TSTP Solution File: COL034-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n032.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 00:47:32 EDT 2022
% Result : Unsatisfiable 0.43s 0.87s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COL034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : woody %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 600
% 0.10/0.28 % DateTime : Tue May 31 08:59:58 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.43/0.84 ********************************************************************************
% 0.43/0.84 * W A L D M E I S T E R \| \ / \|/ *
% 0.43/0.84 * |/ | \/ | *
% 0.43/0.84 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.43/0.84 * A. Jaeger and B. Loechner | | *
% 0.43/0.84 * <waldmeister@informatik.uni-kl.de> | *
% 0.43/0.84 ********************************************************************************
% 0.43/0.84
% 0.43/0.84
% 0.43/0.84 Goals:
% 0.43/0.84 ------
% 0.43/0.84
% 0.43/0.84 ( 1) true ?= false
% 0.43/0.84 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.43/0.84
% 0.43/0.84 Detected structure: KombinatorlogikBT
% 0.43/0.84 ********************************************************************************
% 0.43/0.84 ****************************** COMPLETION - PROOF ******************************
% 0.43/0.84 ********************************************************************************
% 0.43/0.84
% 0.43/0.87 joined goal: 1 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.43/0.87 goal joined
% 0.43/0.87 % SZS status Unsatisfiable
% 0.43/0.87 #START OF PROOF
% 0.43/0.87 % SZS output start CNFRefutation
% 0.43/0.87 cnf('0.1.0.0',axiom,
% 0.43/0.87 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032')).
% 0.43/0.87 cnf('0.1.1.0',plain,
% 0.43/0.87 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.43/0.87 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.43/0.87 cnf('0.1.2.0',plain,
% 0.43/0.87 ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.43/0.87 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_1]).
% 0.43/0.87 cnf('0.2.0.0',axiom,
% 0.43/0.87 ( apply(X1,X1) = apply(m,X1) ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032')).
% 0.43/0.87 cnf('0.2.1.0',plain,
% 0.43/0.87 ( apply(X1,X1) = apply(m,X1) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.43/0.87 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.43/0.87 cnf('0.2.2.0',plain,
% 0.43/0.87 ( apply(X1,X1) = apply(m,X1) ),
% 0.43/0.87 inference(activate,[status(thm)],['0.2.1.0']),
% 0.43/0.87 [equation_1]).
% 0.43/0.87 cnf('0.3.0.0',axiom,
% 0.43/0.87 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032')).
% 0.43/0.87 cnf('0.3.1.0',plain,
% 0.43/0.87 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.43/0.87 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.43/0.87 cnf('0.3.2.0',plain,
% 0.43/0.87 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.43/0.87 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_2]).
% 0.43/0.87 cnf('0.4.0.0',axiom,
% 0.43/0.87 ( eq(X1,X1) = true ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032')).
% 0.43/0.87 cnf('0.4.1.0',plain,
% 0.43/0.87 ( eq(X1,X1) = true ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.43/0.87 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.43/0.87 cnf('0.4.2.0',plain,
% 0.43/0.87 ( eq(X1,X1) = true ),
% 0.43/0.87 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.43/0.87 [u,rule_3]).
% 0.43/0.87 cnf('0.5.0.0',axiom,
% 0.43/0.87 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032')).
% 0.43/0.87 cnf('0.5.1.0',plain,
% 0.43/0.87 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.43/0.87 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.43/0.87 cnf('0.5.2.0',plain,
% 0.43/0.87 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.43/0.87 [u,rule_4]).
% 0.43/0.87 cnf('0.9.0.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(apply(apply(b,X1),X2),f(apply(apply(b,X1),X2))))) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.5.2.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('L.1','L')]).
% 0.43/0.87 cnf('0.9.0.1',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2)))))) ),
% 0.43/0.87 inference(reduction,[status(thm)],['0.9.0.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('R.2.2','L')]).
% 0.43/0.87 cnf('0.9.1.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2)))))) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.9.0.1']),
% 0.43/0.87 [weight('<27,5,3,[1,0,0,1]>')]).
% 0.43/0.87 cnf('0.9.2.0',plain,
% 0.43/0.87 ( eq(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),apply(f(apply(apply(b,X1),X2)),apply(X1,apply(X2,f(apply(apply(b,X1),X2)))))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_7]).
% 0.43/0.87 cnf('0.10.0.0',plain,
% 0.43/0.87 ( apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.3.2.0','0.2.2.0',theory(equality)]),
% 0.43/0.87 [pos('L','L')]).
% 0.43/0.87 cnf('0.10.1.0',plain,
% 0.43/0.87 ( apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.43/0.87 [weight('<169,3,2,[1,0,0,0]>')]).
% 0.43/0.87 cnf('0.10.2.0',plain,
% 0.43/0.87 ( apply(X1,apply(X2,apply(apply(b,X1),X2))) = apply(m,apply(apply(b,X1),X2)) ),
% 0.43/0.87 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.43/0.87 [u,rule_8]).
% 0.43/0.87 cnf('0.11.0.0',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(f(apply(apply(b,apply(t,X2)),X1)),apply(apply(t,X2),apply(X1,f(apply(apply(b,apply(t,X2)),X1)))))) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.43/0.87 [pos('L.1','L')]).
% 0.43/0.87 cnf('0.11.0.1',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(f(apply(apply(b,apply(t,X2)),X1)),apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2))) ),
% 0.43/0.87 inference(reduction,[status(thm)],['0.11.0.0','0.1.2.0',theory(equality)]),
% 0.43/0.87 [pos('R.2.2','L')]).
% 0.43/0.87 cnf('0.11.1.0',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(f(apply(apply(b,apply(t,X2)),X1)),apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2))) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.11.0.1']),
% 0.43/0.87 [weight('<33,9,1,[1,0,0,1]>')]).
% 0.43/0.87 cnf('0.11.2.0',plain,
% 0.43/0.87 ( eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(f(apply(apply(b,apply(t,X2)),X1)),apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_9]).
% 0.43/0.87 cnf('0.33.0.0',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(apply(apply(apply(b,X1),X2),f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),X3))) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('L.1.1','L')]).
% 0.43/0.87 cnf('0.33.0.1',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3))) ),
% 0.43/0.87 inference(reduction,[status(thm)],['0.33.0.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('R.2.2.1','L')]).
% 0.43/0.87 cnf('0.33.1.0',plain,
% 0.43/0.87 ( false = eq(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3))) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.43/0.87 [weight('<49,11,3,[1,0,0,2]>')]).
% 0.43/0.87 cnf('0.33.2.0',plain,
% 0.43/0.87 ( eq(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_26]).
% 0.43/0.87 cnf('0.91.0.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2))),apply(apply(apply(b,X1),apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2))))),X3))) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.33.2.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('L.1','L')]).
% 0.43/0.87 cnf('0.91.0.1',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2))),apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)))) ),
% 0.43/0.87 inference(reduction,[status(thm)],['0.91.0.0','0.3.2.0',theory(equality)]),
% 0.43/0.87 [pos('R.2.2','L')]).
% 0.43/0.87 cnf('0.91.1.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2))),apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)))) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.91.0.1']),
% 0.43/0.87 [weight('<55,33,3,[1,0,0,1]>')]).
% 0.43/0.87 cnf('0.91.2.0',plain,
% 0.43/0.87 ( eq(apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2))),apply(X1,apply(apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,apply(b,X1)),X2)))),X3)))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.91.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_79]).
% 0.43/0.87 cnf('0.93.0.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1)),apply(m,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1))) ),
% 0.43/0.87 inference(cp,[status(thm)],['0.91.2.0','0.10.2.0',theory(equality)]),
% 0.43/0.87 [pos('L.2','L')]).
% 0.43/0.87 cnf('0.93.1.0',plain,
% 0.43/0.87 ( false = eq(apply(X1,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1)),apply(m,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1))) ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.93.0.0']),
% 0.43/0.87 [weight('<40,91,10,[1,0,0,21]>')]).
% 0.43/0.87 cnf('0.93.2.0',plain,
% 0.43/0.87 ( eq(apply(X1,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1)),apply(m,apply(apply(b,f(apply(apply(b,apply(t,X1)),apply(apply(b,apply(b,X1)),b)))),X1))) = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.93.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_81]).
% 0.43/0.87 cnf('0.94.0.0',plain,
% 0.43/0.87 ( false = true ),
% 0.43/0.87 inference(cp,[status(thm)],['0.93.2.0','0.4.2.0',theory(equality)]),
% 0.43/0.87 [pos('L','L')]).
% 0.43/0.87 cnf('0.94.1.0',plain,
% 0.43/0.87 ( false = true ),
% 0.43/0.87 inference(weigh,[status(thm)],['0.94.0.0']),
% 0.43/0.87 [weight('<5,93,4,[1,0,0,0]>')]).
% 0.43/0.87 cnf('0.94.2.0',plain,
% 0.43/0.87 ( true = false ),
% 0.43/0.87 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 0.43/0.87 [x,rule_82]).
% 0.43/0.87 cnf('1.0.0.0',conjecture,
% 0.43/0.87 ( true = false ),
% 0.43/0.87 file('/tmp/WALDMEISTER_4355_n032',conjecture_1)).
% 0.43/0.87 cnf('1.0.0.1',plain,
% 0.43/0.87 ( false = false ),
% 0.43/0.87 inference(reduction,[status(thm)],['1.0.0.0','0.94.2.0',theory(equality)]),
% 0.43/0.87 [pos('L','L')]).
% 0.43/0.87 cnf('1.0.0.2',plain,
% 0.43/0.87 ( $true ),
% 0.43/0.87 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.43/0.87 [conjecture_1]).
% 0.43/0.87
% 0.43/0.87 Proved Goals:
% 0.43/0.87 No. 1: true ?= false, current false ?= false
% 0.43/0.87 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.43/0.87
% 0.43/0.87 1 goal was specified, which was proved.
% 0.43/0.87 % SZS output end CNFRefutation
% 0.43/0.87 #END OF PROOF
% 0.43/0.87
% 0.43/0.87 Problem WALDMEISTER_4355_n032
% 0.43/0.87 CPs.gen 933
% 0.43/0.87 CPs.reexp 0
% 0.43/0.87 Select 173
% 0.43/0.87 R 82
% 0.43/0.87 E 12
% 0.43/0.87 vsize 6.5M
% 0.43/0.87 rss 3.8M
% 0.43/0.87 process.time 0.024s
% 0.43/0.87 wallclock.time 0.024s
% 0.43/0.87 status S
% 0.43/0.87
% 0.43/0.87
% 0.43/0.87 Waldmeister states: Goal proved.
% 0.43/0.87 % SZS status Unsatisfiable
%------------------------------------------------------------------------------