%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n005.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 : 300s
% DateTime : Tue May 5 07:08:06 PM UTC 2026
% Result : Unsatisfiable 0.58s 0.99s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : woody %s
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 11:34:30 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.58/0.99 ********************************************************************************
% 0.58/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.58/0.99 * |/ | \/ | *
% 0.58/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.58/0.99 * A. Jaeger and B. Loechner | | *
% 0.58/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.58/0.99 ********************************************************************************
% 0.58/0.99
% 0.58/0.99
% 0.58/0.99 Goals:
% 0.58/0.99 ------
% 0.58/0.99
% 0.58/0.99 ( 1) true ?= false
% 0.58/0.99 using narrowing to prove btrue ?= eq2(plus_not_idem(x1),bfalse)
% 0.58/0.99
% 0.58/0.99 Detected structure: Orkus
% 0.58/0.99 ********************************************************************************
% 0.58/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.58/0.99 ********************************************************************************
% 0.58/0.99
% 0.58/0.99 joined goal: 1 btrue ?= eq2(plus_not_idem(x1),bfalse) to false
% 0.58/0.99 goal joined
% 0.58/0.99 % SZS status Unsatisfiable
% 0.58/0.99 #START OF PROOF
% 0.58/0.99 % SZS output start CNFRefutation
% 0.58/0.99 cnf('0.1.0.0',axiom,
% 0.58/0.99 ( X1 = x2(z,X1) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.1.1.0',plain,
% 0.58/0.99 ( X1 = x2(z,X1) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.58/0.99 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.58/0.99 cnf('0.1.2.0',plain,
% 0.58/0.99 ( x2(z,X1) = X1 ),
% 0.58/0.99 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_1]).
% 0.58/0.99 cnf('0.2.0.0',axiom,
% 0.58/0.99 ( X1 = impl(btrue,X1) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.2.1.0',plain,
% 0.58/0.99 ( X1 = impl(btrue,X1) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.58/0.99 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.58/0.99 cnf('0.2.2.0',plain,
% 0.58/0.99 ( impl(btrue,X1) = X1 ),
% 0.58/0.99 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_2]).
% 0.58/0.99 cnf('0.6.0.0',axiom,
% 0.58/0.99 ( bfalse = eq2(btrue,bfalse) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.6.1.0',plain,
% 0.58/0.99 ( bfalse = eq2(btrue,bfalse) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.58/0.99 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.58/0.99 cnf('0.6.2.0',plain,
% 0.58/0.99 ( eq2(btrue,bfalse) = bfalse ),
% 0.58/0.99 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_6]).
% 0.58/0.99 cnf('0.7.0.0',axiom,
% 0.58/0.99 ( btrue = eq(X1,X1) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.7.1.0',plain,
% 0.58/0.99 ( btrue = eq(X1,X1) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.58/0.99 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.58/0.99 cnf('0.7.2.0',plain,
% 0.58/0.99 ( eq(X1,X1) = btrue ),
% 0.58/0.99 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_7]).
% 0.58/0.99 cnf('0.8.0.0',axiom,
% 0.58/0.99 ( btrue = eq2(X1,X1) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.8.1.0',plain,
% 0.58/0.99 ( btrue = eq2(X1,X1) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.58/0.99 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.58/0.99 cnf('0.8.2.0',plain,
% 0.58/0.99 ( eq2(X1,X1) = btrue ),
% 0.58/0.99 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_8]).
% 0.58/0.99 cnf('0.12.0.0',axiom,
% 0.58/0.99 ( impl(eq(x2(X1,X1),X1),eq2(btrue,bfalse)) = plus_not_idem(X1) ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.12.1.0',plain,
% 0.58/0.99 ( impl(eq(x2(X1,X1),X1),eq2(btrue,bfalse)) = plus_not_idem(X1) ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.58/0.99 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.58/0.99 cnf('0.12.1.1',plain,
% 0.58/0.99 ( impl(eq(x2(X1,X1),X1),bfalse) = plus_not_idem(X1) ),
% 0.58/0.99 inference(reduction,[status(thm)],['0.12.1.0','0.6.2.0',theory(equality)]),
% 0.58/0.99 [pos('L.2','L')]).
% 0.58/0.99 cnf('0.12.2.0',plain,
% 0.58/0.99 ( impl(eq(x2(X1,X1),X1),bfalse) = plus_not_idem(X1) ),
% 0.58/0.99 inference(orient,[status(thm)],['0.12.1.1',theory(equality)]),
% 0.58/0.99 [u,rule_12]).
% 0.58/0.99 cnf('0.13.0.0',axiom,
% 0.58/0.99 ( eq1(X1,X1) = true ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.13.1.0',plain,
% 0.58/0.99 ( eq1(X1,X1) = true ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.58/0.99 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.58/0.99 cnf('0.13.2.0',plain,
% 0.58/0.99 ( eq1(X1,X1) = true ),
% 0.58/0.99 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.58/0.99 [u,rule_13]).
% 0.58/0.99 cnf('0.14.0.0',axiom,
% 0.58/0.99 ( eq1(btrue,eq2(plus_not_idem(X1),bfalse)) = false ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005')).
% 0.58/0.99 cnf('0.14.1.0',plain,
% 0.58/0.99 ( eq1(btrue,eq2(plus_not_idem(X1),bfalse)) = false ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.58/0.99 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.58/0.99 cnf('0.14.2.0',plain,
% 0.58/0.99 ( eq1(btrue,eq2(plus_not_idem(X1),bfalse)) = false ),
% 0.58/0.99 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.58/0.99 [u,rule_14]).
% 0.58/0.99 cnf('0.15.0.0',plain,
% 0.58/0.99 ( plus_not_idem(z) = impl(eq(z,z),bfalse) ),
% 0.58/0.99 inference(cp,[status(thm)],['0.12.2.0','0.1.2.0',theory(equality)]),
% 0.58/0.99 [pos('L.1.1','L')]).
% 0.58/0.99 cnf('0.15.0.1',plain,
% 0.58/0.99 ( plus_not_idem(z) = impl(btrue,bfalse) ),
% 0.58/0.99 inference(reduction,[status(thm)],['0.15.0.0','0.7.2.0',theory(equality)]),
% 0.58/0.99 [pos('R.1','L')]).
% 0.58/0.99 cnf('0.15.0.2',plain,
% 0.58/0.99 ( plus_not_idem(z) = bfalse ),
% 0.58/0.99 inference(reduction,[status(thm)],['0.15.0.1','0.2.2.0',theory(equality)]),
% 0.58/0.99 [pos('R','L')]).
% 0.58/0.99 cnf('0.15.1.0',plain,
% 0.58/0.99 ( plus_not_idem(z) = bfalse ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.15.0.2']),
% 0.58/0.99 [weight('<11,12,1,[1,0,0,2]>')]).
% 0.58/0.99 cnf('0.15.2.0',plain,
% 0.58/0.99 ( plus_not_idem(z) = bfalse ),
% 0.58/0.99 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.58/0.99 [u,rule_15]).
% 0.58/0.99 cnf('0.16.0.0',plain,
% 0.58/0.99 ( false = eq1(btrue,eq2(bfalse,bfalse)) ),
% 0.58/0.99 inference(cp,[status(thm)],['0.14.2.0','0.15.2.0',theory(equality)]),
% 0.58/0.99 [pos('L.2.1','L')]).
% 0.58/0.99 cnf('0.16.0.1',plain,
% 0.58/0.99 ( false = eq1(btrue,btrue) ),
% 0.58/0.99 inference(reduction,[status(thm)],['0.16.0.0','0.8.2.0',theory(equality)]),
% 0.58/0.99 [pos('R.2','L')]).
% 0.58/0.99 cnf('0.16.0.2',plain,
% 0.58/0.99 ( false = true ),
% 0.58/0.99 inference(reduction,[status(thm)],['0.16.0.1','0.13.2.0',theory(equality)]),
% 0.58/0.99 [pos('R','L')]).
% 0.58/0.99 cnf('0.16.1.0',plain,
% 0.58/0.99 ( false = true ),
% 0.58/0.99 inference(weigh,[status(thm)],['0.16.0.2']),
% 0.58/0.99 [weight('<5,15,14,[0,0,0,3]>')]).
% 0.58/0.99 cnf('0.16.2.0',plain,
% 0.58/0.99 ( true = false ),
% 0.58/0.99 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.58/0.99 [x,rule_16]).
% 0.58/0.99 cnf('1.0.0.0',conjecture,
% 0.58/0.99 ( true = false ),
% 0.58/0.99 file('/tmp/WALDMEISTER_14310_n005',conjecture_1)).
% 0.58/0.99 cnf('1.0.0.1',plain,
% 0.58/0.99 ( false = false ),
% 0.58/0.99 inference(reduction,[status(thm)],['1.0.0.0','0.16.2.0',theory(equality)]),
% 0.58/0.99 [pos('L','L')]).
% 0.58/0.99 cnf('1.0.0.2',plain,
% 0.58/0.99 ( $true ),
% 0.58/0.99 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.58/0.99 [conjecture_1]).
% 0.58/0.99
% 0.58/0.99 Proved Goals:
% 0.58/0.99 No. 1: true ?= false, current false ?= false
% 0.58/0.99 using narrowing to prove btrue ?= eq2(plus_not_idem(x1),bfalse)
% 0.58/0.99
% 0.58/0.99 1 goal was specified, which was proved.
% 0.58/0.99 % SZS output end CNFRefutation
% 0.58/0.99 #END OF PROOF
% 0.58/0.99
% 0.58/0.99 Problem WALDMEISTER_14310_n005
% 0.58/0.99 CPs.gen 8
% 0.58/0.99 CPs.reexp 0
% 0.58/0.99 Select 16
% 0.58/0.99 R 16
% 0.58/0.99 E 0
% 0.58/0.99 vsize 6.5M
% 0.58/0.99 rss 3.8M
% 0.58/0.99 process.time 0.002s
% 0.58/0.99 wallclock.time 0.002s
% 0.58/0.99 status S
% 0.58/0.99
% 0.58/0.99
% 0.58/0.99 Waldmeister states: Goal proved.
% 0.58/0.99 % SZS status Unsatisfiable
%------------------------------------------------------------------------------