TSTP Solution File: KLE090-10 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n006.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 02:35:43 EDT 2022
% Result : Unsatisfiable 0.74s 1.14s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 14:00:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.62/0.99 ********************************************************************************
% 0.62/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/0.99 * |/ | \/ | *
% 0.62/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/0.99 * A. Jaeger and B. Loechner | | *
% 0.62/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/0.99 ********************************************************************************
% 0.62/0.99
% 0.62/0.99
% 0.62/0.99 Goals:
% 0.62/0.99 ------
% 0.62/0.99
% 0.62/0.99 ( 1) addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) ?=? antidomain(sK2_goals_X0)
% 0.62/0.99
% 0.62/0.99 Detected structure: Praeloop
% 0.62/0.99 ********************************************************************************
% 0.62/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.62/0.99 ********************************************************************************
% 0.62/0.99
% 0.74/1.14 joined goal: 1 addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) ?= antidomain(sK2_goals_X0) to antidomain(sK2_goals_X0)
% 0.74/1.14 goal joined
% 0.74/1.14 % SZS status Unsatisfiable
% 0.74/1.14 #START OF PROOF
% 0.74/1.14 % SZS output start CNFRefutation
% 0.74/1.14 cnf('0.1.0.0',axiom,
% 0.74/1.14 ( X1 = multiplication(X1,one) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.1.1.0',plain,
% 0.74/1.14 ( X1 = multiplication(X1,one) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.74/1.14 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.74/1.14 cnf('0.1.2.0',plain,
% 0.74/1.14 ( multiplication(X1,one) = X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_1]).
% 0.74/1.14 cnf('0.2.0.0',axiom,
% 0.74/1.14 ( X1 = multiplication(one,X1) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.2.1.0',plain,
% 0.74/1.14 ( X1 = multiplication(one,X1) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.74/1.14 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.74/1.14 cnf('0.2.2.0',plain,
% 0.74/1.14 ( multiplication(one,X1) = X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_2]).
% 0.74/1.14 cnf('0.3.0.0',axiom,
% 0.74/1.14 ( X1 = addition(X1,X1) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.3.1.0',plain,
% 0.74/1.14 ( X1 = addition(X1,X1) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.74/1.14 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.74/1.14 cnf('0.3.2.0',plain,
% 0.74/1.14 ( addition(X1,X1) = X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_3]).
% 0.74/1.14 cnf('0.4.0.0',axiom,
% 0.74/1.14 ( X1 = addition(X1,zero) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.4.1.0',plain,
% 0.74/1.14 ( X1 = addition(X1,zero) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.74/1.14 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.74/1.14 cnf('0.4.2.0',plain,
% 0.74/1.14 ( addition(X1,zero) = X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_4]).
% 0.74/1.14 cnf('0.5.0.0',axiom,
% 0.74/1.14 ( X1 = ifeq2(X2,X2,X1,X3) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.5.1.0',plain,
% 0.74/1.14 ( X1 = ifeq2(X2,X2,X1,X3) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.74/1.14 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.74/1.14 cnf('0.5.2.0',plain,
% 0.74/1.14 ( ifeq2(X1,X1,X2,X3) = X2 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_5]).
% 0.74/1.14 cnf('0.6.0.0',axiom,
% 0.74/1.14 ( X1 = ifeq(X2,X2,X1,X3) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.6.1.0',plain,
% 0.74/1.14 ( X1 = ifeq(X2,X2,X1,X3) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.74/1.14 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.74/1.14 cnf('0.6.2.0',plain,
% 0.74/1.14 ( ifeq(X1,X1,X2,X3) = X2 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_6]).
% 0.74/1.14 cnf('0.7.0.0',axiom,
% 0.74/1.14 ( X1 = ifeq(leq(X2,X1),true,addition(X2,X1),X1) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.7.1.0',plain,
% 0.74/1.14 ( X1 = ifeq(leq(X2,X1),true,addition(X2,X1),X1) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.74/1.14 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.74/1.14 cnf('0.7.2.0',plain,
% 0.74/1.14 ( ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_7]).
% 0.74/1.14 cnf('0.9.0.0',axiom,
% 0.74/1.14 ( multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.9.1.0',plain,
% 0.74/1.14 ( multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.74/1.14 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.74/1.14 cnf('0.9.2.0',plain,
% 0.74/1.14 ( addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_9]).
% 0.74/1.14 cnf('0.12.0.0',axiom,
% 0.74/1.14 ( multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.12.1.0',plain,
% 0.74/1.14 ( multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.74/1.14 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.74/1.14 cnf('0.12.2.0',plain,
% 0.74/1.14 ( addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_12]).
% 0.74/1.14 cnf('0.13.0.0',axiom,
% 0.74/1.14 ( multiplication(antidomain(X1),X1) = zero ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.13.1.0',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),X1) = zero ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.74/1.14 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.74/1.14 cnf('0.13.2.0',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),X1) = zero ),
% 0.74/1.14 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_13]).
% 0.74/1.14 cnf('0.15.0.0',axiom,
% 0.74/1.14 ( addition(X1,X2) = addition(X2,X1) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.15.1.0',plain,
% 0.74/1.14 ( addition(X1,X2) = addition(X2,X1) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.74/1.14 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.74/1.14 cnf('0.15.2.0',plain,
% 0.74/1.14 ( addition(X1,X2) = addition(X2,X1) ),
% 0.74/1.14 inference(activate,[status(thm)],['0.15.1.0']),
% 0.74/1.14 [equation_1]).
% 0.74/1.14 cnf('0.16.0.0',axiom,
% 0.74/1.14 ( addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.16.1.0',plain,
% 0.74/1.14 ( addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.74/1.14 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.74/1.14 cnf('0.16.2.0',plain,
% 0.74/1.14 ( addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_15]).
% 0.74/1.14 cnf('0.20.0.0',axiom,
% 0.74/1.14 ( addition(antidomain(antidomain(X1)),antidomain(X1)) = one ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.20.1.0',plain,
% 0.74/1.14 ( addition(antidomain(antidomain(X1)),antidomain(X1)) = one ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.74/1.14 [weight('<19,0,0,[0,0,0,20]>')]).
% 0.74/1.14 cnf('0.20.1.1',plain,
% 0.74/1.14 ( addition(antidomain(X1),antidomain(antidomain(X1))) = one ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.20.1.0','0.15.2.0',theory(equality)]),
% 0.74/1.14 [pos('L','L')]).
% 0.74/1.14 cnf('0.20.2.0',plain,
% 0.74/1.14 ( addition(antidomain(X1),antidomain(antidomain(X1))) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.20.1.1',theory(equality)]),
% 0.74/1.14 [u,rule_19]).
% 0.74/1.14 cnf('0.21.0.0',axiom,
% 0.74/1.14 ( addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1 ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.21.1.0',plain,
% 0.74/1.14 ( addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1 ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.74/1.14 [weight('<20,0,0,[0,0,0,21]>')]).
% 0.74/1.14 cnf('0.21.2.0',plain,
% 0.74/1.14 ( addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_20]).
% 0.74/1.14 cnf('0.23.0.0',axiom,
% 0.74/1.14 ( antidomain(antidomain(X1)) = domain(X1) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.23.1.0',plain,
% 0.74/1.14 ( antidomain(antidomain(X1)) = domain(X1) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.74/1.14 [weight('<22,0,0,[0,0,0,23]>')]).
% 0.74/1.14 cnf('0.23.2.0',plain,
% 0.74/1.14 ( antidomain(antidomain(X1)) = domain(X1) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_22]).
% 0.74/1.14 cnf('0.24.0.0',axiom,
% 0.74/1.14 ( true = ifeq2(addition(X1,X2),X2,leq(X1,X2),true) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.24.1.0',plain,
% 0.74/1.14 ( true = ifeq2(addition(X1,X2),X2,leq(X1,X2),true) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.74/1.14 [weight('<23,0,0,[0,0,0,24]>')]).
% 0.74/1.14 cnf('0.24.2.0',plain,
% 0.74/1.14 ( ifeq2(addition(X1,X2),X2,leq(X1,X2),true) = true ),
% 0.74/1.14 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_23]).
% 0.74/1.14 cnf('0.26.0.0',plain,
% 0.74/1.14 ( zero = antidomain(one) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.13.2.0','0.1.2.0',theory(equality)]),
% 0.74/1.14 [pos('L','L')]).
% 0.74/1.14 cnf('0.26.1.0',plain,
% 0.74/1.14 ( zero = antidomain(one) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.74/1.14 [weight('<11,13,1,[1,0,0,0]>')]).
% 0.74/1.14 cnf('0.26.2.0',plain,
% 0.74/1.14 ( antidomain(one) = zero ),
% 0.74/1.14 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_25]).
% 0.74/1.14 cnf('0.28.0.0',plain,
% 0.74/1.14 ( domain(one) = antidomain(zero) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.23.2.0','0.26.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1','L')]).
% 0.74/1.14 cnf('0.28.1.0',plain,
% 0.74/1.14 ( domain(one) = antidomain(zero) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.74/1.14 [weight('<14,26,23,[0,0,0,1]>')]).
% 0.74/1.14 cnf('0.28.2.0',plain,
% 0.74/1.14 ( antidomain(zero) = domain(one) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_27]).
% 0.74/1.14 cnf('0.29.0.0',plain,
% 0.74/1.14 ( addition(zero,X1) = X1 ),
% 0.74/1.14 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 0.74/1.14 [pos('L','L')]).
% 0.74/1.14 cnf('0.29.1.0',plain,
% 0.74/1.14 ( addition(zero,X1) = X1 ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.74/1.14 [weight('<19,15,4,[1,0,0,0]>')]).
% 0.74/1.14 cnf('0.29.2.0',plain,
% 0.74/1.14 ( addition(zero,X1) = X1 ),
% 0.74/1.14 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_28]).
% 0.74/1.14 cnf('0.41.0.0',plain,
% 0.74/1.14 ( addition(antidomain(X1),antidomain(antidomain(X1))) = one ),
% 0.74/1.14 inference(interreduction_right,[status(thm)],['0.20.2.0'])).
% 0.74/1.14 cnf('0.41.0.1',plain,
% 0.74/1.14 ( addition(antidomain(X1),domain(X1)) = one ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.41.0.0','0.23.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.41.1.0',plain,
% 0.74/1.14 ( addition(antidomain(X1),domain(X1)) = one ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.41.0.1']),
% 0.74/1.14 [weight('<41,20,23,[0,0,0,0]>')]).
% 0.74/1.14 cnf('0.41.1.1',plain,
% 0.74/1.14 ( addition(domain(X1),antidomain(X1)) = one ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.41.1.0','0.15.2.0',theory(equality)]),
% 0.74/1.14 [pos('L','L')]).
% 0.74/1.14 cnf('0.41.2.0',plain,
% 0.74/1.14 ( addition(domain(X1),antidomain(X1)) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.41.1.1',theory(equality)]),
% 0.74/1.14 [u,rule_40]).
% 0.74/1.14 cnf('0.42.0.0',plain,
% 0.74/1.14 ( one = addition(domain(one),zero) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.41.2.0','0.26.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.42.0.1',plain,
% 0.74/1.14 ( one = domain(one) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.42.0.0','0.4.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.42.1.0',plain,
% 0.74/1.14 ( one = domain(one) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.42.0.1']),
% 0.74/1.14 [weight('<11,41,26,[1,0,0,3]>')]).
% 0.74/1.14 cnf('0.42.2.0',plain,
% 0.74/1.14 ( domain(one) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_41]).
% 0.74/1.14 cnf('0.43.0.0',plain,
% 0.74/1.14 ( antidomain(zero) = domain(one) ),
% 0.74/1.14 inference(interreduction_right,[status(thm)],['0.28.2.0'])).
% 0.74/1.14 cnf('0.43.0.1',plain,
% 0.74/1.14 ( antidomain(zero) = one ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.43.0.0','0.42.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.43.1.0',plain,
% 0.74/1.14 ( antidomain(zero) = one ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.43.0.1']),
% 0.74/1.14 [weight('<11,28,42,[0,0,0,0]>')]).
% 0.74/1.14 cnf('0.43.2.0',plain,
% 0.74/1.14 ( antidomain(zero) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_42]).
% 0.74/1.14 cnf('0.47.0.0',plain,
% 0.74/1.14 ( addition(X1,addition(X1,X2)) = addition(X1,X2) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1','L')]).
% 0.74/1.14 cnf('0.47.1.0',plain,
% 0.74/1.14 ( addition(X1,addition(X1,X2)) = addition(X1,X2) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.74/1.14 [weight('<53,16,3,[1,0,0,1]>')]).
% 0.74/1.14 cnf('0.47.2.0',plain,
% 0.74/1.14 ( addition(X1,addition(X1,X2)) = addition(X1,X2) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_46]).
% 0.74/1.14 cnf('0.50.0.0',plain,
% 0.74/1.14 ( true = ifeq2(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.24.2.0','0.47.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1','L')]).
% 0.74/1.14 cnf('0.50.0.1',plain,
% 0.74/1.14 ( true = leq(X1,addition(X1,X2)) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.50.0.0','0.5.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.50.1.0',plain,
% 0.74/1.14 ( true = leq(X1,addition(X1,X2)) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.50.0.1']),
% 0.74/1.14 [weight('<41,47,24,[0,0,0,1]>')]).
% 0.74/1.14 cnf('0.50.2.0',plain,
% 0.74/1.14 ( leq(X1,addition(X1,X2)) = true ),
% 0.74/1.14 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_49]).
% 0.74/1.14 cnf('0.53.0.0',plain,
% 0.74/1.14 ( true = leq(X1,addition(X2,X1)) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.50.2.0','0.15.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.53.1.0',plain,
% 0.74/1.14 ( true = leq(X1,addition(X2,X1)) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.53.0.0']),
% 0.74/1.14 [weight('<41,50,15,[1,0,0,2]>')]).
% 0.74/1.14 cnf('0.53.2.0',plain,
% 0.74/1.14 ( leq(X1,addition(X2,X1)) = true ),
% 0.74/1.14 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_52]).
% 0.74/1.14 cnf('0.55.0.0',plain,
% 0.74/1.14 ( true = leq(antidomain(X1),one) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.53.2.0','0.41.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.55.1.0',plain,
% 0.74/1.14 ( true = leq(antidomain(X1),one) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.55.0.0']),
% 0.74/1.14 [weight('<29,53,41,[1,0,0,2]>')]).
% 0.74/1.14 cnf('0.55.2.0',plain,
% 0.74/1.14 ( leq(antidomain(X1),one) = true ),
% 0.74/1.14 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_54]).
% 0.74/1.14 cnf('0.57.0.0',plain,
% 0.74/1.14 ( one = ifeq(true,true,addition(antidomain(X1),one),one) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.7.2.0','0.55.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1','L')]).
% 0.74/1.14 cnf('0.57.0.1',plain,
% 0.74/1.14 ( one = addition(antidomain(X1),one) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.57.0.0','0.6.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.57.1.0',plain,
% 0.74/1.14 ( one = addition(antidomain(X1),one) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.57.0.1']),
% 0.74/1.14 [weight('<29,55,7,[0,0,0,1]>')]).
% 0.74/1.14 cnf('0.57.1.1',plain,
% 0.74/1.14 ( one = addition(one,antidomain(X1)) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.57.1.0','0.15.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.57.2.0',plain,
% 0.74/1.14 ( addition(one,antidomain(X1)) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.57.1.1',theory(equality)]),
% 0.74/1.14 [x,rule_56]).
% 0.74/1.14 cnf('0.200.0.0',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),zero) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.9.2.0','0.13.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.200.0.1',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.200.0.0','0.4.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.200.1.0',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.200.0.1']),
% 0.74/1.14 [weight('<76,13,9,[0,0,0,4]>')]).
% 0.74/1.14 cnf('0.200.2.0',plain,
% 0.74/1.14 ( multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.200.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_199]).
% 0.74/1.14 cnf('0.202.0.0',plain,
% 0.74/1.14 ( multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = multiplication(antidomain(sK1_goals_X1),sK1_goals_X1) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.200.2.0','0.21.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2','L')]).
% 0.74/1.14 cnf('0.202.0.1',plain,
% 0.74/1.14 ( multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.202.0.0','0.13.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.202.1.0',plain,
% 0.74/1.14 ( multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.202.0.1']),
% 0.74/1.14 [weight('<29,200,21,[1,0,0,3]>')]).
% 0.74/1.14 cnf('0.202.2.0',plain,
% 0.74/1.14 ( multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero ),
% 0.74/1.14 inference(orient,[status(thm)],['0.202.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_201]).
% 0.74/1.14 cnf('0.215.0.0',axiom,
% 0.74/1.14 ( addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))) ),
% 0.74/1.14 file('/tmp/WALDMEISTER_6917_n006')).
% 0.74/1.14 cnf('0.215.1.0',plain,
% 0.74/1.14 ( addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.215.0.0']),
% 0.74/1.14 [weight('<0,0,0,[0,0,0,19]>')]).
% 0.74/1.14 cnf('0.215.1.1',plain,
% 0.74/1.14 ( addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.215.1.0','0.23.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.2.1.2','L')]).
% 0.74/1.14 cnf('0.215.1.2',plain,
% 0.74/1.14 ( addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.215.1.1','0.23.2.0',theory(equality)]),
% 0.74/1.14 [pos('R.1.2','L')]).
% 0.74/1.14 cnf('0.215.2.0',plain,
% 0.74/1.14 ( addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))) ),
% 0.74/1.14 inference(orient,[status(thm)],['0.215.1.2',theory(equality)]),
% 0.74/1.14 [u,rule_214]).
% 0.74/1.14 cnf('0.225.0.0',plain,
% 0.74/1.14 ( antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) = addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0)))) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.215.2.0','0.202.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1.1','L')]).
% 0.74/1.14 cnf('0.225.0.1',plain,
% 0.74/1.14 ( antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) = addition(one,antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0)))) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.225.0.0','0.43.2.0',theory(equality)]),
% 0.74/1.14 [pos('R.1','L')]).
% 0.74/1.14 cnf('0.225.0.2',plain,
% 0.74/1.14 ( antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) = one ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.225.0.1','0.57.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.225.1.0',plain,
% 0.74/1.14 ( antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) = one ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.225.0.2']),
% 0.74/1.14 [weight('<55,215,202,[1,0,0,2]>')]).
% 0.74/1.14 cnf('0.225.2.0',plain,
% 0.74/1.14 ( antidomain(multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) = one ),
% 0.74/1.14 inference(orient,[status(thm)],['0.225.1.0',theory(equality)]),
% 0.74/1.14 [u,rule_224]).
% 0.74/1.14 cnf('0.226.0.0',plain,
% 0.74/1.14 ( zero = multiplication(one,multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0))) ),
% 0.74/1.14 inference(cp,[status(thm)],['0.13.2.0','0.225.2.0',theory(equality)]),
% 0.74/1.14 [pos('L.1','L')]).
% 0.74/1.14 cnf('0.226.0.1',plain,
% 0.74/1.14 ( zero = multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0)) ),
% 0.74/1.14 inference(reduction,[status(thm)],['0.226.0.0','0.2.2.0',theory(equality)]),
% 0.74/1.14 [pos('R','L')]).
% 0.74/1.14 cnf('0.226.1.0',plain,
% 0.74/1.14 ( zero = multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0)) ),
% 0.74/1.14 inference(weigh,[status(thm)],['0.226.0.1']),
% 0.74/1.14 [weight('<41,225,13,[0,0,0,1]>')]).
% 0.74/1.14 cnf('0.226.2.0',plain,
% 0.74/1.14 ( multiplication(antidomain(sK1_goals_X1),domain(sK2_goals_X0)) = zero ),
% 0.74/1.14 inference(orient,[status(thm)],['0.226.1.0',theory(equality)]),
% 0.74/1.14 [x,rule_225]).
% 0.74/1.14 cnf('0.619.0.0',plain,
% 0.74/1.14 ( multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)) ),
% 0.74/1.15 inference(cp,[status(thm)],['0.12.2.0','0.2.2.0',theory(equality)]),
% 0.74/1.15 [pos('L.1','L')]).
% 0.74/1.15 cnf('0.619.1.0',plain,
% 0.74/1.15 ( multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)) ),
% 0.74/1.15 inference(weigh,[status(thm)],['0.619.0.0']),
% 0.74/1.15 [weight('<?,12,2,[1,0,0,1]>')]).
% 0.74/1.15 cnf('0.619.2.0',plain,
% 0.74/1.15 ( multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)) ),
% 0.74/1.15 inference(activate,[status(thm)],['0.619.1.0']),
% 0.74/1.15 [equation_4]).
% 0.74/1.15 cnf('0.623.0.0',plain,
% 0.74/1.15 ( addition(X1,multiplication(antidomain(X2),X1)) = multiplication(one,X1) ),
% 0.74/1.15 inference(cp,[status(thm)],['0.619.2.0','0.57.2.0',theory(equality)]),
% 0.74/1.15 [pos('L.1','L')]).
% 0.74/1.15 cnf('0.623.0.1',plain,
% 0.74/1.15 ( addition(X1,multiplication(antidomain(X2),X1)) = X1 ),
% 0.74/1.15 inference(reduction,[status(thm)],['0.623.0.0','0.2.2.0',theory(equality)]),
% 0.74/1.15 [pos('R','L')]).
% 0.74/1.15 cnf('0.623.1.0',plain,
% 0.74/1.15 ( addition(X1,multiplication(antidomain(X2),X1)) = X1 ),
% 0.74/1.15 inference(weigh,[status(thm)],['0.623.0.1']),
% 0.74/1.15 [weight('<55,619,57,[1,0,0,1]>')]).
% 0.74/1.15 cnf('0.623.2.0',plain,
% 0.74/1.15 ( addition(X1,multiplication(antidomain(X2),X1)) = X1 ),
% 0.74/1.15 inference(orient,[status(thm)],['0.623.1.0',theory(equality)]),
% 0.74/1.15 [u,rule_619]).
% 0.74/1.15 cnf('0.844.0.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),addition(domain(sK2_goals_X0),X1)) = addition(zero,multiplication(antidomain(sK1_goals_X1),X1)) ),
% 0.74/1.15 inference(cp,[status(thm)],['0.9.2.0','0.226.2.0',theory(equality)]),
% 0.74/1.15 [pos('L.1','L')]).
% 0.74/1.15 cnf('0.844.0.1',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),addition(domain(sK2_goals_X0),X1)) = multiplication(antidomain(sK1_goals_X1),X1) ),
% 0.74/1.15 inference(reduction,[status(thm)],['0.844.0.0','0.29.2.0',theory(equality)]),
% 0.74/1.15 [pos('R','L')]).
% 0.74/1.15 cnf('0.844.1.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),addition(domain(sK2_goals_X0),X1)) = multiplication(antidomain(sK1_goals_X1),X1) ),
% 0.74/1.15 inference(weigh,[status(thm)],['0.844.0.1']),
% 0.74/1.15 [weight('<95,226,9,[0,0,0,1]>')]).
% 0.74/1.15 cnf('0.844.2.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),addition(domain(sK2_goals_X0),X1)) = multiplication(antidomain(sK1_goals_X1),X1) ),
% 0.74/1.15 inference(orient,[status(thm)],['0.844.1.0',theory(equality)]),
% 0.74/1.15 [u,rule_839]).
% 0.74/1.15 cnf('0.845.0.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = multiplication(antidomain(sK1_goals_X1),one) ),
% 0.74/1.15 inference(cp,[status(thm)],['0.844.2.0','0.41.2.0',theory(equality)]),
% 0.74/1.15 [pos('L.2','L')]).
% 0.74/1.15 cnf('0.845.0.1',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1) ),
% 0.74/1.15 inference(reduction,[status(thm)],['0.845.0.0','0.1.2.0',theory(equality)]),
% 0.74/1.15 [pos('R','L')]).
% 0.74/1.15 cnf('0.845.1.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1) ),
% 0.74/1.15 inference(weigh,[status(thm)],['0.845.0.1']),
% 0.74/1.15 [weight('<47,844,41,[1,0,0,3]>')]).
% 0.74/1.15 cnf('0.845.2.0',plain,
% 0.74/1.15 ( multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1) ),
% 0.74/1.15 inference(orient,[status(thm)],['0.845.1.0',theory(equality)]),
% 0.74/1.15 [u,rule_840]).
% 0.74/1.15 cnf('1.0.0.0',conjecture,
% 0.74/1.15 ( addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0) ),
% 0.74/1.15 file('/tmp/WALDMEISTER_6917_n006',conjecture_1)).
% 0.74/1.15 cnf('1.0.0.1',plain,
% 0.74/1.15 ( addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = antidomain(sK2_goals_X0) ),
% 0.74/1.15 inference(reduction,[status(thm)],['1.0.0.0','0.15.2.0',theory(equality)]),
% 0.74/1.15 [pos('L','L')]).
% 0.74/1.15 cnf('1.0.0.2',plain,
% 0.74/1.15 ( addition(antidomain(sK2_goals_X0),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))) = antidomain(sK2_goals_X0) ),
% 0.74/1.15 inference(reduction,[status(thm)],['1.0.0.1','0.845.2.0',theory(equality)]),
% 0.74/1.15 [pos('L.2','R')]).
% 0.74/1.15 cnf('1.0.0.3',plain,
% 0.74/1.15 ( antidomain(sK2_goals_X0) = antidomain(sK2_goals_X0) ),
% 0.74/1.15 inference(reduction,[status(thm)],['1.0.0.2','0.623.2.0',theory(equality)]),
% 0.74/1.15 [pos('L','L')]).
% 0.74/1.15 cnf('1.0.0.4',plain,
% 0.74/1.15 ( $true ),
% 0.74/1.15 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 0.74/1.15 [conjecture_1]).
% 0.74/1.15
% 0.74/1.15 Proved Goals:
% 0.74/1.15 No. 1: addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) ?= antidomain(sK2_goals_X0) joined, current: antidomain(sK2_goals_X0) = antidomain(sK2_goals_X0)
% 0.74/1.15 1 goal was specified, which was proved.
% 0.74/1.15 % SZS output end CNFRefutation
% 0.74/1.15 #END OF PROOF
% 0.74/1.15
% 0.74/1.15 Problem WALDMEISTER_6917_n006
% 0.74/1.15 CPs.gen 45591
% 0.74/1.15 CPs.reexp 0
% 0.74/1.15 Select 2660
% 0.74/1.15 R 840
% 0.74/1.15 E 5
% 0.74/1.15 vsize 7.0M
% 0.74/1.15 rss 4.2M
% 0.74/1.15 process.time 0.151s
% 0.74/1.15 wallclock.time 0.151s
% 0.74/1.15 status S
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Waldmeister states: Goal proved.
% 0.74/1.15 % SZS status Unsatisfiable
%------------------------------------------------------------------------------