TSTP Solution File: COL003-1 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n026.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 00:47:27 EDT 2022
% Result : Unsatisfiable 0.88s 1.27s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 16:40:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.65/1.06 ********************************************************************************
% 0.65/1.06 * W A L D M E I S T E R \| \ / \|/ *
% 0.65/1.06 * |/ | \/ | *
% 0.65/1.06 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.65/1.06 * A. Jaeger and B. Loechner | | *
% 0.65/1.06 * <waldmeister@informatik.uni-kl.de> | *
% 0.65/1.06 ********************************************************************************
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Goals:
% 0.65/1.06 ------
% 0.65/1.06
% 0.65/1.06 ( 1) true ?= false
% 0.65/1.06 using narrowing to prove x1 ?= apply(const1,x1)
% 0.65/1.06
% 0.65/1.06 Detected structure: KombinatorlogikB
% 0.65/1.06 ********************************************************************************
% 0.65/1.06 ****************************** COMPLETION - PROOF ******************************
% 0.65/1.06 ********************************************************************************
% 0.65/1.06
% 0.88/1.27 joined goal: 3 apply(const2,const1) ?= apply(const1,apply(const2,const1)) to apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)))
% 0.88/1.27 goal joined
% 0.88/1.27 % SZS status Unsatisfiable
% 0.88/1.27 #START OF PROOF
% 0.88/1.27 % SZS output start CNFRefutation
% 0.88/1.27 cnf('0.35.0.0',axiom,
% 0.88/1.27 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.35.1.0',plain,
% 0.88/1.27 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.88/1.27 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.88/1.27 cnf('0.35.2.0',plain,
% 0.88/1.27 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.88/1.27 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.88/1.27 [x,rule_33]).
% 0.88/1.27 cnf('0.36.0.0',axiom,
% 0.88/1.27 ( apply(apply(X1,X2),X2) = apply(apply(w,X1),X2) ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.36.1.0',plain,
% 0.88/1.27 ( apply(apply(X1,X2),X2) = apply(apply(w,X1),X2) ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.88/1.27 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.88/1.27 cnf('0.36.2.0',plain,
% 0.88/1.27 ( apply(apply(w,X1),X2) = apply(apply(X1,X2),X2) ),
% 0.88/1.27 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.88/1.27 [x,rule_34]).
% 0.88/1.27 cnf('0.37.0.0',axiom,
% 0.88/1.27 ( const2 = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))) ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.37.1.0',plain,
% 0.88/1.27 ( const2 = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))) ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.37.0.0']),
% 0.88/1.27 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.88/1.27 cnf('0.37.2.0',plain,
% 0.88/1.27 ( const2 = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))) ),
% 0.88/1.27 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.88/1.27 [u,rule_35]).
% 0.88/1.27 cnf('3.0.0.0',conjecture,
% 0.88/1.27 ( apply(const2,const1) = apply(const1,apply(const2,const1)) ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026',conjecture_3)).
% 0.88/1.27 cnf('3.0.0.1',plain,
% 0.88/1.27 ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),const1) = apply(const1,apply(const2,const1)) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.0','0.37.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1','L')]).
% 0.88/1.27 cnf('3.0.0.2',plain,
% 0.88/1.27 ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),const1) = apply(const1,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),const1)) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.1','0.37.2.0',theory(equality)]),
% 0.88/1.27 [pos('R.2.1','L')]).
% 0.88/1.27 cnf('3.0.0.3',plain,
% 0.88/1.27 ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),const1) = apply(const1,apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.2','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('R.2','L')]).
% 0.88/1.27 cnf('3.0.0.4',plain,
% 0.88/1.27 ( apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.3','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('3.0.0.5',plain,
% 0.88/1.27 ( apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(w,apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.4','0.36.2.0',theory(equality)]),
% 0.88/1.27 [pos('R.2','L')]).
% 0.88/1.27 cnf('3.0.0.6',plain,
% 0.88/1.27 ( apply(apply(w,apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(w,apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.5','0.36.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('3.0.0.7',plain,
% 0.88/1.27 ( apply(apply(w,apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.6','0.36.2.0',theory(equality)]),
% 0.88/1.27 [pos('R.2','L')]).
% 0.88/1.27 cnf('3.0.0.8',plain,
% 0.88/1.27 ( apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.7','0.36.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('3.0.0.9',plain,
% 0.88/1.27 ( apply(apply(apply(w,apply(apply(apply(b,b),b),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.8','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1.1','L')]).
% 0.88/1.27 cnf('3.0.0.10',plain,
% 0.88/1.27 ( apply(apply(apply(apply(apply(apply(b,b),b),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.9','0.36.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1','L')]).
% 0.88/1.27 cnf('3.0.0.11',plain,
% 0.88/1.27 ( apply(apply(apply(apply(b,apply(b,const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.10','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1.1.1','L')]).
% 0.88/1.27 cnf('3.0.0.12',plain,
% 0.88/1.27 ( apply(apply(apply(b,const1),apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.11','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1','L')]).
% 0.88/1.27 cnf('3.0.0.13',plain,
% 0.88/1.27 ( apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) ),
% 0.88/1.27 inference(reduction,[status(thm)],['3.0.0.12','0.35.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('3.0.0.14',plain,
% 0.88/1.27 ( $true ),
% 0.88/1.27 inference(trivial,[status(thm)],['3.0.0.13',theory(equality)]),
% 0.88/1.27 [conjecture_3]).
% 0.88/1.27 joined goal: 1 x1 ?= apply(const1,x1) to false
% 0.88/1.27 goal joined
% 0.88/1.27 #START OF PROOF
% 0.88/1.27 % SZS output start CNFRefutation
% 0.88/1.27 cnf('0.38.0.0',axiom,
% 0.88/1.27 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.38.1.0',plain,
% 0.88/1.27 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.88/1.27 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.88/1.27 cnf('0.38.2.0',plain,
% 0.88/1.27 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.88/1.27 inference(activate,[status(thm)],['0.38.1.0']),
% 0.88/1.27 [equation_3]).
% 0.88/1.27 cnf('0.39.0.0',axiom,
% 0.88/1.27 ( eq(X1,X1) = true ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.39.1.0',plain,
% 0.88/1.27 ( eq(X1,X1) = true ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.88/1.27 [weight('<10,0,0,[0,0,0,12]>')]).
% 0.88/1.27 cnf('0.39.2.0',plain,
% 0.88/1.27 ( eq(X1,X1) = true ),
% 0.88/1.27 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.88/1.27 [u,rule_36]).
% 0.88/1.27 cnf('0.40.0.0',axiom,
% 0.88/1.27 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026')).
% 0.88/1.27 cnf('0.40.1.0',plain,
% 0.88/1.27 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.88/1.27 [weight('<11,0,0,[0,0,0,11]>')]).
% 0.88/1.27 cnf('0.40.2.0',plain,
% 0.88/1.27 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.88/1.27 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.88/1.27 [u,rule_37]).
% 0.88/1.27 cnf('0.41.0.0',plain,
% 0.88/1.27 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.88/1.27 inference(cp,[status(thm)],['0.40.2.0','0.38.2.0',theory(equality)]),
% 0.88/1.27 [pos('L.1','L')]).
% 0.88/1.27 cnf('0.41.1.0',plain,
% 0.88/1.27 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.41.0.0']),
% 0.88/1.27 [weight('<0,40,38,[1,0,0,1]>')]).
% 0.88/1.27 cnf('0.41.2.0',plain,
% 0.88/1.27 ( eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) = false ),
% 0.88/1.27 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.88/1.27 [x,rule_38]).
% 0.88/1.27 cnf('0.42.0.0',plain,
% 0.88/1.27 ( false = true ),
% 0.88/1.27 inference(cp,[status(thm)],['0.41.2.0','0.39.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('0.42.1.0',plain,
% 0.88/1.27 ( false = true ),
% 0.88/1.27 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.88/1.27 [weight('<5,41,39,[1,0,0,0]>')]).
% 0.88/1.27 cnf('0.42.2.0',plain,
% 0.88/1.27 ( true = false ),
% 0.88/1.27 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.88/1.27 [x,rule_39]).
% 0.88/1.27 cnf('1.0.0.0',conjecture,
% 0.88/1.27 ( true = false ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026',conjecture_1)).
% 0.88/1.27 cnf('1.0.0.1',plain,
% 0.88/1.27 ( false = false ),
% 0.88/1.27 inference(reduction,[status(thm)],['1.0.0.0','0.42.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('1.0.0.2',plain,
% 0.88/1.27 ( $true ),
% 0.88/1.27 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.88/1.27 [conjecture_1]).
% 0.88/1.27 joined goal: 4 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.88/1.27 goal joined
% 0.88/1.27 #START OF PROOF
% 0.88/1.27 % SZS output start CNFRefutation
% 0.88/1.27 cnf('4.0.0.0',conjecture,
% 0.88/1.27 ( true = false ),
% 0.88/1.27 file('/tmp/WALDMEISTER_27046_n026',conjecture_4)).
% 0.88/1.27 cnf('4.0.0.1',plain,
% 0.88/1.27 ( false = false ),
% 0.88/1.27 inference(reduction,[status(thm)],['4.0.0.0','0.42.2.0',theory(equality)]),
% 0.88/1.27 [pos('L','L')]).
% 0.88/1.27 cnf('4.0.0.2',plain,
% 0.88/1.27 ( $true ),
% 0.88/1.27 inference(trivial,[status(thm)],['4.0.0.1',theory(equality)]),
% 0.88/1.27 [conjecture_4]).
% 0.88/1.27
% 0.88/1.27 Proved Goals:
% 0.88/1.27 No. 1: true ?= false, current false ?= false
% 0.88/1.27 using narrowing to prove x1 ?= apply(const1,x1)
% 0.88/1.27
% 0.88/1.27 No. 3: apply(const2,const1) ?= apply(const1,apply(const2,const1)) joined, current: apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1))) = apply(const1,apply(apply(apply(apply(apply(b,w),apply(apply(b,b),b)),const1),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)),apply(apply(apply(b,w),apply(apply(b,b),b)),const1)))
% 0.88/1.27 No. 4: true ?= false, current false ?= false
% 0.88/1.27 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.88/1.27
% 0.88/1.27 1 goal was specified, which was proved.
% 0.88/1.27 % SZS output end CNFRefutation
% 0.88/1.27 #END OF PROOF
% 0.88/1.27
% 0.88/1.27 Problem WALDMEISTER_27046_n026
% 0.88/1.27 CPs.gen 104
% 0.88/1.27 CPs.reexp 0
% 0.88/1.27 Select 115
% 0.88/1.27 R 39
% 0.88/1.27 E 3
% 0.88/1.27 vsize 6.4M
% 0.88/1.27 rss 3.7M
% 0.88/1.27 process.time 0.004s
% 0.88/1.27 wallclock.time 0.212s
% 0.88/1.27 status S
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Waldmeister states: Goal proved.
% 0.88/1.27 % SZS status Unsatisfiable
% 0.88/1.27
% 0.88/1.27 Problem WALDMEISTER_27046_n026
% 0.88/1.27 CPs.gen 12034
% 0.88/1.27 CPs.reexp 0
% 0.88/1.27 Select 356
% 0.88/1.27 R 77
% 0.88/1.27 E 42
% 0.88/1.27 vsize 6.4M
% 0.88/1.27 rss 3.6M
% 0.88/1.27 process.time 0.209s
% 0.88/1.27 wallclock.time 0.213s
% 0.88/1.27 status S
%------------------------------------------------------------------------------