TSTP Solution File: COL036-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL036-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n029.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 0.64s 1.06s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL036-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : woody %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 05:04:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.61/1.00 ********************************************************************************
% 0.61/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.61/1.00 * |/ | \/ | *
% 0.61/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.61/1.00 * A. Jaeger and B. Loechner | | *
% 0.61/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.61/1.00 ********************************************************************************
% 0.61/1.00
% 0.61/1.00
% 0.61/1.00 Goals:
% 0.61/1.00 ------
% 0.61/1.00
% 0.61/1.00 ( 1) true ?= false
% 0.61/1.00 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.61/1.00
% 0.61/1.00 Detected structure: KombinatorlogikBT
% 0.61/1.00 ********************************************************************************
% 0.61/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.61/1.00 ********************************************************************************
% 0.61/1.00
% 0.64/1.06 joined goal: 1 apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.64/1.06 goal joined
% 0.64/1.06 % SZS status Unsatisfiable
% 0.64/1.06 #START OF PROOF
% 0.64/1.06 % SZS output start CNFRefutation
% 0.64/1.06 cnf('0.1.0.0',axiom,
% 0.64/1.06 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029')).
% 0.64/1.06 cnf('0.1.1.0',plain,
% 0.64/1.06 ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.64/1.06 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.64/1.06 cnf('0.1.2.0',plain,
% 0.64/1.06 ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.64/1.06 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_1]).
% 0.64/1.06 cnf('0.2.0.0',axiom,
% 0.64/1.06 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029')).
% 0.64/1.06 cnf('0.2.1.0',plain,
% 0.64/1.06 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.64/1.06 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.64/1.06 cnf('0.2.2.0',plain,
% 0.64/1.06 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.64/1.06 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_2]).
% 0.64/1.06 cnf('0.3.0.0',axiom,
% 0.64/1.06 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029')).
% 0.64/1.06 cnf('0.3.1.0',plain,
% 0.64/1.06 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.64/1.06 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.64/1.06 cnf('0.3.2.0',plain,
% 0.64/1.06 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.64/1.06 inference(activate,[status(thm)],['0.3.1.0']),
% 0.64/1.06 [equation_1]).
% 0.64/1.06 cnf('0.4.0.0',axiom,
% 0.64/1.06 ( eq(X1,X1) = true ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029')).
% 0.64/1.06 cnf('0.4.1.0',plain,
% 0.64/1.06 ( eq(X1,X1) = true ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.64/1.06 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.64/1.06 cnf('0.4.2.0',plain,
% 0.64/1.06 ( eq(X1,X1) = true ),
% 0.64/1.06 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.64/1.06 [u,rule_3]).
% 0.64/1.06 cnf('0.5.0.0',axiom,
% 0.64/1.06 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029')).
% 0.64/1.06 cnf('0.5.1.0',plain,
% 0.64/1.06 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.64/1.06 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.64/1.06 cnf('0.5.2.0',plain,
% 0.64/1.06 ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.64/1.06 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.64/1.06 [u,rule_4]).
% 0.64/1.06 cnf('0.6.0.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),X1),X2) = apply(apply(X1,X2),X2) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.3.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.06 [pos('L','L')]).
% 0.64/1.06 cnf('0.6.1.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),X1),X2) = apply(apply(X1,X2),X2) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.64/1.06 [weight('<168,3,1,[1,0,0,0]>')]).
% 0.64/1.06 cnf('0.6.2.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),X1),X2) = apply(apply(X1,X2),X2) ),
% 0.64/1.06 inference(activate,[status(thm)],['0.6.1.0']),
% 0.64/1.06 [equation_2]).
% 0.64/1.06 cnf('0.9.0.0',plain,
% 0.64/1.06 ( 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))))) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.5.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.06 [pos('L.1','L')]).
% 0.64/1.06 cnf('0.9.0.1',plain,
% 0.64/1.06 ( 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)))))) ),
% 0.64/1.06 inference(reduction,[status(thm)],['0.9.0.0','0.2.2.0',theory(equality)]),
% 0.64/1.06 [pos('R.2.2','L')]).
% 0.64/1.06 cnf('0.9.1.0',plain,
% 0.64/1.06 ( 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)))))) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.9.0.1']),
% 0.64/1.06 [weight('<27,5,2,[1,0,0,1]>')]).
% 0.64/1.06 cnf('0.9.2.0',plain,
% 0.64/1.06 ( 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 ),
% 0.64/1.06 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_6]).
% 0.64/1.06 cnf('0.11.0.0',plain,
% 0.64/1.06 ( 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)))))) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.64/1.06 [pos('L.1','L')]).
% 0.64/1.06 cnf('0.11.0.1',plain,
% 0.64/1.06 ( 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))) ),
% 0.64/1.06 inference(reduction,[status(thm)],['0.11.0.0','0.1.2.0',theory(equality)]),
% 0.64/1.06 [pos('R.2.2','L')]).
% 0.64/1.06 cnf('0.11.1.0',plain,
% 0.64/1.06 ( 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))) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.11.0.1']),
% 0.64/1.06 [weight('<33,9,1,[1,0,0,1]>')]).
% 0.64/1.06 cnf('0.11.2.0',plain,
% 0.64/1.06 ( 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 ),
% 0.64/1.06 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_7]).
% 0.64/1.06 cnf('0.24.0.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),apply(b,X1)),X2) = apply(X1,apply(X2,X2)) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 0.64/1.06 [pos('R','L')]).
% 0.64/1.06 cnf('0.24.1.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),apply(b,X1)),X2) = apply(X1,apply(X2,X2)) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.64/1.06 [weight('<224,6,2,[1,1,0,0]>')]).
% 0.64/1.06 cnf('0.24.2.0',plain,
% 0.64/1.06 ( apply(apply(apply(s,t),apply(b,X1)),X2) = apply(X1,apply(X2,X2)) ),
% 0.64/1.06 inference(activate,[status(thm)],['0.24.1.0']),
% 0.64/1.06 [equation_7]).
% 0.64/1.06 cnf('0.62.0.0',plain,
% 0.64/1.06 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.2.2.0','0.3.2.0',theory(equality)]),
% 0.64/1.06 [pos('L.1','L')]).
% 0.64/1.06 cnf('0.62.1.0',plain,
% 0.64/1.06 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.64/1.06 [weight('<288,3,2,[0,0,0,1]>')]).
% 0.64/1.06 cnf('0.62.2.0',plain,
% 0.64/1.06 ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.64/1.06 inference(activate,[status(thm)],['0.62.1.0']),
% 0.64/1.06 [equation_12]).
% 0.64/1.06 cnf('0.63.0.0',plain,
% 0.64/1.06 ( 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 ),
% 0.64/1.06 inference(interreduction_right,[status(thm)],['0.11.2.0'])).
% 0.64/1.06 cnf('0.63.1.0',plain,
% 0.64/1.06 ( 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 ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.63.0.0']),
% 0.64/1.06 [weight('<33,11,62,[0,0,0,0]>')]).
% 0.64/1.06 cnf('0.63.1.1',plain,
% 0.64/1.06 ( eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(apply(apply(apply(s,b),X1),f(apply(apply(b,apply(t,X2)),X1))),X2)) = false ),
% 0.64/1.06 inference(reduction,[status(thm)],['0.63.1.0','0.62.2.0',theory(equality)]),
% 0.64/1.06 [pos('L.2','L')]).
% 0.64/1.06 cnf('0.63.2.0',plain,
% 0.64/1.06 ( eq(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),apply(apply(apply(apply(s,b),X1),f(apply(apply(b,apply(t,X2)),X1))),X2)) = false ),
% 0.64/1.06 inference(orient,[status(thm)],['0.63.1.1',theory(equality)]),
% 0.64/1.06 [u,rule_51]).
% 0.64/1.06 cnf('0.117.0.0',plain,
% 0.64/1.06 ( false = eq(apply(apply(apply(X1,X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2),apply(apply(apply(apply(apply(s,t),apply(b,apply(s,b))),X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2)) ),
% 0.64/1.06 inference(cp,[status(thm)],['0.63.2.0','0.24.2.0',theory(equality)]),
% 0.64/1.06 [pos('L.2.1.1','R')]).
% 0.64/1.06 cnf('0.117.1.0',plain,
% 0.64/1.06 ( false = eq(apply(apply(apply(X1,X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2),apply(apply(apply(apply(apply(s,t),apply(b,apply(s,b))),X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2)) ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.117.0.0']),
% 0.64/1.06 [weight('<40,63,24,[1,0,1,15]>')]).
% 0.64/1.06 cnf('0.117.2.0',plain,
% 0.64/1.06 ( eq(apply(apply(apply(X1,X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2),apply(apply(apply(apply(apply(s,t),apply(b,apply(s,b))),X1),f(apply(apply(b,apply(t,X2)),apply(X1,X1)))),X2)) = false ),
% 0.64/1.06 inference(orient,[status(thm)],['0.117.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_95]).
% 0.64/1.06 cnf('0.118.0.0',plain,
% 0.64/1.06 ( false = true ),
% 0.64/1.06 inference(cp,[status(thm)],['0.117.2.0','0.4.2.0',theory(equality)]),
% 0.64/1.06 [pos('L','L')]).
% 0.64/1.06 cnf('0.118.1.0',plain,
% 0.64/1.06 ( false = true ),
% 0.64/1.06 inference(weigh,[status(thm)],['0.118.0.0']),
% 0.64/1.06 [weight('<5,117,4,[1,0,0,0]>')]).
% 0.64/1.06 cnf('0.118.2.0',plain,
% 0.64/1.06 ( true = false ),
% 0.64/1.06 inference(orient,[status(thm)],['0.118.1.0',theory(equality)]),
% 0.64/1.06 [x,rule_96]).
% 0.64/1.06 cnf('1.0.0.0',conjecture,
% 0.64/1.06 ( true = false ),
% 0.64/1.06 file('/tmp/WALDMEISTER_26411_n029',conjecture_1)).
% 0.64/1.06 cnf('1.0.0.1',plain,
% 0.64/1.06 ( false = false ),
% 0.64/1.06 inference(reduction,[status(thm)],['1.0.0.0','0.118.2.0',theory(equality)]),
% 0.64/1.06 [pos('L','L')]).
% 0.64/1.06 cnf('1.0.0.2',plain,
% 0.64/1.06 ( $true ),
% 0.64/1.06 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.64/1.06 [conjecture_1]).
% 0.64/1.06
% 0.64/1.06 Proved Goals:
% 0.64/1.06 No. 1: true ?= false, current false ?= false
% 0.64/1.06 using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.64/1.06
% 0.64/1.06 1 goal was specified, which was proved.
% 0.64/1.06 % SZS output end CNFRefutation
% 0.64/1.06 #END OF PROOF
% 0.64/1.06
% 0.64/1.06 Problem WALDMEISTER_26411_n029
% 0.64/1.06 CPs.gen 2483
% 0.64/1.06 CPs.reexp 0
% 0.64/1.06 Select 241
% 0.64/1.06 R 96
% 0.64/1.06 E 22
% 0.64/1.06 vsize 6.5M
% 0.64/1.06 rss 3.8M
% 0.64/1.06 process.time 0.060s
% 0.64/1.06 wallclock.time 0.060s
% 0.64/1.06 status S
% 0.64/1.06
% 0.64/1.06
% 0.64/1.06 Waldmeister states: Goal proved.
% 0.64/1.06 % SZS status Unsatisfiable
%------------------------------------------------------------------------------