TSTP Solution File: CAT010-10 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %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 : 600s
% DateTime : Fri Jul 15 00:10:48 EDT 2022
% Result : Unsatisfiable 0.87s 1.26s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n026.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 : Sun May 29 22:31:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.64/1.03 ********************************************************************************
% 0.64/1.03 * W A L D M E I S T E R \| \ / \|/ *
% 0.64/1.03 * |/ | \/ | *
% 0.64/1.03 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.64/1.03 * A. Jaeger and B. Loechner | | *
% 0.64/1.03 * <waldmeister@informatik.uni-kl.de> | *
% 0.64/1.03 ********************************************************************************
% 0.64/1.03
% 0.64/1.03
% 0.64/1.03 Goals:
% 0.64/1.03 ------
% 0.64/1.03
% 0.64/1.03 ( 1) codomain(compose(a,b)) ?=? codomain(a)
% 0.64/1.03
% 0.64/1.03 Detected structure: Orkus
% 0.64/1.03 ********************************************************************************
% 0.64/1.03 ****************************** COMPLETION - PROOF ******************************
% 0.64/1.03 ********************************************************************************
% 0.64/1.03
% 0.87/1.26 joined goal: 1 codomain(compose(a,b)) ?= codomain(a) to codomain(a)
% 0.87/1.26 goal joined
% 0.87/1.26 % SZS status Unsatisfiable
% 0.87/1.26 #START OF PROOF
% 0.87/1.26 % SZS output start CNFRefutation
% 0.87/1.26 cnf('0.2.0.0',axiom,
% 0.87/1.26 ( X1 = compose(codomain(X1),X1) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.2.1.0',plain,
% 0.87/1.26 ( X1 = compose(codomain(X1),X1) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.87/1.26 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.87/1.26 cnf('0.2.2.0',plain,
% 0.87/1.26 ( compose(codomain(X1),X1) = X1 ),
% 0.87/1.26 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_2]).
% 0.87/1.26 cnf('0.3.0.0',axiom,
% 0.87/1.26 ( X1 = ifeq(X2,X2,X1,X3) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.3.1.0',plain,
% 0.87/1.26 ( X1 = ifeq(X2,X2,X1,X3) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.87/1.26 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.87/1.26 cnf('0.3.2.0',plain,
% 0.87/1.26 ( ifeq(X1,X1,X2,X3) = X2 ),
% 0.87/1.26 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_3]).
% 0.87/1.26 cnf('0.4.0.0',axiom,
% 0.87/1.26 ( X1 = ifeq2(X2,X2,X1,X3) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.4.1.0',plain,
% 0.87/1.26 ( X1 = ifeq2(X2,X2,X1,X3) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.87/1.26 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.87/1.26 cnf('0.4.2.0',plain,
% 0.87/1.26 ( ifeq2(X1,X1,X2,X3) = X2 ),
% 0.87/1.26 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_4]).
% 0.87/1.26 cnf('0.7.0.0',axiom,
% 0.87/1.26 ( true = there_exists(compose(a,b)) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.7.1.0',plain,
% 0.87/1.26 ( true = there_exists(compose(a,b)) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.87/1.26 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.87/1.26 cnf('0.7.2.0',plain,
% 0.87/1.26 ( there_exists(compose(a,b)) = true ),
% 0.87/1.26 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_7]).
% 0.87/1.26 cnf('0.9.0.0',axiom,
% 0.87/1.26 ( true = ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.9.1.0',plain,
% 0.87/1.26 ( true = ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.87/1.26 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.87/1.26 cnf('0.9.2.0',plain,
% 0.87/1.26 ( ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true ),
% 0.87/1.26 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_9]).
% 0.87/1.26 cnf('0.10.0.0',axiom,
% 0.87/1.26 ( true = ifeq(there_exists(domain(X1)),true,there_exists(X1),true) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.10.1.0',plain,
% 0.87/1.26 ( true = ifeq(there_exists(domain(X1)),true,there_exists(X1),true) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.87/1.26 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.87/1.26 cnf('0.10.2.0',plain,
% 0.87/1.26 ( ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true ),
% 0.87/1.26 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_10]).
% 0.87/1.26 cnf('0.14.0.0',axiom,
% 0.87/1.26 ( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.14.1.0',plain,
% 0.87/1.26 ( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.87/1.26 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.87/1.26 cnf('0.14.2.0',plain,
% 0.87/1.26 ( compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_14]).
% 0.87/1.26 cnf('0.15.0.0',axiom,
% 0.87/1.26 ( codomain(X1) = ifeq2(there_exists(compose(X2,X1)),true,domain(X2),codomain(X1)) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026')).
% 0.87/1.26 cnf('0.15.1.0',plain,
% 0.87/1.26 ( codomain(X1) = ifeq2(there_exists(compose(X2,X1)),true,domain(X2),codomain(X1)) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.87/1.26 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.87/1.26 cnf('0.15.2.0',plain,
% 0.87/1.26 ( ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_15]).
% 0.87/1.26 cnf('0.16.0.0',plain,
% 0.87/1.26 ( codomain(b) = ifeq2(true,true,domain(a),codomain(b)) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.15.2.0','0.7.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1','L')]).
% 0.87/1.26 cnf('0.16.0.1',plain,
% 0.87/1.26 ( codomain(b) = domain(a) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.16.0.0','0.4.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.16.1.0',plain,
% 0.87/1.26 ( codomain(b) = domain(a) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.16.0.1']),
% 0.87/1.26 [weight('<14,15,7,[1,0,0,1]>')]).
% 0.87/1.26 cnf('0.16.2.0',plain,
% 0.87/1.26 ( domain(a) = codomain(b) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_16]).
% 0.87/1.26 cnf('0.17.0.0',plain,
% 0.87/1.26 ( true = ifeq(true,true,there_exists(domain(a)),true) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.9.2.0','0.7.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1','L')]).
% 0.87/1.26 cnf('0.17.0.1',plain,
% 0.87/1.26 ( true = there_exists(domain(a)) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.17.0.0','0.3.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.17.1.0',plain,
% 0.87/1.26 ( true = there_exists(domain(a)) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.17.0.1']),
% 0.87/1.26 [weight('<19,9,7,[1,0,0,1]>')]).
% 0.87/1.26 cnf('0.17.1.1',plain,
% 0.87/1.26 ( true = there_exists(codomain(b)) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.17.1.0','0.16.2.0',theory(equality)]),
% 0.87/1.26 [pos('R.1','L')]).
% 0.87/1.26 cnf('0.17.2.0',plain,
% 0.87/1.26 ( there_exists(codomain(b)) = true ),
% 0.87/1.26 inference(orient,[status(thm)],['0.17.1.1',theory(equality)]),
% 0.87/1.26 [x,rule_17]).
% 0.87/1.26 cnf('0.28.0.0',plain,
% 0.87/1.26 ( compose(codomain(X1),compose(X1,X2)) = compose(X1,X2) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.14.2.0','0.2.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1','L')]).
% 0.87/1.26 cnf('0.28.1.0',plain,
% 0.87/1.26 ( compose(codomain(X1),compose(X1,X2)) = compose(X1,X2) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.87/1.26 [weight('<69,14,2,[1,0,0,1]>')]).
% 0.87/1.26 cnf('0.28.2.0',plain,
% 0.87/1.26 ( compose(codomain(X1),compose(X1,X2)) = compose(X1,X2) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.87/1.26 [u,rule_28]).
% 0.87/1.26 cnf('0.57.0.0',plain,
% 0.87/1.26 ( true = ifeq(there_exists(codomain(b)),true,there_exists(a),true) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.10.2.0','0.16.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1.1','L')]).
% 0.87/1.26 cnf('0.57.1.0',plain,
% 0.87/1.26 ( true = ifeq(there_exists(codomain(b)),true,there_exists(a),true) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.87/1.26 [weight('<89,16,10,[0,0,0,2]>')]).
% 0.87/1.26 cnf('0.57.1.1',plain,
% 0.87/1.26 ( true = ifeq(true,true,there_exists(a),true) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.57.1.0','0.17.2.0',theory(equality)]),
% 0.87/1.26 [pos('R.1','L')]).
% 0.87/1.26 cnf('0.57.1.2',plain,
% 0.87/1.26 ( true = there_exists(a) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.57.1.1','0.3.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.57.2.0',plain,
% 0.87/1.26 ( there_exists(a) = true ),
% 0.87/1.26 inference(orient,[status(thm)],['0.57.1.2',theory(equality)]),
% 0.87/1.26 [x,rule_57]).
% 0.87/1.26 cnf('0.356.0.0',plain,
% 0.87/1.26 ( codomain(X1) = ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.15.2.0','0.2.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1.1','L')]).
% 0.87/1.26 cnf('0.356.1.0',plain,
% 0.87/1.26 ( codomain(X1) = ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.356.0.0']),
% 0.87/1.26 [weight('<119,15,2,[1,0,0,2]>')]).
% 0.87/1.26 cnf('0.356.2.0',plain,
% 0.87/1.26 ( ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) = codomain(X1) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.356.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_356]).
% 0.87/1.26 cnf('0.357.0.0',plain,
% 0.87/1.26 ( codomain(a) = ifeq2(true,true,domain(codomain(a)),codomain(a)) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.356.2.0','0.57.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1','L')]).
% 0.87/1.26 cnf('0.357.0.1',plain,
% 0.87/1.26 ( codomain(a) = domain(codomain(a)) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.357.0.0','0.4.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.357.1.0',plain,
% 0.87/1.26 ( codomain(a) = domain(codomain(a)) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.357.0.1']),
% 0.87/1.26 [weight('<23,356,57,[1,0,0,1]>')]).
% 0.87/1.26 cnf('0.357.2.0',plain,
% 0.87/1.26 ( domain(codomain(a)) = codomain(a) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.357.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_357]).
% 0.87/1.26 cnf('0.723.0.0',plain,
% 0.87/1.26 ( codomain(compose(X1,X2)) = ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.15.2.0','0.28.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1.1','L')]).
% 0.87/1.26 cnf('0.723.1.0',plain,
% 0.87/1.26 ( codomain(compose(X1,X2)) = ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.723.0.0']),
% 0.87/1.26 [weight('<?,28,15,[0,0,0,2]>')]).
% 0.87/1.26 cnf('0.723.2.0',plain,
% 0.87/1.26 ( ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) = codomain(compose(X1,X2)) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.723.1.0',theory(equality)]),
% 0.87/1.26 [x,rule_723]).
% 0.87/1.26 cnf('0.724.0.0',plain,
% 0.87/1.26 ( codomain(compose(a,b)) = ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))) ),
% 0.87/1.26 inference(cp,[status(thm)],['0.723.2.0','0.7.2.0',theory(equality)]),
% 0.87/1.26 [pos('L.1','L')]).
% 0.87/1.26 cnf('0.724.0.1',plain,
% 0.87/1.26 ( codomain(compose(a,b)) = domain(codomain(a)) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.724.0.0','0.4.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.724.0.2',plain,
% 0.87/1.26 ( codomain(compose(a,b)) = codomain(a) ),
% 0.87/1.26 inference(reduction,[status(thm)],['0.724.0.1','0.357.2.0',theory(equality)]),
% 0.87/1.26 [pos('R','L')]).
% 0.87/1.26 cnf('0.724.1.0',plain,
% 0.87/1.26 ( codomain(compose(a,b)) = codomain(a) ),
% 0.87/1.26 inference(weigh,[status(thm)],['0.724.0.2']),
% 0.87/1.26 [weight('<34,723,7,[1,0,0,1]>')]).
% 0.87/1.26 cnf('0.724.2.0',plain,
% 0.87/1.26 ( codomain(compose(a,b)) = codomain(a) ),
% 0.87/1.26 inference(orient,[status(thm)],['0.724.1.0',theory(equality)]),
% 0.87/1.26 [u,rule_724]).
% 0.87/1.26 cnf('1.0.0.0',conjecture,
% 0.87/1.26 ( codomain(compose(a,b)) = codomain(a) ),
% 0.87/1.26 file('/tmp/WALDMEISTER_3293_n026',conjecture_1)).
% 0.87/1.26 cnf('1.0.0.1',plain,
% 0.87/1.26 ( codomain(a) = codomain(a) ),
% 0.87/1.26 inference(reduction,[status(thm)],['1.0.0.0','0.724.2.0',theory(equality)]),
% 0.87/1.26 [pos('L','L')]).
% 0.87/1.26 cnf('1.0.0.2',plain,
% 0.87/1.26 ( $true ),
% 0.87/1.26 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.87/1.26 [conjecture_1]).
% 0.87/1.26
% 0.87/1.26 Proved Goals:
% 0.87/1.26 No. 1: codomain(compose(a,b)) ?= codomain(a) joined, current: codomain(a) = codomain(a)
% 0.87/1.26 1 goal was specified, which was proved.
% 0.87/1.26 % SZS output end CNFRefutation
% 0.87/1.26 #END OF PROOF
% 0.87/1.26
% 0.87/1.26 Problem WALDMEISTER_3293_n026
% 0.87/1.26 CPs.gen 51025
% 0.87/1.26 CPs.reexp 0
% 0.87/1.26 Select 1170
% 0.87/1.26 R 724
% 0.87/1.26 E 0
% 0.87/1.26 vsize 7.7M
% 0.87/1.26 rss 5.2M
% 0.87/1.26 process.time 0.227s
% 0.87/1.26 wallclock.time 0.227s
% 0.87/1.26 status S
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 Waldmeister states: Goal proved.
% 0.87/1.26 % SZS status Unsatisfiable
%------------------------------------------------------------------------------