TSTP Solution File: LCL161-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LCL161-1 : 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 : Sun Jul 17 16:03:56 EDT 2022
% Result : Unsatisfiable 0.59s 0.96s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n029.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 : Mon Jul 4 13:45:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.96 ********************************************************************************
% 0.59/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.96 * |/ | \/ | *
% 0.59/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.96 * A. Jaeger and B. Loechner | | *
% 0.59/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.96 ********************************************************************************
% 0.59/0.96
% 0.59/0.96
% 0.59/0.96 Goals:
% 0.59/0.96 ------
% 0.59/0.96
% 0.59/0.96 ( 1) implies(truth,x) ?=? x
% 0.59/0.96
% 0.59/0.96 Detected structure: AlternativeWajsbergAlgebra
% 0.59/0.96 ********************************************************************************
% 0.59/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.96 ********************************************************************************
% 0.59/0.96
% 0.59/0.96 joined goal: 1 implies(truth,x) ?= x to x
% 0.59/0.96 goal joined
% 0.59/0.96 % SZS status Unsatisfiable
% 0.59/0.96 #START OF PROOF
% 0.59/0.96 % SZS output start CNFRefutation
% 0.59/0.96 cnf('0.1.0.0',axiom,
% 0.59/0.96 ( X1 = xor(X1,falsehood) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.1.1.0',plain,
% 0.59/0.96 ( X1 = xor(X1,falsehood) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/0.96 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/0.96 cnf('0.1.2.0',plain,
% 0.59/0.96 ( xor(X1,falsehood) = X1 ),
% 0.59/0.96 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_1]).
% 0.59/0.96 cnf('0.2.0.0',axiom,
% 0.59/0.96 ( X1 = and_star(X1,truth) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.2.1.0',plain,
% 0.59/0.96 ( X1 = and_star(X1,truth) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.59/0.96 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.59/0.96 cnf('0.2.2.0',plain,
% 0.59/0.96 ( and_star(X1,truth) = X1 ),
% 0.59/0.96 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_2]).
% 0.59/0.96 cnf('0.3.0.0',axiom,
% 0.59/0.96 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.3.1.0',plain,
% 0.59/0.96 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.59/0.96 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.59/0.96 cnf('0.3.2.0',plain,
% 0.59/0.96 ( xor(X1,X2) = xor(X2,X1) ),
% 0.59/0.96 inference(activate,[status(thm)],['0.3.1.0']),
% 0.59/0.96 [equation_1]).
% 0.59/0.96 cnf('0.5.0.0',axiom,
% 0.59/0.96 ( xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.5.1.0',plain,
% 0.59/0.96 ( xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.59/0.96 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.59/0.96 cnf('0.5.2.0',plain,
% 0.59/0.96 ( xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_4]).
% 0.59/0.96 cnf('0.6.0.0',axiom,
% 0.59/0.96 ( xor(X1,truth) = not(X1) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.6.1.0',plain,
% 0.59/0.96 ( xor(X1,truth) = not(X1) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.59/0.96 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.59/0.96 cnf('0.6.2.0',plain,
% 0.59/0.96 ( xor(X1,truth) = not(X1) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.59/0.96 [u,rule_5]).
% 0.59/0.96 cnf('0.7.0.0',axiom,
% 0.59/0.96 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.7.1.0',plain,
% 0.59/0.96 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.59/0.96 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.59/0.96 cnf('0.7.2.0',plain,
% 0.59/0.96 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.59/0.96 [u,rule_6]).
% 0.59/0.96 cnf('0.8.0.0',axiom,
% 0.59/0.96 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.8.1.0',plain,
% 0.59/0.96 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.59/0.96 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.59/0.96 cnf('0.8.2.0',plain,
% 0.59/0.96 ( and_star(X1,X2) = and_star(X2,X1) ),
% 0.59/0.96 inference(activate,[status(thm)],['0.8.1.0']),
% 0.59/0.96 [equation_2]).
% 0.59/0.96 cnf('0.13.0.0',axiom,
% 0.59/0.96 ( falsehood = not(truth) ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029')).
% 0.59/0.96 cnf('0.13.1.0',plain,
% 0.59/0.96 ( falsehood = not(truth) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.59/0.96 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.59/0.96 cnf('0.13.2.0',plain,
% 0.59/0.96 ( not(truth) = falsehood ),
% 0.59/0.96 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_10]).
% 0.59/0.96 cnf('0.16.0.0',plain,
% 0.59/0.96 ( and_star(truth,X1) = X1 ),
% 0.59/0.96 inference(cp,[status(thm)],['0.8.2.0','0.2.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('0.16.1.0',plain,
% 0.59/0.96 ( and_star(truth,X1) = X1 ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.59/0.96 [weight('<19,8,2,[1,0,0,0]>')]).
% 0.59/0.96 cnf('0.16.2.0',plain,
% 0.59/0.96 ( and_star(truth,X1) = X1 ),
% 0.59/0.96 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.59/0.96 [u,rule_13]).
% 0.59/0.96 cnf('0.20.0.0',plain,
% 0.59/0.96 ( not(X1) = xor(truth,X1) ),
% 0.59/0.96 inference(cp,[status(thm)],['0.6.2.0','0.3.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('0.20.1.0',plain,
% 0.59/0.96 ( not(X1) = xor(truth,X1) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.59/0.96 [weight('<23,6,3,[1,0,0,0]>')]).
% 0.59/0.96 cnf('0.20.2.0',plain,
% 0.59/0.96 ( xor(truth,X1) = not(X1) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_17]).
% 0.59/0.96 cnf('0.22.0.0',plain,
% 0.59/0.96 ( xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(interreduction_right,[status(thm)],['0.7.2.0'])).
% 0.59/0.96 cnf('0.22.0.1',plain,
% 0.59/0.96 ( not(and_star(X1,xor(truth,X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.22.0.0','0.20.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('0.22.0.2',plain,
% 0.59/0.96 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.22.0.1','0.20.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2','L')]).
% 0.59/0.96 cnf('0.22.1.0',plain,
% 0.59/0.96 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.22.0.2']),
% 0.59/0.96 [weight('<53,7,20,[0,0,0,0]>')]).
% 0.59/0.96 cnf('0.22.2.0',plain,
% 0.59/0.96 ( not(and_star(X1,not(X2))) = implies(X1,X2) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.59/0.96 [u,rule_19]).
% 0.59/0.96 cnf('0.25.0.0',plain,
% 0.59/0.96 ( implies(truth,X1) = not(not(X1)) ),
% 0.59/0.96 inference(cp,[status(thm)],['0.22.2.0','0.16.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1','L')]).
% 0.59/0.96 cnf('0.25.1.0',plain,
% 0.59/0.96 ( implies(truth,X1) = not(not(X1)) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.59/0.96 [weight('<27,22,16,[1,0,0,1]>')]).
% 0.59/0.96 cnf('0.25.2.0',plain,
% 0.59/0.96 ( not(not(X1)) = implies(truth,X1) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_22]).
% 0.59/0.96 cnf('0.32.0.0',plain,
% 0.59/0.96 ( xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/0.96 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.59/0.96 cnf('0.32.0.1',plain,
% 0.59/0.96 ( xor(not(X1),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.32.0.0','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1','L')]).
% 0.59/0.96 cnf('0.32.1.0',plain,
% 0.59/0.96 ( xor(not(X1),X2) = xor(X1,xor(truth,X2)) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.32.0.1']),
% 0.59/0.96 [weight('<59,5,6,[0,0,0,0]>')]).
% 0.59/0.96 cnf('0.32.1.1',plain,
% 0.59/0.96 ( xor(not(X1),X2) = xor(X1,not(X2)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.32.1.0','0.20.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.2','L')]).
% 0.59/0.96 cnf('0.32.2.0',plain,
% 0.59/0.96 ( xor(not(X1),X2) = xor(X1,not(X2)) ),
% 0.59/0.96 inference(orient,[status(thm)],['0.32.1.1',theory(equality)]),
% 0.59/0.96 [u,rule_29]).
% 0.59/0.96 cnf('0.33.0.0',plain,
% 0.59/0.96 ( xor(X1,not(truth)) = not(not(X1)) ),
% 0.59/0.96 inference(cp,[status(thm)],['0.32.2.0','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('0.33.0.1',plain,
% 0.59/0.96 ( xor(X1,falsehood) = not(not(X1)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.33.0.0','0.13.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.2','L')]).
% 0.59/0.96 cnf('0.33.0.2',plain,
% 0.59/0.96 ( X1 = not(not(X1)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.33.0.1','0.1.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('0.33.0.3',plain,
% 0.59/0.96 ( X1 = implies(truth,X1) ),
% 0.59/0.96 inference(reduction,[status(thm)],['0.33.0.2','0.25.2.0',theory(equality)]),
% 0.59/0.96 [pos('R','L')]).
% 0.59/0.96 cnf('0.33.1.0',plain,
% 0.59/0.96 ( X1 = implies(truth,X1) ),
% 0.59/0.96 inference(weigh,[status(thm)],['0.33.0.3']),
% 0.59/0.96 [weight('<19,32,6,[1,0,0,0]>')]).
% 0.59/0.96 cnf('0.33.2.0',plain,
% 0.59/0.96 ( implies(truth,X1) = X1 ),
% 0.59/0.96 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.59/0.96 [x,rule_30]).
% 0.59/0.96 cnf('1.0.0.0',conjecture,
% 0.59/0.96 ( implies(truth,x) = x ),
% 0.59/0.96 file('/tmp/WALDMEISTER_8029_n029',conjecture_1)).
% 0.59/0.96 cnf('1.0.0.1',plain,
% 0.59/0.96 ( x = x ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.0','0.33.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('1.0.0.2',plain,
% 0.59/0.96 ( $true ),
% 0.59/0.96 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.59/0.96 [conjecture_1]).
% 0.59/0.96
% 0.59/0.96 Proved Goals:
% 0.59/0.96 No. 1: implies(truth,x) ?= x joined, current: x = x
% 0.59/0.96 1 goal was specified, which was proved.
% 0.59/0.96 % SZS output end CNFRefutation
% 0.59/0.96 #END OF PROOF
% 0.59/0.96
% 0.59/0.96 Problem WALDMEISTER_8029_n029
% 0.59/0.96 CPs.gen 179
% 0.59/0.96 CPs.reexp 0
% 0.59/0.96 Select 36
% 0.59/0.96 R 30
% 0.59/0.96 E 3
% 0.59/0.96 vsize 6.5M
% 0.59/0.96 rss 3.8M
% 0.59/0.96 process.time 0.003s
% 0.59/0.96 wallclock.time 0.003s
% 0.59/0.96 status S
% 0.59/0.96
% 0.59/0.96
% 0.59/0.96 Waldmeister states: Goal proved.
% 0.59/0.96 % SZS status Unsatisfiable
%------------------------------------------------------------------------------