TSTP Solution File: COL004-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.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 00:47:28 EDT 2022
% Result : Unsatisfiable 0.63s 1.02s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : woody %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 04:20:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.60/0.98 ********************************************************************************
% 0.60/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/0.98 * |/ | \/ | *
% 0.60/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/0.98 * A. Jaeger and B. Loechner | | *
% 0.60/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/0.98 ********************************************************************************
% 0.60/0.98
% 0.60/0.98
% 0.60/0.98 Goals:
% 0.60/0.98 ------
% 0.60/0.98
% 0.60/0.98 ( 1) true ?= false
% 0.60/0.98 using narrowing to prove apply(apply(x1,f(x1)),g(x1)) ?= apply(g(x1),apply(apply(f(x1),f(x1)),g(x1)))
% 0.60/0.98
% 0.60/0.98 Detected structure: KombinatorlogikS
% 0.60/0.98 ********************************************************************************
% 0.60/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.60/0.98 ********************************************************************************
% 0.60/0.98
% 0.63/1.02 joined goal: 1 apply(apply(x1,f(x1)),g(x1)) ?= apply(g(x1),apply(apply(f(x1),f(x1)),g(x1))) to false
% 0.63/1.02 goal joined
% 0.63/1.02 % SZS status Unsatisfiable
% 0.63/1.02 #START OF PROOF
% 0.63/1.02 % SZS output start CNFRefutation
% 0.63/1.02 cnf('0.1.0.0',axiom,
% 0.63/1.02 ( X1 = apply(apply(k,X1),X2) ),
% 0.63/1.02 file('/tmp/WALDMEISTER_13254_n019')).
% 0.63/1.02 cnf('0.1.1.0',plain,
% 0.63/1.02 ( X1 = apply(apply(k,X1),X2) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.63/1.02 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.63/1.02 cnf('0.1.2.0',plain,
% 0.63/1.02 ( apply(apply(k,X1),X2) = X1 ),
% 0.63/1.02 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.63/1.02 [x,rule_1]).
% 0.63/1.02 cnf('0.2.0.0',axiom,
% 0.63/1.02 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.63/1.02 file('/tmp/WALDMEISTER_13254_n019')).
% 0.63/1.02 cnf('0.2.1.0',plain,
% 0.63/1.02 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.63/1.02 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.63/1.02 cnf('0.2.2.0',plain,
% 0.63/1.02 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.63/1.02 inference(activate,[status(thm)],['0.2.1.0']),
% 0.63/1.02 [equation_1]).
% 0.63/1.02 cnf('0.3.0.0',axiom,
% 0.63/1.02 ( eq(X1,X1) = true ),
% 0.63/1.02 file('/tmp/WALDMEISTER_13254_n019')).
% 0.63/1.02 cnf('0.3.1.0',plain,
% 0.63/1.02 ( eq(X1,X1) = true ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.63/1.02 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.63/1.02 cnf('0.3.2.0',plain,
% 0.63/1.02 ( eq(X1,X1) = true ),
% 0.63/1.02 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.63/1.02 [u,rule_2]).
% 0.63/1.02 cnf('0.4.0.0',axiom,
% 0.63/1.02 ( eq(apply(apply(X1,f(X1)),g(X1)),apply(g(X1),apply(apply(f(X1),f(X1)),g(X1)))) = false ),
% 0.63/1.02 file('/tmp/WALDMEISTER_13254_n019')).
% 0.63/1.02 cnf('0.4.1.0',plain,
% 0.63/1.02 ( eq(apply(apply(X1,f(X1)),g(X1)),apply(g(X1),apply(apply(f(X1),f(X1)),g(X1)))) = false ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.63/1.02 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.63/1.02 cnf('0.4.2.0',plain,
% 0.63/1.02 ( eq(apply(apply(X1,f(X1)),g(X1)),apply(g(X1),apply(apply(f(X1),f(X1)),g(X1)))) = false ),
% 0.63/1.02 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.63/1.02 [u,rule_3]).
% 0.63/1.02 cnf('0.6.0.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,k),X1),X2) = X2 ),
% 0.63/1.02 inference(cp,[status(thm)],['0.2.2.0','0.1.2.0',theory(equality)]),
% 0.63/1.02 [pos('L','L')]).
% 0.63/1.02 cnf('0.6.1.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,k),X1),X2) = X2 ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.63/1.02 [weight('<8,2,1,[1,0,0,0]>')]).
% 0.63/1.02 cnf('0.6.2.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,k),X1),X2) = X2 ),
% 0.63/1.02 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.63/1.02 [u,rule_5]).
% 0.63/1.02 cnf('0.10.0.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.2.2.0','0.1.2.0',theory(equality)]),
% 0.63/1.02 [pos('L.1','L')]).
% 0.63/1.02 cnf('0.10.1.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.63/1.02 [weight('<14,2,1,[1,0,0,1]>')]).
% 0.63/1.02 cnf('0.10.2.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.63/1.02 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.63/1.02 [u,rule_9]).
% 0.63/1.02 cnf('0.13.0.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.2.2.0','0.6.2.0',theory(equality)]),
% 0.63/1.02 [pos('L.1','L')]).
% 0.63/1.02 cnf('0.13.1.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.63/1.02 [weight('<16,6,2,[0,0,0,1]>')]).
% 0.63/1.02 cnf('0.13.2.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)) ),
% 0.63/1.02 inference(activate,[status(thm)],['0.13.1.0']),
% 0.63/1.02 [equation_3]).
% 0.63/1.02 cnf('0.13.2.2',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),false)),X2),X1) = apply(X1,apply(X2,X1)) ),
% 0.63/1.02 inference(instl,[status(thm)],['0.13.2.0',theory(equality)])).
% 0.63/1.02 cnf('0.14.0.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,f(X1)),g(X1)),apply(apply(apply(s,apply(apply(s,k),X2)),apply(f(X1),f(X1))),g(X1))) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.4.2.0','0.13.2.0',theory(equality)]),
% 0.63/1.02 [pos('L.2','R')]).
% 0.63/1.02 cnf('0.14.1.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,f(X1)),g(X1)),apply(apply(apply(s,apply(apply(s,k),X2)),apply(f(X1),f(X1))),g(X1))) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.63/1.02 [weight('<92,13,4,[0,1,0,8]>')]).
% 0.63/1.02 cnf('0.14.2.0',plain,
% 0.63/1.02 ( eq(apply(apply(X1,f(X1)),g(X1)),apply(apply(apply(s,apply(apply(s,k),X2)),apply(f(X1),f(X1))),g(X1))) = false ),
% 0.63/1.02 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.63/1.02 [x,rule_11]).
% 0.63/1.02 cnf('0.20.0.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(f(apply(apply(s,apply(k,X1)),X2)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.14.2.0','0.10.2.0',theory(equality)]),
% 0.63/1.02 [pos('L.1.1','L')]).
% 0.63/1.02 cnf('0.20.1.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(f(apply(apply(s,apply(k,X1)),X2)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.63/1.02 [weight('<550,14,10,[1,0,0,2]>')]).
% 0.63/1.02 cnf('0.20.2.0',plain,
% 0.63/1.02 ( eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(f(apply(apply(s,apply(k,X1)),X2)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) = false ),
% 0.63/1.02 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.63/1.02 [x,rule_16]).
% 0.63/1.02 cnf('0.72.0.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),apply(apply(s,k),X2)),X3) = apply(X3,X3) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.13.2.0','0.6.2.0',theory(equality)]),
% 0.63/1.02 [pos('R.2','L')]).
% 0.63/1.02 cnf('0.72.1.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),apply(apply(s,k),X2)),X3) = apply(X3,X3) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.72.0.0']),
% 0.63/1.02 [weight('<18,13,6,[1,1,0,2]>')]).
% 0.63/1.02 cnf('0.72.2.0',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),X1)),apply(apply(s,k),X2)),X3) = apply(X3,X3) ),
% 0.63/1.02 inference(activate,[status(thm)],['0.72.1.0']),
% 0.63/1.02 [equation_11]).
% 0.63/1.02 cnf('0.72.2.2',plain,
% 0.63/1.02 ( apply(apply(apply(s,apply(apply(s,k),false)),apply(apply(s,k),false)),X1) = apply(X1,X1) ),
% 0.63/1.02 inference(instl,[status(thm)],['0.72.2.0',theory(equality)])).
% 0.63/1.02 cnf('0.73.0.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(apply(s,k),X4)),apply(apply(s,k),X5)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) ),
% 0.63/1.02 inference(cp,[status(thm)],['0.20.2.0','0.72.2.0',theory(equality)]),
% 0.63/1.02 [pos('L.2.1.2','R')]).
% 0.63/1.02 cnf('0.73.1.0',plain,
% 0.63/1.02 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(apply(s,k),X4)),apply(apply(s,k),X5)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.73.0.0']),
% 0.63/1.02 [weight('<0,72,20,[0,1,0,31]>')]).
% 0.63/1.02 cnf('0.73.2.0',plain,
% 0.63/1.02 ( eq(apply(apply(X1,apply(X2,f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2))),apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(apply(s,k),X4)),apply(apply(s,k),X5)),f(apply(apply(s,apply(k,X1)),X2)))),g(apply(apply(s,apply(k,X1)),X2)))) = false ),
% 0.63/1.02 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 0.63/1.02 [x,rule_62]).
% 0.63/1.02 cnf('0.74.0.0',plain,
% 0.63/1.02 ( false = true ),
% 0.63/1.02 inference(cp,[status(thm)],['0.73.2.0','0.3.2.0',theory(equality)]),
% 0.63/1.02 [pos('L','L')]).
% 0.63/1.02 cnf('0.74.1.0',plain,
% 0.63/1.02 ( false = true ),
% 0.63/1.02 inference(weigh,[status(thm)],['0.74.0.0']),
% 0.63/1.02 [weight('<2,73,3,[1,0,0,0]>')]).
% 0.63/1.02 cnf('0.74.2.0',plain,
% 0.63/1.02 ( true = false ),
% 0.63/1.02 inference(orient,[status(thm)],['0.74.1.0',theory(equality)]),
% 0.63/1.02 [x,rule_63]).
% 0.63/1.02 cnf('1.0.0.0',conjecture,
% 0.63/1.02 ( true = false ),
% 0.63/1.02 file('/tmp/WALDMEISTER_13254_n019',conjecture_1)).
% 0.63/1.02 cnf('1.0.0.1',plain,
% 0.63/1.02 ( false = false ),
% 0.63/1.02 inference(reduction,[status(thm)],['1.0.0.0','0.74.2.0',theory(equality)]),
% 0.63/1.02 [pos('L','L')]).
% 0.63/1.02 cnf('1.0.0.2',plain,
% 0.63/1.02 ( $true ),
% 0.63/1.02 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.63/1.02 [conjecture_1]).
% 0.63/1.02
% 0.63/1.02 Proved Goals:
% 0.63/1.02 No. 1: true ?= false, current false ?= false
% 0.63/1.02 using narrowing to prove apply(apply(x1,f(x1)),g(x1)) ?= apply(g(x1),apply(apply(f(x1),f(x1)),g(x1)))
% 0.63/1.02
% 0.63/1.02 1 goal was specified, which was proved.
% 0.63/1.02 % SZS output end CNFRefutation
% 0.63/1.02 #END OF PROOF
% 0.63/1.02
% 0.63/1.02 Problem WALDMEISTER_13254_n019
% 0.63/1.02 CPs.gen 2087
% 0.63/1.02 CPs.reexp 0
% 0.63/1.02 Select 354
% 0.63/1.02 R 63
% 0.63/1.02 E 11
% 0.63/1.02 vsize 6.5M
% 0.63/1.02 rss 3.7M
% 0.63/1.02 process.time 0.035s
% 0.63/1.02 wallclock.time 0.038s
% 0.63/1.02 status S
% 0.63/1.02
% 0.63/1.02
% 0.63/1.02 Waldmeister states: Goal proved.
% 0.63/1.02 % SZS status Unsatisfiable
% 0.63/1.02
% 0.63/1.02 Problem WALDMEISTER_13254_n019
% 0.63/1.02 CPs.gen 330
% 0.63/1.02 CPs.reexp 0
% 0.63/1.02 Select 30
% 0.63/1.02 R 27
% 0.63/1.02 E 2
% 0.63/1.02 vsize 6.5M
% 0.63/1.02 rss 3.7M
% 0.63/1.02 process.time 0.004s
% 0.63/1.02 wallclock.time 0.037s
% 0.63/1.02 status S
%------------------------------------------------------------------------------