TSTP Solution File: COL037-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL037-1 : 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 0.61s 1.03s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL037-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n017.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 06:59:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.98 * |/ | \/ | *
% 0.57/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.98 * A. Jaeger and B. Loechner | | *
% 0.57/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.57/0.98
% 0.57/0.98 Goals:
% 0.57/0.98 ------
% 0.57/0.98
% 0.57/0.98 ( 1) true ?= false
% 0.57/0.98 using narrowing to prove x1 ?= apply(const1,x1)
% 0.57/0.98
% 0.57/0.98 Detected structure: KombinatorlogikB
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.61/1.03 joined goal: 1 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.61/1.03 goal joined
% 0.61/1.03 % SZS status Unsatisfiable
% 0.61/1.03 #START OF PROOF
% 0.61/1.03 % SZS output start CNFRefutation
% 0.61/1.03 cnf('0.1.0.0',axiom,
% 0.61/1.03 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03 cnf('0.1.1.0',plain,
% 0.61/1.03 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.61/1.03 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.61/1.03 cnf('0.1.2.0',plain,
% 0.61/1.03 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.61/1.03 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.61/1.03 [x,rule_1]).
% 0.61/1.03 cnf('0.2.0.0',axiom,
% 0.61/1.03 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03 cnf('0.2.1.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.61/1.03 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.61/1.03 cnf('0.2.2.0',plain,
% 0.61/1.03 ( apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2) ),
% 0.61/1.03 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.61/1.03 [x,rule_2]).
% 0.61/1.03 cnf('0.3.0.0',axiom,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03 cnf('0.3.1.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.61/1.03 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.61/1.03 cnf('0.3.2.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03 inference(activate,[status(thm)],['0.3.1.0']),
% 0.61/1.03 [equation_1]).
% 0.61/1.03 cnf('0.4.0.0',axiom,
% 0.61/1.03 ( eq(X1,X1) = true ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03 cnf('0.4.1.0',plain,
% 0.61/1.03 ( eq(X1,X1) = true ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.61/1.03 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.61/1.03 cnf('0.4.2.0',plain,
% 0.61/1.03 ( eq(X1,X1) = true ),
% 0.61/1.03 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.61/1.03 [u,rule_3]).
% 0.61/1.03 cnf('0.5.0.0',axiom,
% 0.61/1.03 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03 cnf('0.5.1.0',plain,
% 0.61/1.03 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.03 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.03 cnf('0.5.2.0',plain,
% 0.61/1.03 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.03 [u,rule_4]).
% 0.61/1.03 cnf('0.6.0.0',plain,
% 0.61/1.03 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.1.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.1','L')]).
% 0.61/1.03 cnf('0.6.1.0',plain,
% 0.61/1.03 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.03 [weight('<16,3,1,[0,0,0,1]>')]).
% 0.61/1.03 cnf('0.6.2.0',plain,
% 0.61/1.03 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03 inference(activate,[status(thm)],['0.6.1.0']),
% 0.61/1.03 [equation_2]).
% 0.61/1.03 cnf('0.10.0.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.2.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.1','L')]).
% 0.61/1.03 cnf('0.10.1.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.03 [weight('<16,3,2,[0,0,0,1]>')]).
% 0.61/1.03 cnf('0.10.2.0',plain,
% 0.61/1.03 ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03 inference(activate,[status(thm)],['0.10.1.0']),
% 0.61/1.03 [equation_4]).
% 0.61/1.03 cnf('0.11.0.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(f(apply(apply(apply(s,c),X1),X2)),apply(apply(X2,f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2)))) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.5.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.2.2','R')]).
% 0.61/1.03 cnf('0.11.1.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(f(apply(apply(apply(s,c),X1),X2)),apply(apply(X2,f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2)))) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.61/1.03 [weight('<546,10,5,[0,1,0,8]>')]).
% 0.61/1.03 cnf('0.11.1.1',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(apply(apply(apply(s,b),X2),f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2))) ),
% 0.61/1.03 inference(reduction,[status(thm)],['0.11.1.0','0.6.2.0',theory(equality)]),
% 0.61/1.03 [pos('R.2','L')]).
% 0.61/1.03 cnf('0.11.2.0',plain,
% 0.61/1.03 ( eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(apply(apply(apply(s,b),X2),f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2))) = false ),
% 0.61/1.03 inference(orient,[status(thm)],['0.11.1.1',theory(equality)]),
% 0.61/1.03 [x,rule_7]).
% 0.61/1.03 cnf('0.12.0.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.3.2.0','0.2.2.0',theory(equality)]),
% 0.61/1.03 [pos('L','L')]).
% 0.61/1.03 cnf('0.12.1.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.61/1.03 [weight('<16,3,2,[1,0,0,0]>')]).
% 0.61/1.03 cnf('0.12.2.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03 inference(activate,[status(thm)],['0.12.1.0']),
% 0.61/1.03 [equation_5]).
% 0.61/1.03 cnf('0.13.0.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(c,X1),apply(X2,X1)),f(apply(apply(apply(s,c),X2),X1))),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.1.1','R')]).
% 0.61/1.03 cnf('0.13.0.1',plain,
% 0.61/1.03 ( false = eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03 inference(reduction,[status(thm)],['0.13.0.0','0.2.2.0',theory(equality)]),
% 0.61/1.03 [pos('R.1','L')]).
% 0.61/1.03 cnf('0.13.1.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.13.0.1']),
% 0.61/1.03 [weight('<320,11,3,[1,0,1,2]>')]).
% 0.61/1.03 cnf('0.13.2.0',plain,
% 0.61/1.03 ( eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) = false ),
% 0.61/1.03 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.61/1.03 [x,rule_8]).
% 0.61/1.03 cnf('0.24.0.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.12.2.0','0.1.2.0',theory(equality)]),
% 0.61/1.03 [pos('R','L')]).
% 0.61/1.03 cnf('0.24.1.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.61/1.03 [weight('<18,12,1,[1,1,0,0]>')]).
% 0.61/1.03 cnf('0.24.2.0',plain,
% 0.61/1.03 ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03 inference(activate,[status(thm)],['0.24.1.0']),
% 0.61/1.03 [equation_10]).
% 0.61/1.03 cnf('0.25.0.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(X1,X2),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.13.2.0','0.24.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.2.1.1','R')]).
% 0.61/1.03 cnf('0.25.1.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(X1,X2),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.61/1.03 [weight('<0,24,13,[0,1,0,17]>')]).
% 0.61/1.03 cnf('0.25.1.1',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03 inference(reduction,[status(thm)],['0.25.1.0','0.10.2.0',theory(equality)]),
% 0.61/1.03 [pos('R.1','L')]).
% 0.61/1.03 cnf('0.25.2.0',plain,
% 0.61/1.03 ( eq(apply(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)),f(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X2),X3),f(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)))),apply(X1,apply(apply(X2,X3),X3)))) = false ),
% 0.61/1.03 inference(orient,[status(thm)],['0.25.1.1',theory(equality)]),
% 0.61/1.03 [x,rule_15]).
% 0.61/1.03 cnf('0.26.0.0',plain,
% 0.61/1.03 ( false = eq(apply(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))))),apply(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))))))) ),
% 0.61/1.03 inference(cp,[status(thm)],['0.25.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.03 [pos('L.2','L')]).
% 0.61/1.03 cnf('0.26.0.1',plain,
% 0.61/1.03 ( false = true ),
% 0.61/1.03 inference(reduction,[status(thm)],['0.26.0.0','0.4.2.0',theory(equality)]),
% 0.61/1.03 [pos('R','L')]).
% 0.61/1.03 cnf('0.26.1.0',plain,
% 0.61/1.03 ( false = true ),
% 0.61/1.03 inference(weigh,[status(thm)],['0.26.0.1']),
% 0.61/1.03 [weight('<2,25,10,[1,0,0,25]>')]).
% 0.61/1.03 cnf('0.26.2.0',plain,
% 0.61/1.03 ( true = false ),
% 0.61/1.03 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.61/1.03 [x,rule_16]).
% 0.61/1.03 cnf('1.0.0.0',conjecture,
% 0.61/1.03 ( true = false ),
% 0.61/1.03 file('/tmp/WALDMEISTER_18610_n017',conjecture_1)).
% 0.61/1.03 cnf('1.0.0.1',plain,
% 0.61/1.03 ( false = false ),
% 0.61/1.03 inference(reduction,[status(thm)],['1.0.0.0','0.26.2.0',theory(equality)]),
% 0.61/1.03 [pos('L','L')]).
% 0.61/1.03 cnf('1.0.0.2',plain,
% 0.61/1.03 ( $true ),
% 0.61/1.03 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.61/1.03 [conjecture_1]).
% 0.61/1.03
% 0.61/1.03 Proved Goals:
% 0.61/1.03 No. 1: true ?= false, current false ?= false
% 0.61/1.03 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.61/1.03
% 0.61/1.03 1 goal was specified, which was proved.
% 0.61/1.03 % SZS output end CNFRefutation
% 0.61/1.03 #END OF PROOF
% 0.61/1.03
% 0.61/1.03 Problem WALDMEISTER_18610_n017
% 0.61/1.03 CPs.gen 2059
% 0.61/1.03 CPs.reexp 0
% 0.61/1.03 Select 32
% 0.61/1.03 R 16
% 0.61/1.03 E 10
% 0.61/1.03 vsize 6.5M
% 0.61/1.03 rss 3.6M
% 0.61/1.03 process.time 0.046s
% 0.61/1.03 wallclock.time 0.047s
% 0.61/1.03 status S
% 0.61/1.03
% 0.61/1.03
% 0.61/1.03 Waldmeister states: Goal proved.
% 0.61/1.03 % SZS status Unsatisfiable
% 0.61/1.03
% 0.61/1.03 Problem WALDMEISTER_18610_n017
% 0.61/1.03 CPs.gen 0
% 0.61/1.03 CPs.reexp 0
% 0.61/1.03 Select 0
% 0.61/1.03 R 0
% 0.61/1.03 E 0
% 0.61/1.03 vsize 6.0M
% 0.61/1.03 rss 3.2M
% 0.61/1.03 process.time 0.001s
% 0.61/1.03 wallclock.time 0.046s
% 0.61/1.03 status S
%------------------------------------------------------------------------------