TSTP Solution File: COL062-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n023.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 00:47:38 EDT 2022
% Result : Unsatisfiable 0.64s 1.05s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : woody %s
% 0.14/0.34 % Computer : n023.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 13:37:26 EDT 2022
% 0.14/0.34 % 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) true ?= false
% 0.64/1.03 using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(f(x1),h(x1)),g(x1))
% 0.64/1.03
% 0.64/1.03 Detected structure: KombinatorlogikBT
% 0.64/1.03 ********************************************************************************
% 0.64/1.03 ****************************** COMPLETION - PROOF ******************************
% 0.64/1.03 ********************************************************************************
% 0.64/1.03
% 0.64/1.05 joined goal: 1 apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(f(x1),h(x1)),g(x1)) to false
% 0.64/1.05 goal joined
% 0.64/1.05 % SZS status Unsatisfiable
% 0.64/1.05 #START OF PROOF
% 0.64/1.05 % SZS output start CNFRefutation
% 0.64/1.05 cnf('0.1.0.0',axiom,
% 0.64/1.05 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.64/1.05 file('/tmp/WALDMEISTER_22342_n023')).
% 0.64/1.05 cnf('0.1.1.0',plain,
% 0.64/1.05 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.64/1.05 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.64/1.05 cnf('0.1.2.0',plain,
% 0.64/1.05 ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.64/1.05 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_1]).
% 0.64/1.05 cnf('0.2.0.0',axiom,
% 0.64/1.05 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.64/1.05 file('/tmp/WALDMEISTER_22342_n023')).
% 0.64/1.05 cnf('0.2.1.0',plain,
% 0.64/1.05 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.64/1.05 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.64/1.05 cnf('0.2.2.0',plain,
% 0.64/1.05 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.64/1.05 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_2]).
% 0.64/1.05 cnf('0.3.0.0',axiom,
% 0.64/1.05 ( eq(X1,X1) = true ),
% 0.64/1.05 file('/tmp/WALDMEISTER_22342_n023')).
% 0.64/1.05 cnf('0.3.1.0',plain,
% 0.64/1.05 ( eq(X1,X1) = true ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.64/1.05 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.64/1.05 cnf('0.3.2.0',plain,
% 0.64/1.05 ( eq(X1,X1) = true ),
% 0.64/1.05 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.64/1.05 [u,rule_3]).
% 0.64/1.05 cnf('0.4.0.0',axiom,
% 0.64/1.05 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(f(X1),h(X1)),g(X1))) = false ),
% 0.64/1.05 file('/tmp/WALDMEISTER_22342_n023')).
% 0.64/1.05 cnf('0.4.1.0',plain,
% 0.64/1.05 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(f(X1),h(X1)),g(X1))) = false ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.64/1.05 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.64/1.05 cnf('0.4.2.0',plain,
% 0.64/1.05 ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(apply(f(X1),h(X1)),g(X1))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.64/1.05 [u,rule_4]).
% 0.64/1.05 cnf('0.9.0.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1.1','L')]).
% 0.64/1.05 cnf('0.9.1.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.64/1.05 [weight('<44,4,2,[1,0,0,3]>')]).
% 0.64/1.05 cnf('0.9.2.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))),g(apply(apply(b,X1),X2)))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_9]).
% 0.64/1.05 cnf('0.17.0.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1.1','L')]).
% 0.64/1.05 cnf('0.17.1.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.64/1.05 [weight('<56,9,1,[1,0,0,3]>')]).
% 0.64/1.05 cnf('0.17.2.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))),g(apply(apply(b,apply(t,X2)),X1)))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_17]).
% 0.64/1.05 cnf('0.55.0.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.17.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1.1.1','L')]).
% 0.64/1.05 cnf('0.55.1.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.55.0.0']),
% 0.64/1.05 [weight('<82,17,2,[1,0,0,4]>')]).
% 0.64/1.05 cnf('0.55.2.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_55]).
% 0.64/1.05 cnf('0.56.0.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.55.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1','L')]).
% 0.64/1.05 cnf('0.56.1.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.64/1.05 [weight('<80,55,2,[1,0,0,2]>')]).
% 0.64/1.05 cnf('0.56.2.0',plain,
% 0.64/1.05 ( 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(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_56]).
% 0.64/1.05 cnf('0.57.0.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.56.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1','L')]).
% 0.64/1.05 cnf('0.57.1.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.64/1.05 [weight('<78,56,1,[1,0,0,2]>')]).
% 0.64/1.05 cnf('0.57.2.0',plain,
% 0.64/1.05 ( eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_57]).
% 0.64/1.05 cnf('0.110.0.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.57.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1.1.1','L')]).
% 0.64/1.05 cnf('0.110.1.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.110.0.0']),
% 0.64/1.05 [weight('<104,57,2,[1,0,0,3]>')]).
% 0.64/1.05 cnf('0.110.2.0',plain,
% 0.64/1.05 ( eq(apply(apply(apply(X1,apply(X2,g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.110.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_110]).
% 0.64/1.05 cnf('0.111.0.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.110.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1','L')]).
% 0.64/1.05 cnf('0.111.1.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.111.0.0']),
% 0.64/1.05 [weight('<102,110,2,[1,0,0,1]>')]).
% 0.64/1.05 cnf('0.111.2.0',plain,
% 0.64/1.05 ( eq(apply(apply(X1,g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))) = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_111]).
% 0.64/1.05 cnf('0.112.0.0',plain,
% 0.64/1.05 ( false = eq(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) ),
% 0.64/1.05 inference(cp,[status(thm)],['0.111.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.05 [pos('L.1','L')]).
% 0.64/1.05 cnf('0.112.0.1',plain,
% 0.64/1.05 ( false = true ),
% 0.64/1.05 inference(reduction,[status(thm)],['0.112.0.0','0.3.2.0',theory(equality)]),
% 0.64/1.05 [pos('R','L')]).
% 0.64/1.05 cnf('0.112.1.0',plain,
% 0.64/1.05 ( false = true ),
% 0.64/1.05 inference(weigh,[status(thm)],['0.112.0.1']),
% 0.64/1.05 [weight('<5,111,1,[1,0,0,1]>')]).
% 0.64/1.05 cnf('0.112.2.0',plain,
% 0.64/1.05 ( true = false ),
% 0.64/1.05 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 0.64/1.05 [x,rule_112]).
% 0.64/1.05 cnf('1.0.0.0',conjecture,
% 0.64/1.05 ( true = false ),
% 0.64/1.05 file('/tmp/WALDMEISTER_22342_n023',conjecture_1)).
% 0.64/1.05 cnf('1.0.0.1',plain,
% 0.64/1.05 ( false = false ),
% 0.64/1.05 inference(reduction,[status(thm)],['1.0.0.0','0.112.2.0',theory(equality)]),
% 0.64/1.05 [pos('L','L')]).
% 0.64/1.05 cnf('1.0.0.2',plain,
% 0.64/1.05 ( $true ),
% 0.64/1.05 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.64/1.05 [conjecture_1]).
% 0.64/1.05
% 0.64/1.05 Proved Goals:
% 0.64/1.05 No. 1: true ?= false, current false ?= false
% 0.64/1.05 using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(apply(f(x1),h(x1)),g(x1))
% 0.64/1.05
% 0.64/1.05 1 goal was specified, which was proved.
% 0.64/1.05 % SZS output end CNFRefutation
% 0.64/1.05 #END OF PROOF
% 0.64/1.05
% 0.64/1.05 Problem WALDMEISTER_22342_n023
% 0.64/1.05 CPs.gen 232
% 0.64/1.05 CPs.reexp 0
% 0.64/1.05 Select 148
% 0.64/1.05 R 112
% 0.64/1.05 E 0
% 0.64/1.05 vsize 6.4M
% 0.64/1.05 rss 3.8M
% 0.64/1.05 process.time 0.018s
% 0.64/1.05 wallclock.time 0.018s
% 0.64/1.05 status S
% 0.64/1.05
% 0.64/1.05
% 0.64/1.05 Waldmeister states: Goal proved.
% 0.64/1.05 % SZS status Unsatisfiable
%------------------------------------------------------------------------------