TSTP Solution File: COL064-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL064-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n029.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 00:47:39 EDT 2022
% Result : Unsatisfiable 0.72s 1.10s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL064-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : woody %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 16:32:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.98 * |/ | \/ | *
% 0.59/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.98 * A. Jaeger and B. Loechner | | *
% 0.59/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.59/0.98
% 0.59/0.98 Goals:
% 0.59/0.98 ------
% 0.59/0.98
% 0.59/0.98 ( 1) true ?= false
% 0.59/0.98 using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(h(x1),f(x1)),g(x1))
% 0.59/0.98
% 0.59/0.98 Detected structure: KombinatorlogikBT
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.72/1.10 joined goal: 1 apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(h(x1),f(x1)),g(x1)) to false
% 0.72/1.10 goal joined
% 0.72/1.10 % SZS status Unsatisfiable
% 0.72/1.10 #START OF PROOF
% 0.72/1.10 % SZS output start CNFRefutation
% 0.72/1.10 cnf('0.1.0.0',axiom,
% 0.72/1.10 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.72/1.10 file('/tmp/WALDMEISTER_9729_n029')).
% 0.72/1.10 cnf('0.1.1.0',plain,
% 0.72/1.10 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.72/1.10 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.72/1.10 cnf('0.1.2.0',plain,
% 0.72/1.10 ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.72/1.10 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_1]).
% 0.72/1.10 cnf('0.2.0.0',axiom,
% 0.72/1.10 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.72/1.10 file('/tmp/WALDMEISTER_9729_n029')).
% 0.72/1.10 cnf('0.2.1.0',plain,
% 0.72/1.10 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.72/1.10 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.72/1.10 cnf('0.2.2.0',plain,
% 0.72/1.10 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.72/1.10 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_2]).
% 0.72/1.10 cnf('0.3.0.0',axiom,
% 0.72/1.10 ( eq(X1,X1) = true ),
% 0.72/1.10 file('/tmp/WALDMEISTER_9729_n029')).
% 0.72/1.10 cnf('0.3.1.0',plain,
% 0.72/1.10 ( eq(X1,X1) = true ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.72/1.10 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.72/1.10 cnf('0.3.2.0',plain,
% 0.72/1.10 ( eq(X1,X1) = true ),
% 0.72/1.10 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.72/1.10 [u,rule_3]).
% 0.72/1.10 cnf('0.4.0.0',axiom,
% 0.72/1.10 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(h(X1),f(X1)),g(X1))) = false ),
% 0.72/1.10 file('/tmp/WALDMEISTER_9729_n029')).
% 0.72/1.10 cnf('0.4.1.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(h(X1),f(X1)),g(X1))) = false ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.72/1.10 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.72/1.10 cnf('0.4.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(h(X1),f(X1)),g(X1))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.72/1.10 [u,rule_4]).
% 0.72/1.10 cnf('0.9.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(apply(h(apply(apply(b,X1),X2)),f(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1.1','L')]).
% 0.72/1.10 cnf('0.9.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(apply(h(apply(apply(b,X1),X2)),f(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.72/1.10 [weight('<44,4,2,[1,0,0,3]>')]).
% 0.72/1.10 cnf('0.9.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(apply(h(apply(apply(b,X1),X2)),f(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_9]).
% 0.72/1.10 cnf('0.17.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(apply(h(apply(apply(b,apply(t,X2)),X1)),f(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1.1','L')]).
% 0.72/1.10 cnf('0.17.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(apply(h(apply(apply(b,apply(t,X2)),X1)),f(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.72/1.10 [weight('<56,9,1,[1,0,0,3]>')]).
% 0.72/1.10 cnf('0.17.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(apply(h(apply(apply(b,apply(t,X2)),X1)),f(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_17]).
% 0.72/1.10 cnf('0.55.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.17.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1.1.1','L')]).
% 0.72/1.10 cnf('0.55.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.55.0.0']),
% 0.72/1.10 [weight('<82,17,2,[1,0,0,4]>')]).
% 0.72/1.10 cnf('0.55.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_55]).
% 0.72/1.10 cnf('0.56.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.55.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1','L')]).
% 0.72/1.10 cnf('0.56.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.72/1.10 [weight('<80,55,2,[1,0,0,2]>')]).
% 0.72/1.10 cnf('0.56.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_56]).
% 0.72/1.10 cnf('0.139.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),apply(X3,g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.56.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1.1','L')]).
% 0.72/1.10 cnf('0.139.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),apply(X3,g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.139.0.0']),
% 0.72/1.10 [weight('<106,56,2,[1,0,0,3]>')]).
% 0.72/1.10 cnf('0.139.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),apply(X3,g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))),h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),apply(apply(h(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2))))),g(apply(apply(b,apply(t,X3)),apply(apply(b,b),apply(apply(b,X1),X2)))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_139]).
% 0.72/1.10 cnf('0.142.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.139.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1','L')]).
% 0.72/1.10 cnf('0.142.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.142.0.0']),
% 0.72/1.10 [weight('<104,139,2,[1,0,0,1]>')]).
% 0.72/1.10 cnf('0.142.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),apply(apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))),apply(apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))),f(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1))))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),apply(apply(b,b),X1)))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_142]).
% 0.72/1.10 cnf('0.143.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.142.2.0','0.1.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1','L')]).
% 0.72/1.10 cnf('0.143.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.143.0.0']),
% 0.72/1.10 [weight('<102,142,1,[1,0,0,1]>')]).
% 0.72/1.10 cnf('0.143.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),apply(apply(b,b),t)))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.143.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_143]).
% 0.72/1.10 cnf('0.290.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.143.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1.1.1','L')]).
% 0.72/1.10 cnf('0.290.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.290.0.0']),
% 0.72/1.10 [weight('<128,143,2,[1,0,0,3]>')]).
% 0.72/1.10 cnf('0.290.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),apply(apply(b,b),t)))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.290.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_290]).
% 0.72/1.10 cnf('0.292.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.290.2.0','0.2.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1','L')]).
% 0.72/1.10 cnf('0.292.1.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.292.0.0']),
% 0.72/1.10 [weight('<126,290,2,[1,0,0,1]>')]).
% 0.72/1.10 cnf('0.292.2.0',plain,
% 0.72/1.10 ( eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),apply(apply(b,b),t)))))) = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.292.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_292]).
% 0.72/1.10 cnf('0.293.0.0',plain,
% 0.72/1.10 ( false = eq(apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t)))))) ),
% 0.72/1.10 inference(cp,[status(thm)],['0.292.2.0','0.1.2.0',theory(equality)]),
% 0.72/1.10 [pos('L.1','L')]).
% 0.72/1.10 cnf('0.293.0.1',plain,
% 0.72/1.10 ( false = true ),
% 0.72/1.10 inference(reduction,[status(thm)],['0.293.0.0','0.3.2.0',theory(equality)]),
% 0.72/1.10 [pos('R','L')]).
% 0.72/1.10 cnf('0.293.1.0',plain,
% 0.72/1.10 ( false = true ),
% 0.72/1.10 inference(weigh,[status(thm)],['0.293.0.1']),
% 0.72/1.10 [weight('<5,292,1,[1,0,0,1]>')]).
% 0.72/1.10 cnf('0.293.2.0',plain,
% 0.72/1.10 ( true = false ),
% 0.72/1.10 inference(orient,[status(thm)],['0.293.1.0',theory(equality)]),
% 0.72/1.10 [x,rule_293]).
% 0.72/1.10 cnf('1.0.0.0',conjecture,
% 0.72/1.10 ( true = false ),
% 0.72/1.10 file('/tmp/WALDMEISTER_9729_n029',conjecture_1)).
% 0.72/1.10 cnf('1.0.0.1',plain,
% 0.72/1.10 ( false = false ),
% 0.72/1.10 inference(reduction,[status(thm)],['1.0.0.0','0.293.2.0',theory(equality)]),
% 0.72/1.10 [pos('L','L')]).
% 0.72/1.10 cnf('1.0.0.2',plain,
% 0.72/1.10 ( $true ),
% 0.72/1.10 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.72/1.10 [conjecture_1]).
% 0.72/1.10
% 0.72/1.10 Proved Goals:
% 0.72/1.10 No. 1: true ?= false, current false ?= false
% 0.72/1.10 using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(h(x1),f(x1)),g(x1))
% 0.72/1.10
% 0.72/1.10 1 goal was specified, which was proved.
% 0.72/1.10 % SZS output end CNFRefutation
% 0.72/1.10 #END OF PROOF
% 0.72/1.10
% 0.72/1.10 Problem WALDMEISTER_9729_n029
% 0.72/1.10 CPs.gen 657
% 0.72/1.10 CPs.reexp 0
% 0.72/1.10 Select 425
% 0.72/1.10 R 293
% 0.72/1.10 E 0
% 0.72/1.10 vsize 6.6M
% 0.72/1.10 rss 3.8M
% 0.72/1.10 process.time 0.118s
% 0.72/1.10 wallclock.time 0.118s
% 0.72/1.10 status S
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Waldmeister states: Goal proved.
% 0.72/1.10 % SZS status Unsatisfiable
%------------------------------------------------------------------------------