[status(thm)],[45,6]),
[iquote('hyper,45,6')] ).
cnf(66,plain,
multiplication(dollar_c2,dollar_f1(dollar_c2)) = zero,
inference(hyper,[status(thm)],[45,5]),
[iquote('hyper,45,5')] ).
cnf(78,plain,
multiplication(dollar_f1(dollar_c1),dollar_c1) = zero,
inference(hyper,[status(thm)],[47,6]),
[iquote('hyper,47,6')] ).
cnf(81,plain,
multiplication(dollar_c1,dollar_f1(dollar_c1)) = zero,
inference(hyper,[status(thm)],[47,5]),
[iquote('hyper,47,5')] ).
cnf(95,plain,
( zero = A
| ~ le_q(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[19,1]),
[iquote('para_into,18.1.1,1.2.1')] ).
cnf(97,plain,
( ~ complement(zero,A)
| A = one ),
inference(para_from,[status(thm),theory(equality)],[19,7]),
[iquote('para_from,18.1.1,7.2.1')] ).
cnf(99,plain,
( ~ le_q(A,zero)
| A = zero ),
inference(para_from,[status(thm),theory(equality)],[19,1]),
[iquote('para_from,18.1.1,1.2.1')] ).
cnf(100,plain,
le_q(A,A),
inference(hyper,[status(thm)],[20,2]),
[iquote('hyper,20,2')] ).
cnf(105,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,16])]),
[iquote('para_from,20.1.1,16.1.1.1,flip.1')] ).
cnf(108,plain,
( multiplication(A,multiplication(B,C)) = zero
| ~ complement(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,5]),36])]),
[iquote('para_into,23.1.1.1,5.2.1,demod,36,flip.1')] ).
cnf(119,plain,
( ~ complement(A,one)
| A = zero ),
inference(para_from,[status(thm),theory(equality)],[26,6]),
[iquote('para_from,25.1.1,6.2.1')] ).
cnf(121,plain,
complement(zero,one),
inference(hyper,[status(thm)],[28,8,26,19]),
[iquote('hyper,27,8,25,18')] ).
cnf(126,plain,
( addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,C)
| ~ le_q(B,C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,1])]),
[iquote('para_into,29.1.1.2,1.2.1,flip.1')] ).
cnf(160,plain,
( c(A) = zero
| complement(dollar_f1(A),A) ),
inference(hyper,[status(thm)],[37,3]),
[iquote('hyper,37,3')] ).
cnf(171,plain,
multiplication(dollar_c2,multiplication(c(dollar_c2),A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[50,24]),36])]),
[iquote('para_from,50.1.1,23.1.1.1,demod,36,flip.1')] ).
cnf(181,plain,
le_q(multiplication(dollar_c3,c(dollar_c1)),multiplication(c(dollar_c2),dollar_c3)),
inference(hyper,[status(thm)],[40,2]),
[iquote('hyper,40,2')] ).
cnf(208,plain,
addition(dollar_f1(dollar_c2),dollar_c2) = one,
inference(para_into,[status(thm),theory(equality)],[61,14]),
[iquote('para_into,61.1.1,14.1.1')] ).
cnf(219,plain,
complement(dollar_c2,dollar_f1(dollar_c2)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,8]),66,208]),13,13,13]),
[iquote('para_from,63.1.1,8.2.1,demod,66,208,unit_del,13,13,13')] ).
cnf(224,plain,
c(dollar_c2) = dollar_f1(dollar_c2),
inference(hyper,[status(thm)],[219,10,38]),
[iquote('hyper,219,10,38')] ).
cnf(249,plain,
le_q(multiplication(dollar_c3,c(dollar_c1)),multiplication(dollar_f1(dollar_c2),dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[181]),224]),
[iquote('back_demod,181,demod,224')] ).
cnf(256,plain,
multiplication(dollar_c2,multiplication(dollar_f1(dollar_c2),A)) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[171]),224]),
[iquote('back_demod,171,demod,224')] ).
cnf(289,plain,
addition(dollar_f1(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[57,47]),
[iquote('hyper,57,47')] ).
cnf(342,plain,
complement(dollar_c1,dollar_f1(dollar_c1)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[78,8]),81,289]),13,13,13]),
[iquote('para_from,78.1.1,8.2.1,demod,81,289,unit_del,13,13,13')] ).
cnf(344,plain,
c(dollar_c1) = dollar_f1(dollar_c1),
inference(hyper,[status(thm)],[342,10,39]),
[iquote('hyper,342,10,39')] ).
cnf(377,plain,
le_q(multiplication(dollar_c3,dollar_f1(dollar_c1)),multiplication(dollar_f1(dollar_c2),dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[249]),344]),
[iquote('back_demod,249,demod,344')] ).
cnf(392,plain,
multiplication(dollar_c2,multiplication(dollar_c3,dollar_f1(dollar_c1))) != zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[43]),344]),
[iquote('back_demod,43,demod,344')] ).
cnf(425,plain,
( multiplication(A,B) = zero
| ~ le_q(A,zero) ),
inference(para_from,[status(thm),theory(equality)],[95,36]),
[iquote('para_from,95.1.1,35.1.1.1')] ).
cnf(484,plain,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| ~ complement(zero,addition(B,A)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[97,8]),13]),
[iquote('para_from,97.2.1,8.4.1,unit_del,13')] ).
cnf(1474,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[105,2]),
[iquote('hyper,105,2')] ).
cnf(1514,plain,
le_q(dollar_f1(dollar_c2),one),
inference(para_into,[status(thm),theory(equality)],[1474,208]),
[iquote('para_into,1474.1.2,207.1.1')] ).
cnf(1585,plain,
addition(one,dollar_f1(dollar_c2)) = one,
inference(hyper,[status(thm)],[1514,58]),
[iquote('hyper,1514,58')] ).
cnf(2701,plain,
( multiplication(A,B) = multiplication(A,multiplication(C,D))
| ~ le_q(B,multiplication(C,D))
| ~ complement(C,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[126,108]),19]),
[iquote('para_into,126.1.1.2,108.1.1,demod,19')] ).
cnf(3638,plain,
~ le_q(multiplication(dollar_c3,dollar_f1(dollar_c1)),zero),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[392,99]),34]),13]),
[iquote('para_into,392.1.1.2,99.2.1,demod,34,unit_del,13')] ).
cnf(3718,plain,
~ le_q(dollar_f1(dollar_c2),zero),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[425,377]),3638]),
[iquote('para_from,425.1.1,377.1.2,unit_del,3638')] ).
cnf(3727,plain,
~ complement(dollar_f1(dollar_c2),one),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3718,119]),100]),
[iquote('para_into,3718.1.1,119.2.1,unit_del,100')] ).
cnf(3814,plain,
dollar_f1(dollar_c2) != zero,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[484,1585]),28,26]),3727,121])]),
[iquote('para_into,484.4.2,1585.1.1,demod,28,26,unit_del,3727,121,factor_simp')] ).
cnf(4081,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2701,377,160]),256,224]),392,3814]),
[iquote('hyper,2701,377,160,demod,256,224,unit_del,392,3814')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.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 : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:40:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.18 ----- Otter 3.3f, August 2004 -----
% 2.00/2.18 The process was started by sandbox on n026.cluster.edu,
% 2.00/2.18 Wed Jul 27 06:40:54 2022
% 2.00/2.18 The command was "./otter". The process ID is 27319.
% 2.00/2.18
% 2.00/2.18 set(prolog_style_variables).
% 2.00/2.18 set(auto).
% 2.00/2.18 dependent: set(auto1).
% 2.00/2.18 dependent: set(process_input).
% 2.00/2.18 dependent: clear(print_kept).
% 2.00/2.18 dependent: clear(print_new_demod).
% 2.00/2.18 dependent: clear(print_back_demod).
% 2.00/2.18 dependent: clear(print_back_sub).
% 2.00/2.18 dependent: set(control_memory).
% 2.00/2.18 dependent: assign(max_mem, 12000).
% 2.00/2.18 dependent: assign(pick_given_ratio, 4).
% 2.00/2.18 dependent: assign(stats_level, 1).
% 2.00/2.18 dependent: assign(max_seconds, 10800).
% 2.00/2.18 clear(print_given).
% 2.00/2.18
% 2.00/2.18 formula_list(usable).
% 2.00/2.18 all A (A=A).
% 2.00/2.18 all A B (addition(A,B)=addition(B,A)).
% 2.00/2.18 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 2.00/2.18 all A (addition(A,zero)=A).
% 2.00/2.18 all A (addition(A,A)=A).
% 2.00/2.18 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 2.00/2.18 all A (multiplication(A,one)=A).
% 2.00/2.18 all A (multiplication(one,A)=A).
% 2.00/2.18 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 2.00/2.18 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 2.00/2.18 all A (multiplication(A,zero)=zero).
% 2.00/2.18 all A (multiplication(zero,A)=zero).
% 2.00/2.18 all A B (le_q(A,B)<->addition(A,B)=B).
% 2.00/2.18 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 2.00/2.18 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 2.00/2.18 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 2.00/2.18 all X0 (-test(X0)->c(X0)=zero).
% 2.00/2.18 -(all X0 X1 X2 (test(X1)&test(X2)-> (addition(multiplication(X0,c(X2)),multiplication(c(X1),X0))=multiplication(c(X1),X0)->multiplication(multiplication(X1,X0),c(X2))=zero))).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 -------> usable clausifies to:
% 2.00/2.18
% 2.00/2.18 list(usable).
% 2.00/2.18 0 [] A=A.
% 2.00/2.18 0 [] addition(A,B)=addition(B,A).
% 2.00/2.18 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 2.00/2.18 0 [] addition(A,zero)=A.
% 2.00/2.18 0 [] addition(A,A)=A.
% 2.00/2.18 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 2.00/2.18 0 [] multiplication(A,one)=A.
% 2.00/2.18 0 [] multiplication(one,A)=A.
% 2.00/2.18 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.00/2.18 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.00/2.18 0 [] multiplication(A,zero)=zero.
% 2.00/2.18 0 [] multiplication(zero,A)=zero.
% 2.00/2.18 0 [] -le_q(A,B)|addition(A,B)=B.
% 2.00/2.18 0 [] le_q(A,B)|addition(A,B)!=B.
% 2.00/2.18 0 [] -test(X0)|complement($f1(X0),X0).
% 2.00/2.18 0 [] test(X0)| -complement(X1,X0).
% 2.00/2.18 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 2.00/2.18 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 2.00/2.18 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 2.00/2.18 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 2.00/2.18 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 2.00/2.18 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 2.00/2.18 0 [] test(X0)|c(X0)=zero.
% 2.00/2.18 0 [] test($c2).
% 2.00/2.18 0 [] test($c1).
% 2.00/2.18 0 [] addition(multiplication($c3,c($c1)),multiplication(c($c2),$c3))=multiplication(c($c2),$c3).
% 2.00/2.18 0 [] multiplication(multiplication($c2,$c3),c($c1))!=zero.
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.00/2.18
% 2.00/2.18 This ia a non-Horn set with equality. The strategy will be
% 2.00/2.18 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.00/2.18 deletion, with positive clauses in sos and nonpositive
% 2.00/2.18 clauses in usable.
% 2.00/2.18
% 2.00/2.18 dependent: set(knuth_bendix).
% 2.00/2.18 dependent: set(anl_eq).
% 2.00/2.18 dependent: set(para_from).
% 2.00/2.18 dependent: set(para_into).
% 2.00/2.18 dependent: clear(para_from_right).
% 2.00/2.18 dependent: clear(para_into_right).
% 2.00/2.18 dependent: set(para_from_vars).
% 2.00/2.18 dependent: set(eq_units_both_ways).
% 2.00/2.18 dependent: set(dynamic_demod_all).
% 2.00/2.18 dependent: set(dynamic_demod).
% 2.00/2.18 dependent: set(order_eq).
% 2.00/2.18 dependent: set(back_demod).
% 2.00/2.18 dependent: set(lrpo).
% 2.00/2.18 dependent: set(hyper_res).
% 2.00/2.18 dependent: set(unit_deletion).
% 2.00/2.18 dependent: set(factor).
% 2.00/2.18
% 2.00/2.18 ------------> process usable:
% 2.00/2.18 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 2.00/2.18 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 2.00/2.18 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 2.00/2.18 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 2.00/2.18 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 27.10/27.27 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 27.10/27.27 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 27.10/27.27 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 27.10/27.27 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 27.10/27.27 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 27.10/27.27 ** KEPT (pick-wt=8): 11 [] multiplication(multiplication($c2,$c3),c($c1))!=zero.
% 27.10/27.27
% 27.10/27.27 ------------> process sos:
% 27.10/27.27 ** KEPT (pick-wt=3): 13 [] A=A.
% 27.10/27.27 ** KEPT (pick-wt=7): 14 [] addition(A,B)=addition(B,A).
% 27.10/27.27 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 27.10/27.27 ---> New Demodulator: 17 [new_demod,16] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 27.10/27.27 ** KEPT (pick-wt=5): 18 [] addition(A,zero)=A.
% 27.10/27.27 ---> New Demodulator: 19 [new_demod,18] addition(A,zero)=A.
% 27.10/27.27 ** KEPT (pick-wt=5): 20 [] addition(A,A)=A.
% 27.10/27.27 ---> New Demodulator: 21 [new_demod,20] addition(A,A)=A.
% 27.10/27.27 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 27.10/27.27 ---> New Demodulator: 24 [new_demod,23] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 27.10/27.27 ** KEPT (pick-wt=5): 25 [] multiplication(A,one)=A.
% 27.10/27.27 ---> New Demodulator: 26 [new_demod,25] multiplication(A,one)=A.
% 27.10/27.27 ** KEPT (pick-wt=5): 27 [] multiplication(one,A)=A.
% 27.10/27.27 ---> New Demodulator: 28 [new_demod,27] multiplication(one,A)=A.
% 27.10/27.27 ** KEPT (pick-wt=13): 29 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 27.10/27.27 ---> New Demodulator: 30 [new_demod,29] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 27.10/27.27 ** KEPT (pick-wt=13): 31 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 27.10/27.27 ---> New Demodulator: 32 [new_demod,31] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 27.10/27.27 ** KEPT (pick-wt=5): 33 [] multiplication(A,zero)=zero.
% 27.10/27.27 ---> New Demodulator: 34 [new_demod,33] multiplication(A,zero)=zero.
% 27.10/27.27 ** KEPT (pick-wt=5): 35 [] multiplication(zero,A)=zero.
% 27.10/27.27 ---> New Demodulator: 36 [new_demod,35] multiplication(zero,A)=zero.
% 27.10/27.27 ** KEPT (pick-wt=6): 37 [] test(A)|c(A)=zero.
% 27.10/27.27 ** KEPT (pick-wt=2): 38 [] test($c2).
% 27.10/27.27 ** KEPT (pick-wt=2): 39 [] test($c1).
% 27.10/27.27 ** KEPT (pick-wt=14): 40 [] addition(multiplication($c3,c($c1)),multiplication(c($c2),$c3))=multiplication(c($c2),$c3).
% 27.10/27.27 ---> New Demodulator: 41 [new_demod,40] addition(multiplication($c3,c($c1)),multiplication(c($c2),$c3))=multiplication(c($c2),$c3).
% 27.10/27.27 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 27.10/27.27 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] addition(A,B)=addition(B,A).
% 27.10/27.27 >>>> Starting back demodulation with 17.
% 27.10/27.27 >>>> Starting back demodulation with 19.
% 27.10/27.27 >>>> Starting back demodulation with 21.
% 27.10/27.27 >> back demodulating 12 with 21.
% 27.10/27.27 >>>> Starting back demodulation with 24.
% 27.10/27.27 >> back demodulating 11 with 24.
% 27.10/27.27 >>>> Starting back demodulation with 26.
% 27.10/27.27 >>>> Starting back demodulation with 28.
% 27.10/27.27 >>>> Starting back demodulation with 30.
% 27.10/27.27 >>>> Starting back demodulation with 32.
% 27.10/27.27 >>>> Starting back demodulation with 34.
% 27.10/27.27 >>>> Starting back demodulation with 36.
% 27.10/27.27 >>>> Starting back demodulation with 41.
% 27.10/27.27
% 27.10/27.27 ======= end of input processing =======
% 27.10/27.27
% 27.10/27.27 =========== start of search ===========
% 27.10/27.27
% 27.10/27.27
% 27.10/27.27 Resetting weight limit to 7.
% 27.10/27.27
% 27.10/27.27
% 27.10/27.27 Resetting weight limit to 7.
% 27.10/27.27
% 27.10/27.27 sos_size=2602
% 27.10/27.27
% 27.10/27.27 -- HEY sandbox, WE HAVE A PROOF!! --
% 27.10/27.27
% 27.10/27.27 -----> EMPTY CLAUSE at 25.09 sec ----> 4081 [hyper,2701,377,160,demod,256,224,unit_del,392,3814] $F.
% 27.10/27.27
% 27.10/27.27 Length of proof is 46. Level of proof is 10.
% 27.10/27.27
% 27.10/27.27 ---------------- PROOF ----------------
% 27.10/27.27 % SZS status Theorem
% 27.10/27.27 % SZS output start Refutation
% See solution above
% 27.10/27.27 ------------ end of proof -------------
% 27.10/27.27
% 27.10/27.27
% 27.10/27.27 Search stopped by max_proofs option.
% 27.10/27.27
% 27.10/27.27
% 27.10/27.27 Search stopped by max_proofs option.
% 27.10/27.27
% 27.10/27.27 ============ end of search ============
% 27.10/27.27
% 27.10/27.27 -------------- statistics -------------
% 27.10/27.27 clauses given 1939
% 27.10/27.27 clauses generated 1124642
% 27.10/27.27 clauses kept 3920
% 27.10/27.27 clauses forward subsumed 66215
% 27.10/27.27 clauses back subsumed 1437
% 27.10/27.27 Kbytes malloced 5859
% 27.10/27.27
% 27.10/27.27 ----------- times (seconds) -----------
% 27.10/27.27 user CPU time 25.09 (0 hr, 0 min, 25 sec)
% 27.10/27.27 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 27.10/27.27 wall-clock time 27 (0 hr, 0 min, 27 sec)
% 27.10/27.27
% 27.10/27.27 That finishes the proof of the theorem.
% 27.10/27.27
% 27.10/27.27 Process 27319 finished Wed Jul 27 06:41:21 2022
% 27.15/27.27 Otter interrupted
% 27.15/27.27 PROOF FOUND
%------------------------------------------------------------------------------