TSTP Solution File: COL041-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL041-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n017.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 0.71s 1.09s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL041-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n017.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 07:46:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.97 * |/ | \/ | *
% 0.57/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.97 * A. Jaeger and B. Loechner | | *
% 0.57/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.57/0.97
% 0.57/0.97 Goals:
% 0.57/0.97 ------
% 0.57/0.97
% 0.57/0.97 ( 1) true ?= false
% 0.57/0.97 using narrowing to prove x1 ?= apply(const1,x1)
% 0.57/0.97
% 0.57/0.97 Detected structure: KombinatorlogikB
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.71/1.09 joined goal: 3 apply(const2,const1) ?= apply(const1,apply(const2,const1)) to apply(const1,apply(m,apply(apply(apply(c,b),m),const1)))
% 0.71/1.09 goal joined
% 0.71/1.09 % SZS status Unsatisfiable
% 0.71/1.09 #START OF PROOF
% 0.71/1.09 % SZS output start CNFRefutation
% 0.71/1.09 cnf('0.28.0.0',axiom,
% 0.71/1.09 ( apply(X1,X1) = apply(m,X1) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.28.1.0',plain,
% 0.71/1.09 ( apply(X1,X1) = apply(m,X1) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.71/1.09 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.71/1.09 cnf('0.28.2.0',plain,
% 0.71/1.09 ( apply(m,X1) = apply(X1,X1) ),
% 0.71/1.09 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.71/1.09 [x,rule_25]).
% 0.71/1.09 cnf('0.29.0.0',axiom,
% 0.71/1.09 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.29.1.0',plain,
% 0.71/1.09 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.71/1.09 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.71/1.09 cnf('0.29.2.0',plain,
% 0.71/1.09 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.71/1.09 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.71/1.09 [x,rule_26]).
% 0.71/1.09 cnf('0.30.0.0',axiom,
% 0.71/1.09 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.30.1.0',plain,
% 0.71/1.09 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.71/1.09 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.71/1.09 cnf('0.30.2.0',plain,
% 0.71/1.09 ( apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2) ),
% 0.71/1.09 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.71/1.09 [x,rule_27]).
% 0.71/1.09 cnf('0.31.0.0',axiom,
% 0.71/1.09 ( const2 = apply(apply(b,m),apply(apply(c,b),m)) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.31.1.0',plain,
% 0.71/1.09 ( const2 = apply(apply(b,m),apply(apply(c,b),m)) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.71/1.09 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.71/1.09 cnf('0.31.2.0',plain,
% 0.71/1.09 ( const2 = apply(apply(b,m),apply(apply(c,b),m)) ),
% 0.71/1.09 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.71/1.09 [u,rule_28]).
% 0.71/1.09 cnf('3.0.0.0',conjecture,
% 0.71/1.09 ( apply(const2,const1) = apply(const1,apply(const2,const1)) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017',conjecture_3)).
% 0.71/1.09 cnf('3.0.0.1',plain,
% 0.71/1.09 ( apply(apply(apply(b,m),apply(apply(c,b),m)),const1) = apply(const1,apply(const2,const1)) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.0','0.31.2.0',theory(equality)]),
% 0.71/1.09 [pos('L.1','L')]).
% 0.71/1.09 cnf('3.0.0.2',plain,
% 0.71/1.09 ( apply(apply(apply(b,m),apply(apply(c,b),m)),const1) = apply(const1,apply(apply(apply(b,m),apply(apply(c,b),m)),const1)) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.1','0.31.2.0',theory(equality)]),
% 0.71/1.09 [pos('R.2.1','L')]).
% 0.71/1.09 cnf('3.0.0.3',plain,
% 0.71/1.09 ( apply(apply(apply(b,m),apply(apply(c,b),m)),const1) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.2','0.29.2.0',theory(equality)]),
% 0.71/1.09 [pos('R.2','L')]).
% 0.71/1.09 cnf('3.0.0.4',plain,
% 0.71/1.09 ( apply(m,apply(apply(apply(c,b),m),const1)) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.3','0.29.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('3.0.0.5',plain,
% 0.71/1.09 ( apply(apply(apply(apply(c,b),m),const1),apply(apply(apply(c,b),m),const1)) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.4','0.28.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('3.0.0.6',plain,
% 0.71/1.09 ( apply(apply(apply(b,const1),m),apply(apply(apply(c,b),m),const1)) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.5','0.30.2.0',theory(equality)]),
% 0.71/1.09 [pos('L.1','L')]).
% 0.71/1.09 cnf('3.0.0.7',plain,
% 0.71/1.09 ( apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) ),
% 0.71/1.09 inference(reduction,[status(thm)],['3.0.0.6','0.29.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('3.0.0.8',plain,
% 0.71/1.09 ( $true ),
% 0.71/1.09 inference(trivial,[status(thm)],['3.0.0.7',theory(equality)]),
% 0.71/1.09 [conjecture_3]).
% 0.71/1.09 joined goal: 1 x1 ?= apply(const1,x1) to false
% 0.71/1.09 goal joined
% 0.71/1.09 #START OF PROOF
% 0.71/1.09 % SZS output start CNFRefutation
% 0.71/1.09 cnf('0.32.0.0',axiom,
% 0.71/1.09 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.32.1.0',plain,
% 0.71/1.09 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.32.0.0']),
% 0.71/1.09 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.71/1.09 cnf('0.32.2.0',plain,
% 0.71/1.09 ( apply(const2,X1) = apply(X1,apply(const2,X1)) ),
% 0.71/1.09 inference(activate,[status(thm)],['0.32.1.0']),
% 0.71/1.09 [equation_4]).
% 0.71/1.09 cnf('0.33.0.0',axiom,
% 0.71/1.09 ( eq(X1,X1) = true ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.33.1.0',plain,
% 0.71/1.09 ( eq(X1,X1) = true ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.33.0.0']),
% 0.71/1.09 [weight('<12,0,0,[0,0,0,14]>')]).
% 0.71/1.09 cnf('0.33.2.0',plain,
% 0.71/1.09 ( eq(X1,X1) = true ),
% 0.71/1.09 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.71/1.09 [u,rule_29]).
% 0.71/1.09 cnf('0.34.0.0',axiom,
% 0.71/1.09 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017')).
% 0.71/1.09 cnf('0.34.1.0',plain,
% 0.71/1.09 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.34.0.0']),
% 0.71/1.09 [weight('<13,0,0,[0,0,0,13]>')]).
% 0.71/1.09 cnf('0.34.2.0',plain,
% 0.71/1.09 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.71/1.09 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.71/1.09 [u,rule_30]).
% 0.71/1.09 cnf('0.35.0.0',plain,
% 0.71/1.09 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.71/1.09 inference(cp,[status(thm)],['0.34.2.0','0.32.2.0',theory(equality)]),
% 0.71/1.09 [pos('L.1','L')]).
% 0.71/1.09 cnf('0.35.1.0',plain,
% 0.71/1.09 ( false = eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.71/1.09 [weight('<0,34,32,[1,0,0,1]>')]).
% 0.71/1.09 cnf('0.35.2.0',plain,
% 0.71/1.09 ( eq(apply(f(const2),apply(const2,f(const2))),apply(f(const2),apply(const2,f(const2)))) = false ),
% 0.71/1.09 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.71/1.09 [x,rule_31]).
% 0.71/1.09 cnf('0.36.0.0',plain,
% 0.71/1.09 ( false = true ),
% 0.71/1.09 inference(cp,[status(thm)],['0.35.2.0','0.33.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('0.36.1.0',plain,
% 0.71/1.09 ( false = true ),
% 0.71/1.09 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.71/1.09 [weight('<5,35,33,[1,0,0,0]>')]).
% 0.71/1.09 cnf('0.36.2.0',plain,
% 0.71/1.09 ( true = false ),
% 0.71/1.09 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.71/1.09 [x,rule_32]).
% 0.71/1.09 cnf('1.0.0.0',conjecture,
% 0.71/1.09 ( true = false ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017',conjecture_1)).
% 0.71/1.09 cnf('1.0.0.1',plain,
% 0.71/1.09 ( false = false ),
% 0.71/1.09 inference(reduction,[status(thm)],['1.0.0.0','0.36.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('1.0.0.2',plain,
% 0.71/1.09 ( $true ),
% 0.71/1.09 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.71/1.09 [conjecture_1]).
% 0.71/1.09 joined goal: 4 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.71/1.09 goal joined
% 0.71/1.09 #START OF PROOF
% 0.71/1.09 % SZS output start CNFRefutation
% 0.71/1.09 cnf('4.0.0.0',conjecture,
% 0.71/1.09 ( true = false ),
% 0.71/1.09 file('/tmp/WALDMEISTER_23812_n017',conjecture_4)).
% 0.71/1.09 cnf('4.0.0.1',plain,
% 0.71/1.09 ( false = false ),
% 0.71/1.09 inference(reduction,[status(thm)],['4.0.0.0','0.36.2.0',theory(equality)]),
% 0.71/1.09 [pos('L','L')]).
% 0.71/1.09 cnf('4.0.0.2',plain,
% 0.71/1.09 ( $true ),
% 0.71/1.09 inference(trivial,[status(thm)],['4.0.0.1',theory(equality)]),
% 0.71/1.09 [conjecture_4]).
% 0.71/1.09
% 0.71/1.09 Proved Goals:
% 0.71/1.09 No. 1: true ?= false, current false ?= false
% 0.71/1.09 using narrowing to prove x1 ?= apply(const1,x1)
% 0.71/1.09
% 0.71/1.09 No. 3: apply(const2,const1) ?= apply(const1,apply(const2,const1)) joined, current: apply(const1,apply(m,apply(apply(apply(c,b),m),const1))) = apply(const1,apply(m,apply(apply(apply(c,b),m),const1)))
% 0.71/1.09 No. 4: true ?= false, current false ?= false
% 0.71/1.09 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.71/1.09
% 0.71/1.09 1 goal was specified, which was proved.
% 0.71/1.09 % SZS output end CNFRefutation
% 0.71/1.09 #END OF PROOF
% 0.71/1.09
% 0.71/1.09 Problem WALDMEISTER_23812_n017
% 0.71/1.09 CPs.gen 137
% 0.71/1.09 CPs.reexp 0
% 0.71/1.09 Select 150
% 0.71/1.09 R 32
% 0.71/1.09 E 4
% 0.71/1.09 vsize 6.5M
% 0.71/1.09 rss 3.7M
% 0.71/1.09 process.time 0.004s
% 0.71/1.09 wallclock.time 0.119s
% 0.71/1.09 status S
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Waldmeister states: Goal proved.
% 0.71/1.09 % SZS status Unsatisfiable
% 0.71/1.09
% 0.71/1.09 Problem WALDMEISTER_23812_n017
% 0.71/1.09 CPs.gen 5933
% 0.71/1.09 CPs.reexp 0
% 0.71/1.09 Select 356
% 0.71/1.09 R 86
% 0.71/1.09 E 32
% 0.71/1.09 vsize 6.5M
% 0.71/1.09 rss 3.7M
% 0.71/1.09 process.time 0.116s
% 0.71/1.09 wallclock.time 0.120s
% 0.71/1.09 status S
%------------------------------------------------------------------------------