%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL042-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n022.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 00:47:33 EDT 2022
% Result : Unsatisfiable 0.70s 1.13s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL042-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : woody %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 16:38:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.96 * |/ | \/ | *
% 0.57/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.96 * A. Jaeger and B. Loechner | | *
% 0.57/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 0.57/0.96
% 0.57/0.96 Goals:
% 0.57/0.96 ------
% 0.57/0.96
% 0.57/0.96 ( 1) true ?= false
% 0.57/0.96 using narrowing to prove x1 ?= apply(const1,x1)
% 0.57/0.96
% 0.57/0.96 Detected structure: KombinatorlogikB
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 0.70/1.13 joined goal: 3 apply(const2,const1) ?= apply(const1,apply(const2,const1)) to apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1)))
% 0.70/1.13 goal joined
% 0.70/1.13 % SZS status Unsatisfiable
% 0.70/1.13 #START OF PROOF
% 0.70/1.13 % SZS output start CNFRefutation
% 0.70/1.13 cnf('0.38.0.0',axiom,
% 0.70/1.13 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.38.1.0',plain,
% 0.70/1.13 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.70/1.13 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.70/1.13 cnf('0.38.2.0',plain,
% 0.70/1.13 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.70/1.13 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.70/1.13 [x,rule_36]).
% 0.70/1.13 cnf('0.39.0.0',axiom,
% 0.70/1.13 ( apply(apply(X1,X2),X2) = apply(apply(w1,X2),X1) ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.39.1.0',plain,
% 0.70/1.13 ( apply(apply(X1,X2),X2) = apply(apply(w1,X2),X1) ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.70/1.13 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.70/1.13 cnf('0.39.2.0',plain,
% 0.70/1.13 ( apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1) ),
% 0.70/1.13 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.70/1.13 [x,rule_37]).
% 0.70/1.13 cnf('0.40.0.0',axiom,
% 0.70/1.13 ( const2 = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))) ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.40.1.0',plain,
% 0.70/1.13 ( const2 = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))) ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.70/1.13 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.70/1.13 cnf('0.40.2.0',plain,
% 0.70/1.13 ( const2 = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))) ),
% 0.70/1.13 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.70/1.13 [u,rule_38]).
% 0.70/1.13 cnf('3.0.0.0',conjecture,
% 0.70/1.13 ( apply(const2,const1) = apply(const1,apply(const2,const1)) ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022',conjecture_3)).
% 0.70/1.13 cnf('3.0.0.1',plain,
% 0.70/1.13 ( apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),const1) = apply(const1,apply(const2,const1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.0','0.40.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1','L')]).
% 0.70/1.13 cnf('3.0.0.2',plain,
% 0.70/1.13 ( apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),const1) = apply(const1,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),const1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.1','0.40.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2.1','L')]).
% 0.70/1.13 cnf('3.0.0.3',plain,
% 0.70/1.13 ( apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),const1) = apply(const1,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.2','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2','L')]).
% 0.70/1.13 cnf('3.0.0.4',plain,
% 0.70/1.13 ( apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.3','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('3.0.0.5',plain,
% 0.70/1.13 ( apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1)) = apply(const1,apply(apply(apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1),w1),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.4','0.39.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2','L')]).
% 0.70/1.13 cnf('3.0.0.6',plain,
% 0.70/1.13 ( apply(apply(apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1),w1),w1) = apply(const1,apply(apply(apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1),w1),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.5','0.39.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('3.0.0.7',plain,
% 0.70/1.13 ( apply(apply(apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),const1),w1),w1) = apply(const1,apply(apply(apply(apply(b,w1),apply(apply(apply(b,b),b),const1)),w1),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.6','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2.1.1','L')]).
% 0.70/1.13 cnf('3.0.0.8',plain,
% 0.70/1.13 ( apply(apply(apply(apply(b,w1),apply(apply(apply(b,b),b),const1)),w1),w1) = apply(const1,apply(apply(apply(apply(b,w1),apply(apply(apply(b,b),b),const1)),w1),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.7','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1.1','L')]).
% 0.70/1.13 cnf('3.0.0.9',plain,
% 0.70/1.13 ( apply(apply(apply(apply(b,w1),apply(apply(apply(b,b),b),const1)),w1),w1) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.8','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2.1','L')]).
% 0.70/1.13 cnf('3.0.0.10',plain,
% 0.70/1.13 ( apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),w1) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),w1)) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.9','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1','L')]).
% 0.70/1.13 cnf('3.0.0.11',plain,
% 0.70/1.13 ( apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),w1) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.10','0.39.2.0',theory(equality)]),
% 0.70/1.13 [pos('R.2','L')]).
% 0.70/1.13 cnf('3.0.0.12',plain,
% 0.70/1.13 ( apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1)) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.11','0.39.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('3.0.0.13',plain,
% 0.70/1.13 ( apply(apply(apply(apply(apply(apply(b,b),b),const1),w1),apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1)) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.12','0.39.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('3.0.0.14',plain,
% 0.70/1.13 ( apply(apply(apply(apply(b,apply(b,const1)),w1),apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1)) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.13','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1.1.1','L')]).
% 0.70/1.13 cnf('3.0.0.15',plain,
% 0.70/1.13 ( apply(apply(apply(b,const1),apply(w1,apply(apply(apply(apply(b,b),b),const1),w1))),apply(apply(apply(apply(b,b),b),const1),w1)) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.14','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1','L')]).
% 0.70/1.13 cnf('3.0.0.16',plain,
% 0.70/1.13 ( apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) ),
% 0.70/1.13 inference(reduction,[status(thm)],['3.0.0.15','0.38.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('3.0.0.17',plain,
% 0.70/1.13 ( $true ),
% 0.70/1.13 inference(trivial,[status(thm)],['3.0.0.16',theory(equality)]),
% 0.70/1.13 [conjecture_3]).
% 0.70/1.13 joined goal: 1 x1 ?= apply(const1,x1) to false
% 0.70/1.13 goal joined
% 0.70/1.13 #START OF PROOF
% 0.70/1.13 % SZS output start CNFRefutation
% 0.70/1.13 cnf('0.41.0.0',axiom,
% 0.70/1.13 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.41.1.0',plain,
% 0.70/1.13 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.41.0.0']),
% 0.70/1.13 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.70/1.13 cnf('0.41.2.0',plain,
% 0.70/1.13 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.70/1.13 inference(activate,[status(thm)],['0.41.1.0']),
% 0.70/1.13 [equation_3]).
% 0.70/1.13 cnf('0.42.0.0',axiom,
% 0.70/1.13 ( eq(X1,X1) = true ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.42.1.0',plain,
% 0.70/1.13 ( eq(X1,X1) = true ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.70/1.13 [weight('<10,0,0,[0,0,0,12]>')]).
% 0.70/1.13 cnf('0.42.2.0',plain,
% 0.70/1.13 ( eq(X1,X1) = true ),
% 0.70/1.13 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.70/1.13 [u,rule_39]).
% 0.70/1.13 cnf('0.43.0.0',axiom,
% 0.70/1.13 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022')).
% 0.70/1.13 cnf('0.43.1.0',plain,
% 0.70/1.13 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.43.0.0']),
% 0.70/1.13 [weight('<11,0,0,[0,0,0,11]>')]).
% 0.70/1.13 cnf('0.43.2.0',plain,
% 0.70/1.13 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.70/1.13 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 0.70/1.13 [u,rule_40]).
% 0.70/1.13 cnf('0.44.0.0',plain,
% 0.70/1.13 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.70/1.13 inference(cp,[status(thm)],['0.43.2.0','0.41.2.0',theory(equality)]),
% 0.70/1.13 [pos('L.1','L')]).
% 0.70/1.13 cnf('0.44.1.0',plain,
% 0.70/1.13 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.44.0.0']),
% 0.70/1.13 [weight('<0,43,41,[1,0,0,1]>')]).
% 0.70/1.13 cnf('0.44.2.0',plain,
% 0.70/1.13 ( eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) = false ),
% 0.70/1.13 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 0.70/1.13 [x,rule_41]).
% 0.70/1.13 cnf('0.45.0.0',plain,
% 0.70/1.13 ( false = true ),
% 0.70/1.13 inference(cp,[status(thm)],['0.44.2.0','0.42.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('0.45.1.0',plain,
% 0.70/1.13 ( false = true ),
% 0.70/1.13 inference(weigh,[status(thm)],['0.45.0.0']),
% 0.70/1.13 [weight('<5,44,42,[1,0,0,0]>')]).
% 0.70/1.13 cnf('0.45.2.0',plain,
% 0.70/1.13 ( true = false ),
% 0.70/1.13 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.70/1.13 [x,rule_42]).
% 0.70/1.13 cnf('1.0.0.0',conjecture,
% 0.70/1.13 ( true = false ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022',conjecture_1)).
% 0.70/1.13 cnf('1.0.0.1',plain,
% 0.70/1.13 ( false = false ),
% 0.70/1.13 inference(reduction,[status(thm)],['1.0.0.0','0.45.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('1.0.0.2',plain,
% 0.70/1.13 ( $true ),
% 0.70/1.13 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.70/1.13 [conjecture_1]).
% 0.70/1.13 joined goal: 4 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.70/1.13 goal joined
% 0.70/1.13 #START OF PROOF
% 0.70/1.13 % SZS output start CNFRefutation
% 0.70/1.13 cnf('4.0.0.0',conjecture,
% 0.70/1.13 ( true = false ),
% 0.70/1.13 file('/tmp/WALDMEISTER_9996_n022',conjecture_4)).
% 0.70/1.13 cnf('4.0.0.1',plain,
% 0.70/1.13 ( false = false ),
% 0.70/1.13 inference(reduction,[status(thm)],['4.0.0.0','0.45.2.0',theory(equality)]),
% 0.70/1.13 [pos('L','L')]).
% 0.70/1.13 cnf('4.0.0.2',plain,
% 0.70/1.13 ( $true ),
% 0.70/1.13 inference(trivial,[status(thm)],['4.0.0.1',theory(equality)]),
% 0.70/1.13 [conjecture_4]).
% 0.70/1.13
% 0.70/1.13 Proved Goals:
% 0.70/1.13 No. 1: true ?= false, current false ?= false
% 0.70/1.13 using narrowing to prove x1 ?= apply(const1,x1)
% 0.70/1.13
% 0.70/1.13 No. 3: apply(const2,const1) ?= apply(const1,apply(const2,const1)) joined, current: apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1))) = apply(const1,apply(apply(w1,apply(apply(apply(apply(b,b),b),const1),w1)),apply(apply(apply(apply(b,b),b),const1),w1)))
% 0.70/1.13 No. 4: true ?= false, current false ?= false
% 0.70/1.13 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.70/1.13
% 0.70/1.13 1 goal was specified, which was proved.
% 0.70/1.13 % SZS output end CNFRefutation
% 0.70/1.13 #END OF PROOF
% 0.70/1.13
% 0.70/1.13 Problem WALDMEISTER_9996_n022
% 0.70/1.13 CPs.gen 117
% 0.70/1.13 CPs.reexp 0
% 0.70/1.13 Select 128
% 0.70/1.13 R 42
% 0.70/1.13 E 3
% 0.70/1.13 vsize 6.4M
% 0.70/1.13 rss 3.7M
% 0.70/1.13 process.time 0.004s
% 0.70/1.13 wallclock.time 0.170s
% 0.70/1.13 status S
% 0.70/1.13
% 0.70/1.13
% 0.70/1.13 Waldmeister states: Goal proved.
% 0.70/1.13 % SZS status Unsatisfiable
% 0.70/1.13
% 0.70/1.13 Problem WALDMEISTER_9996_n022
% 0.70/1.13 CPs.gen 9777
% 0.70/1.13 CPs.reexp 0
% 0.70/1.13 Select 356
% 0.70/1.13 R 79
% 0.70/1.13 E 35
% 0.70/1.13 vsize 6.4M
% 0.70/1.13 rss 3.6M
% 0.70/1.13 process.time 0.167s
% 0.70/1.13 wallclock.time 0.171s
% 0.70/1.13 status S
%------------------------------------------------------------------------------