%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n004.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 07:08:05 PM UTC 2026
% Result : Unsatisfiable 0.65s 1.04s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.12 % Command : woody %s
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 11:16:02 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.65/1.04 ********************************************************************************
% 0.65/1.04 * W A L D M E I S T E R \| \ / \|/ *
% 0.65/1.04 * |/ | \/ | *
% 0.65/1.04 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.65/1.04 * A. Jaeger and B. Loechner | | *
% 0.65/1.04 * <waldmeister@informatik.uni-kl.de> | *
% 0.65/1.04 ********************************************************************************
% 0.65/1.04
% 0.65/1.04
% 0.65/1.04 Goals:
% 0.65/1.04 ------
% 0.65/1.04
% 0.65/1.04 ( 1) true ?= false
% 0.65/1.04 using narrowing to prove btrue ?= eq2(prop_merge_ord_not3(x2,x1),bfalse)
% 0.65/1.04
% 0.65/1.04 Detected structure: Orkus
% 0.65/1.04 ********************************************************************************
% 0.65/1.04 ****************************** COMPLETION - PROOF ******************************
% 0.65/1.04 ********************************************************************************
% 0.65/1.04
% 0.65/1.04 joined goal: 1 btrue ?= eq2(prop_merge_ord_not3(x2,x1),bfalse) to false
% 0.65/1.04 goal joined
% 0.65/1.04 % SZS status Unsatisfiable
% 0.65/1.04 #START OF PROOF
% 0.65/1.04 % SZS output start CNFRefutation
% 0.65/1.04 cnf('0.1.0.0',axiom,
% 0.65/1.04 ( X1 = merge(nil,X1) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.1.1.0',plain,
% 0.65/1.04 ( X1 = merge(nil,X1) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.65/1.04 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.65/1.04 cnf('0.1.2.0',plain,
% 0.65/1.04 ( merge(nil,X1) = X1 ),
% 0.65/1.04 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_1]).
% 0.65/1.04 cnf('0.2.0.0',axiom,
% 0.65/1.04 ( X1 = impl(btrue,X1) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.2.1.0',plain,
% 0.65/1.04 ( X1 = impl(btrue,X1) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.65/1.04 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.65/1.04 cnf('0.2.2.0',plain,
% 0.65/1.04 ( impl(btrue,X1) = X1 ),
% 0.65/1.04 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_2]).
% 0.65/1.04 cnf('0.4.0.0',axiom,
% 0.65/1.04 ( btrue = ord(nil) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.4.1.0',plain,
% 0.65/1.04 ( btrue = ord(nil) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.65/1.04 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.65/1.04 cnf('0.4.2.0',plain,
% 0.65/1.04 ( ord(nil) = btrue ),
% 0.65/1.04 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_4]).
% 0.65/1.04 cnf('0.6.0.0',axiom,
% 0.65/1.04 ( btrue = eq2(X1,X1) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.6.1.0',plain,
% 0.65/1.04 ( btrue = eq2(X1,X1) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.65/1.04 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.65/1.04 cnf('0.6.2.0',plain,
% 0.65/1.04 ( eq2(X1,X1) = btrue ),
% 0.65/1.04 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_6]).
% 0.65/1.04 cnf('0.9.0.0',axiom,
% 0.65/1.04 ( bfalse = leqNat(s(X1),z) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.9.1.0',plain,
% 0.65/1.04 ( bfalse = leqNat(s(X1),z) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.65/1.04 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.65/1.04 cnf('0.9.2.0',plain,
% 0.65/1.04 ( leqNat(s(X1),z) = bfalse ),
% 0.65/1.04 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_9]).
% 0.65/1.04 cnf('0.11.0.0',axiom,
% 0.65/1.04 ( bfalse = eq2(bfalse,btrue) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.11.1.0',plain,
% 0.65/1.04 ( bfalse = eq2(bfalse,btrue) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.65/1.04 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.65/1.04 cnf('0.11.2.0',plain,
% 0.65/1.04 ( eq2(bfalse,btrue) = bfalse ),
% 0.65/1.04 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_11]).
% 0.65/1.04 cnf('0.14.0.0',axiom,
% 0.65/1.04 ( bfalse = aux2(X1,X2,X3,bfalse) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.14.1.0',plain,
% 0.65/1.04 ( bfalse = aux2(X1,X2,X3,bfalse) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.65/1.04 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.65/1.04 cnf('0.14.2.0',plain,
% 0.65/1.04 ( aux2(X1,X2,X3,bfalse) = bfalse ),
% 0.65/1.04 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_14]).
% 0.65/1.04 cnf('0.19.0.0',axiom,
% 0.65/1.04 ( ord(cons(X1,cons(X2,X3))) = aux2(X1,X2,X3,leqNat(X1,X2)) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.19.1.0',plain,
% 0.65/1.04 ( ord(cons(X1,cons(X2,X3))) = aux2(X1,X2,X3,leqNat(X1,X2)) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.65/1.04 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.65/1.04 cnf('0.19.2.0',plain,
% 0.65/1.04 ( aux2(X1,X2,X3,leqNat(X1,X2)) = ord(cons(X1,cons(X2,X3))) ),
% 0.65/1.04 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_19]).
% 0.65/1.04 cnf('0.23.0.0',axiom,
% 0.65/1.04 ( impl(eq2(ord(X1),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X1,X2)),btrue))) = prop_merge_ord_not3(X1,X2) ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.23.1.0',plain,
% 0.65/1.04 ( impl(eq2(ord(X1),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X1,X2)),btrue))) = prop_merge_ord_not3(X1,X2) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.65/1.04 [weight('<22,0,0,[0,0,0,23]>')]).
% 0.65/1.04 cnf('0.23.2.0',plain,
% 0.65/1.04 ( impl(eq2(ord(X1),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X1,X2)),btrue))) = prop_merge_ord_not3(X1,X2) ),
% 0.65/1.04 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.65/1.04 [u,rule_23]).
% 0.65/1.04 cnf('0.24.0.0',axiom,
% 0.65/1.04 ( eq1(X1,X1) = true ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.24.1.0',plain,
% 0.65/1.04 ( eq1(X1,X1) = true ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.65/1.04 [weight('<23,0,0,[0,0,0,24]>')]).
% 0.65/1.04 cnf('0.24.2.0',plain,
% 0.65/1.04 ( eq1(X1,X1) = true ),
% 0.65/1.04 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.65/1.04 [u,rule_24]).
% 0.65/1.04 cnf('0.25.0.0',axiom,
% 0.65/1.04 ( eq1(btrue,eq2(prop_merge_ord_not3(X2,X1),bfalse)) = false ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004')).
% 0.65/1.04 cnf('0.25.1.0',plain,
% 0.65/1.04 ( eq1(btrue,eq2(prop_merge_ord_not3(X2,X1),bfalse)) = false ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.65/1.04 [weight('<24,0,0,[0,0,0,25]>')]).
% 0.65/1.04 cnf('0.25.2.0',plain,
% 0.65/1.04 ( eq1(btrue,eq2(prop_merge_ord_not3(X1,X2),bfalse)) = false ),
% 0.65/1.04 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.65/1.04 [u,rule_25]).
% 0.65/1.04 cnf('0.29.0.0',plain,
% 0.65/1.04 ( ord(cons(s(X1),cons(z,X2))) = aux2(s(X1),z,X2,bfalse) ),
% 0.65/1.04 inference(cp,[status(thm)],['0.19.2.0','0.9.2.0',theory(equality)]),
% 0.65/1.04 [pos('L.4','L')]).
% 0.65/1.04 cnf('0.29.0.1',plain,
% 0.65/1.04 ( ord(cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.29.0.0','0.14.2.0',theory(equality)]),
% 0.65/1.04 [pos('R','L')]).
% 0.65/1.04 cnf('0.29.1.0',plain,
% 0.65/1.04 ( ord(cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.29.0.1']),
% 0.65/1.04 [weight('<71,19,9,[1,0,0,4]>')]).
% 0.65/1.04 cnf('0.29.2.0',plain,
% 0.65/1.04 ( ord(cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.65/1.04 [u,rule_29]).
% 0.65/1.04 cnf('0.36.0.0',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,X1) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue))) ),
% 0.65/1.04 inference(cp,[status(thm)],['0.23.2.0','0.1.2.0',theory(equality)]),
% 0.65/1.04 [pos('L.2.2.1.1','L')]).
% 0.65/1.04 cnf('0.36.0.1',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,X1) = impl(eq2(btrue,btrue),impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue))) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.36.0.0','0.4.2.0',theory(equality)]),
% 0.65/1.04 [pos('R.1.1','L')]).
% 0.65/1.04 cnf('0.36.0.2',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,X1) = impl(btrue,impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue))) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.36.0.1','0.6.2.0',theory(equality)]),
% 0.65/1.04 [pos('R.1','L')]).
% 0.65/1.04 cnf('0.36.0.3',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,X1) = impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue)) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.36.0.2','0.2.2.0',theory(equality)]),
% 0.65/1.04 [pos('R','L')]).
% 0.65/1.04 cnf('0.36.1.0',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,X1) = impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue)) ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.36.0.3']),
% 0.65/1.04 [weight('<129,23,1,[1,0,0,12]>')]).
% 0.65/1.04 cnf('0.36.2.0',plain,
% 0.65/1.04 ( impl(eq2(ord(X1),bfalse),eq2(ord(X1),btrue)) = prop_merge_ord_not3(nil,X1) ),
% 0.65/1.04 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_36]).
% 0.65/1.04 cnf('0.38.0.0',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = impl(eq2(bfalse,bfalse),eq2(ord(cons(s(X1),cons(z,X2))),btrue)) ),
% 0.65/1.04 inference(cp,[status(thm)],['0.36.2.0','0.29.2.0',theory(equality)]),
% 0.65/1.04 [pos('L.1.1','L')]).
% 0.65/1.04 cnf('0.38.0.1',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = impl(btrue,eq2(ord(cons(s(X1),cons(z,X2))),btrue)) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.38.0.0','0.6.2.0',theory(equality)]),
% 0.65/1.04 [pos('R.1','L')]).
% 0.65/1.04 cnf('0.38.0.2',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = eq2(ord(cons(s(X1),cons(z,X2))),btrue) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.38.0.1','0.2.2.0',theory(equality)]),
% 0.65/1.04 [pos('R','L')]).
% 0.65/1.04 cnf('0.38.0.3',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = eq2(bfalse,btrue) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.38.0.2','0.29.2.0',theory(equality)]),
% 0.65/1.04 [pos('R.1','L')]).
% 0.65/1.04 cnf('0.38.0.4',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.38.0.3','0.11.2.0',theory(equality)]),
% 0.65/1.04 [pos('R','L')]).
% 0.65/1.04 cnf('0.38.1.0',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.38.0.4']),
% 0.65/1.04 [weight('<89,36,29,[1,0,0,2]>')]).
% 0.65/1.04 cnf('0.38.2.0',plain,
% 0.65/1.04 ( prop_merge_ord_not3(nil,cons(s(X1),cons(z,X2))) = bfalse ),
% 0.65/1.04 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.65/1.04 [u,rule_38]).
% 0.65/1.04 cnf('0.39.0.0',plain,
% 0.65/1.04 ( false = eq1(btrue,eq2(bfalse,bfalse)) ),
% 0.65/1.04 inference(cp,[status(thm)],['0.25.2.0','0.38.2.0',theory(equality)]),
% 0.65/1.04 [pos('L.2.1','L')]).
% 0.65/1.04 cnf('0.39.0.1',plain,
% 0.65/1.04 ( false = eq1(btrue,btrue) ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.39.0.0','0.6.2.0',theory(equality)]),
% 0.65/1.04 [pos('R.2','L')]).
% 0.65/1.04 cnf('0.39.0.2',plain,
% 0.65/1.04 ( false = true ),
% 0.65/1.04 inference(reduction,[status(thm)],['0.39.0.1','0.24.2.0',theory(equality)]),
% 0.65/1.04 [pos('R','L')]).
% 0.65/1.04 cnf('0.39.1.0',plain,
% 0.65/1.04 ( false = true ),
% 0.65/1.04 inference(weigh,[status(thm)],['0.39.0.2']),
% 0.65/1.04 [weight('<5,38,25,[0,0,0,3]>')]).
% 0.65/1.04 cnf('0.39.2.0',plain,
% 0.65/1.04 ( true = false ),
% 0.65/1.04 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.65/1.04 [x,rule_39]).
% 0.65/1.04 cnf('1.0.0.0',conjecture,
% 0.65/1.04 ( true = false ),
% 0.65/1.04 file('/tmp/WALDMEISTER_28808_n004',conjecture_1)).
% 0.65/1.04 cnf('1.0.0.1',plain,
% 0.65/1.04 ( false = false ),
% 0.65/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.39.2.0',theory(equality)]),
% 0.65/1.04 [pos('L','L')]).
% 0.65/1.04 cnf('1.0.0.2',plain,
% 0.65/1.04 ( $true ),
% 0.65/1.04 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.65/1.04 [conjecture_1]).
% 0.65/1.04
% 0.65/1.04 Proved Goals:
% 0.65/1.04 No. 1: true ?= false, current false ?= false
% 0.65/1.04 using narrowing to prove btrue ?= eq2(prop_merge_ord_not3(x2,x1),bfalse)
% 0.65/1.04
% 0.65/1.04 1 goal was specified, which was proved.
% 0.65/1.04 % SZS output end CNFRefutation
% 0.65/1.04 #END OF PROOF
% 0.65/1.04
% 0.65/1.04 Problem WALDMEISTER_28808_n004
% 0.65/1.04 CPs.gen 61
% 0.65/1.04 CPs.reexp 0
% 0.65/1.04 Select 46
% 0.65/1.04 R 39
% 0.65/1.04 E 0
% 0.65/1.04 vsize 6.7M
% 0.65/1.04 rss 4.0M
% 0.65/1.04 process.time 0.003s
% 0.65/1.04 wallclock.time 0.003s
% 0.65/1.04 status S
% 0.65/1.04
% 0.65/1.04
% 0.65/1.04 Waldmeister states: Goal proved.
% 0.65/1.04 % SZS status Unsatisfiable
%------------------------------------------------------------------------------