TSTP Solution File: COL065-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL065-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n025.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 00:47:40 EDT 2022
% Result : Unsatisfiable 0.92s 1.35s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL065-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n025.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 : Tue May 31 04:23:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.62/1.01 ********************************************************************************
% 0.62/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.01 * |/ | \/ | *
% 0.62/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.01 * A. Jaeger and B. Loechner | | *
% 0.62/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.01 ********************************************************************************
% 0.62/1.01
% 0.62/1.01
% 0.62/1.01 Goals:
% 0.62/1.01 ------
% 0.62/1.01
% 0.62/1.01 ( 1) true ?= false
% 0.62/1.01 using narrowing to prove apply(apply(apply(apply(x1,f(x1)),g(x1)),h(x1)),i(x1)) ?= apply(apply(f(x1),i(x1)),apply(g(x1),h(x1)))
% 0.62/1.01
% 0.62/1.01 Detected structure: KombinatorlogikBT
% 0.62/1.01 ********************************************************************************
% 0.62/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.62/1.01 ********************************************************************************
% 0.62/1.01
% 0.92/1.35 joined goal: 1 apply(apply(apply(apply(x1,f(x1)),g(x1)),h(x1)),i(x1)) ?= apply(apply(f(x1),i(x1)),apply(g(x1),h(x1))) to false
% 0.92/1.35 goal joined
% 0.92/1.35 % SZS status Unsatisfiable
% 0.92/1.35 #START OF PROOF
% 0.92/1.35 % SZS output start CNFRefutation
% 0.92/1.35 cnf('0.1.0.0',axiom,
% 0.92/1.35 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.92/1.35 file('/tmp/WALDMEISTER_22659_n025')).
% 0.92/1.35 cnf('0.1.1.0',plain,
% 0.92/1.35 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.92/1.35 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.92/1.35 cnf('0.1.2.0',plain,
% 0.92/1.35 ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.92/1.35 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_1]).
% 0.92/1.35 cnf('0.2.0.0',axiom,
% 0.92/1.35 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.92/1.35 file('/tmp/WALDMEISTER_22659_n025')).
% 0.92/1.35 cnf('0.2.1.0',plain,
% 0.92/1.35 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.92/1.35 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.92/1.35 cnf('0.2.2.0',plain,
% 0.92/1.35 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.92/1.35 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_2]).
% 0.92/1.35 cnf('0.3.0.0',axiom,
% 0.92/1.35 ( eq(X1,X1) = true ),
% 0.92/1.35 file('/tmp/WALDMEISTER_22659_n025')).
% 0.92/1.35 cnf('0.3.1.0',plain,
% 0.92/1.35 ( eq(X1,X1) = true ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.92/1.35 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.92/1.35 cnf('0.3.2.0',plain,
% 0.92/1.35 ( eq(X1,X1) = true ),
% 0.92/1.35 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.92/1.35 [u,rule_3]).
% 0.92/1.35 cnf('0.4.0.0',axiom,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),i(X1)),apply(apply(f(X1),i(X1)),apply(g(X1),h(X1)))) = false ),
% 0.92/1.35 file('/tmp/WALDMEISTER_22659_n025')).
% 0.92/1.35 cnf('0.4.1.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),i(X1)),apply(apply(f(X1),i(X1)),apply(g(X1),h(X1)))) = false ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.92/1.35 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.92/1.35 cnf('0.4.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),i(X1)),apply(apply(f(X1),i(X1)),apply(g(X1),h(X1)))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.92/1.35 [u,rule_4]).
% 0.92/1.35 cnf('0.9.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),i(apply(apply(b,X1),X2))),apply(apply(f(apply(apply(b,X1),X2)),i(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1.1.1','L')]).
% 0.92/1.35 cnf('0.9.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),i(apply(apply(b,X1),X2))),apply(apply(f(apply(apply(b,X1),X2)),i(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.92/1.35 [weight('<58,4,2,[1,0,0,4]>')]).
% 0.92/1.35 cnf('0.9.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),i(apply(apply(b,X1),X2))),apply(apply(f(apply(apply(b,X1),X2)),i(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_9]).
% 0.92/1.35 cnf('0.11.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1)))),i(apply(apply(b,b),X1))),apply(apply(f(apply(apply(b,b),X1)),i(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.9.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1','L')]).
% 0.92/1.35 cnf('0.11.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1)))),i(apply(apply(b,b),X1))),apply(apply(f(apply(apply(b,b),X1)),i(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.92/1.35 [weight('<56,9,2,[1,0,0,2]>')]).
% 0.92/1.35 cnf('0.11.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(X1,f(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1)))),i(apply(apply(b,b),X1))),apply(apply(f(apply(apply(b,b),X1)),i(apply(apply(b,b),X1))),apply(g(apply(apply(b,b),X1)),h(apply(apply(b,b),X1))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_11]).
% 0.92/1.35 cnf('0.32.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2))))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(apply(f(apply(apply(b,b),apply(apply(b,X1),X2))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2)))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.11.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1.1','L')]).
% 0.92/1.35 cnf('0.32.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2))))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(apply(f(apply(apply(b,b),apply(apply(b,X1),X2))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2)))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.32.0.0']),
% 0.92/1.35 [weight('<90,11,2,[1,0,0,3]>')]).
% 0.92/1.35 cnf('0.32.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2))))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(apply(f(apply(apply(b,b),apply(apply(b,X1),X2))),i(apply(apply(b,b),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,b),apply(apply(b,X1),X2))),h(apply(apply(b,b),apply(apply(b,X1),X2)))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_32]).
% 0.92/1.35 cnf('0.64.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),X2),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.32.2.0','0.1.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1.1','L')]).
% 0.92/1.35 cnf('0.64.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),X2),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.64.0.0']),
% 0.92/1.35 [weight('<106,32,1,[1,0,0,3]>')]).
% 0.92/1.35 cnf('0.64.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),X2),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),X1)))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_64]).
% 0.92/1.35 cnf('0.240.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),X3),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.64.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1.1.1','L')]).
% 0.92/1.35 cnf('0.240.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),X3),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.240.0.0']),
% 0.92/1.35 [weight('<140,64,2,[1,0,0,4]>')]).
% 0.92/1.35 cnf('0.240.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),X3),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),i(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,b),apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.240.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_240]).
% 0.92/1.35 cnf('0.241.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.240.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1','L')]).
% 0.92/1.35 cnf('0.241.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.241.0.0']),
% 0.92/1.35 [weight('<138,240,2,[1,0,0,2]>')]).
% 0.92/1.35 cnf('0.241.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(X1,f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),i(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),h(apply(apply(b,b),apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.241.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_241]).
% 0.92/1.35 cnf('0.242.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.241.2.0','0.1.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1','L')]).
% 0.92/1.35 cnf('0.242.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.242.0.0']),
% 0.92/1.35 [weight('<136,241,1,[1,0,0,2]>')]).
% 0.92/1.35 cnf('0.242.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X1)),apply(apply(b,b),t))))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.242.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_242]).
% 0.92/1.35 cnf('0.571.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.242.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1.1.1','L')]).
% 0.92/1.35 cnf('0.571.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(apply(X1,apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.571.0.0']),
% 0.92/1.35 [weight('<170,242,2,[1,0,0,3]>')]).
% 0.92/1.35 cnf('0.571.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(apply(X1,apply(X2,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X1),X2))),apply(apply(b,b),t))))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.571.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_571]).
% 0.92/1.35 cnf('0.572.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.571.2.0','0.2.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1','L')]).
% 0.92/1.35 cnf('0.572.1.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.572.0.0']),
% 0.92/1.35 [weight('<168,571,2,[1,0,0,1]>')]).
% 0.92/1.35 cnf('0.572.2.0',plain,
% 0.92/1.35 ( eq(apply(apply(X1,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X1))),apply(apply(b,b),t))))))) = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.572.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_572]).
% 0.92/1.35 cnf('0.573.0.0',plain,
% 0.92/1.35 ( false = eq(apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))) ),
% 0.92/1.35 inference(cp,[status(thm)],['0.572.2.0','0.1.2.0',theory(equality)]),
% 0.92/1.35 [pos('L.1','L')]).
% 0.92/1.35 cnf('0.573.0.1',plain,
% 0.92/1.35 ( false = true ),
% 0.92/1.35 inference(reduction,[status(thm)],['0.573.0.0','0.3.2.0',theory(equality)]),
% 0.92/1.35 [pos('R','L')]).
% 0.92/1.35 cnf('0.573.1.0',plain,
% 0.92/1.35 ( false = true ),
% 0.92/1.35 inference(weigh,[status(thm)],['0.573.0.1']),
% 0.92/1.35 [weight('<5,572,1,[1,0,0,1]>')]).
% 0.92/1.35 cnf('0.573.2.0',plain,
% 0.92/1.35 ( true = false ),
% 0.92/1.35 inference(orient,[status(thm)],['0.573.1.0',theory(equality)]),
% 0.92/1.35 [x,rule_573]).
% 0.92/1.35 cnf('1.0.0.0',conjecture,
% 0.92/1.35 ( true = false ),
% 0.92/1.35 file('/tmp/WALDMEISTER_22659_n025',conjecture_1)).
% 0.92/1.35 cnf('1.0.0.1',plain,
% 0.92/1.35 ( false = false ),
% 0.92/1.35 inference(reduction,[status(thm)],['1.0.0.0','0.573.2.0',theory(equality)]),
% 0.92/1.35 [pos('L','L')]).
% 0.92/1.35 cnf('1.0.0.2',plain,
% 0.92/1.35 ( $true ),
% 0.92/1.35 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.92/1.35 [conjecture_1]).
% 0.92/1.35
% 0.92/1.35 Proved Goals:
% 0.92/1.35 No. 1: true ?= false, current false ?= false
% 0.92/1.35 using narrowing to prove apply(apply(apply(apply(x1,f(x1)),g(x1)),h(x1)),i(x1)) ?= apply(apply(f(x1),i(x1)),apply(g(x1),h(x1)))
% 0.92/1.35
% 0.92/1.35 1 goal was specified, which was proved.
% 0.92/1.35 % SZS output end CNFRefutation
% 0.92/1.35 #END OF PROOF
% 0.92/1.35
% 0.92/1.35 Problem WALDMEISTER_22659_n025
% 0.92/1.35 CPs.gen 1275
% 0.92/1.35 CPs.reexp 0
% 0.92/1.35 Select 817
% 0.92/1.35 R 573
% 0.92/1.35 E 0
% 0.92/1.35 vsize 7.5M
% 0.92/1.35 rss 4.6M
% 0.92/1.35 process.time 0.343s
% 0.92/1.35 wallclock.time 0.343s
% 0.92/1.35 status S
% 0.92/1.35
% 0.92/1.35
% 0.92/1.35 Waldmeister states: Goal proved.
% 0.92/1.35 % SZS status Unsatisfiable
%------------------------------------------------------------------------------