TSTP Solution File: GRP687-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP687-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n027.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 : Sat Jul 16 12:27:53 EDT 2022
% Result : Unsatisfiable 0.57s 0.99s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP687-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n027.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 Jun 13 12:58:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.96 * |/ | \/ | *
% 0.57/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.96 * A. Jaeger and B. Loechner | | *
% 0.57/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 0.57/0.96
% 0.57/0.96 Goals:
% 0.57/0.96 ------
% 0.57/0.96
% 0.57/0.96 ( 1) mult(mult(a,mult(b,b)),c) ?=? mult(a,mult(b,mult(b,c)))
% 0.57/0.96
% 0.57/0.96 Detected structure: Loop
% 0.57/0.96 ********************************************************************************
% 0.57/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.96 ********************************************************************************
% 0.57/0.96
% 0.57/0.99 joined goal: 1 mult(mult(a,mult(b,b)),c) ?= mult(a,mult(b,mult(b,c))) to mult(a,mult(b,mult(b,c)))
% 0.57/0.99 goal joined
% 0.57/0.99 % SZS status Unsatisfiable
% 0.57/0.99 #START OF PROOF
% 0.57/0.99 % SZS output start CNFRefutation
% 0.57/0.99 cnf('0.1.0.0',axiom,
% 0.57/0.99 ( X1 = mult(X2,ld(X2,X1)) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.1.1.0',plain,
% 0.57/0.99 ( X1 = mult(X2,ld(X2,X1)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.57/0.99 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.1.2.0',plain,
% 0.57/0.99 ( mult(X1,ld(X1,X2)) = X2 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_1]).
% 0.57/0.99 cnf('0.2.0.0',axiom,
% 0.57/0.99 ( X1 = mult(X1,unit) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.2.1.0',plain,
% 0.57/0.99 ( X1 = mult(X1,unit) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.57/0.99 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.2.2.0',plain,
% 0.57/0.99 ( mult(X1,unit) = X1 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_2]).
% 0.57/0.99 cnf('0.4.0.0',axiom,
% 0.57/0.99 ( X1 = mult(rd(X1,X2),X2) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.4.1.0',plain,
% 0.57/0.99 ( X1 = mult(rd(X1,X2),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.57/0.99 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.57/0.99 cnf('0.4.2.0',plain,
% 0.57/0.99 ( mult(rd(X1,X2),X2) = X1 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_4]).
% 0.57/0.99 cnf('0.5.0.0',axiom,
% 0.57/0.99 ( X1 = rd(mult(X1,X2),X2) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.5.1.0',plain,
% 0.57/0.99 ( X1 = rd(mult(X1,X2),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.57/0.99 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.57/0.99 cnf('0.5.2.0',plain,
% 0.57/0.99 ( rd(mult(X1,X2),X2) = X1 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_5]).
% 0.57/0.99 cnf('0.6.0.0',axiom,
% 0.57/0.99 ( X1 = ld(X2,mult(X2,X1)) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.6.1.0',plain,
% 0.57/0.99 ( X1 = ld(X2,mult(X2,X1)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.57/0.99 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.57/0.99 cnf('0.6.2.0',plain,
% 0.57/0.99 ( ld(X1,mult(X1,X2)) = X2 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_6]).
% 0.57/0.99 cnf('0.7.0.0',axiom,
% 0.57/0.99 ( mult(mult(X1,X1),mult(X2,X3)) = mult(mult(X1,mult(X1,X2)),X3) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027')).
% 0.57/0.99 cnf('0.7.1.0',plain,
% 0.57/0.99 ( mult(mult(X1,X1),mult(X2,X3)) = mult(mult(X1,mult(X1,X2)),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.57/0.99 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.57/0.99 cnf('0.7.2.0',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X1,X2)),X3) = mult(mult(X1,X1),mult(X2,X3)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_7]).
% 0.57/0.99 cnf('0.11.0.0',plain,
% 0.57/0.99 ( unit = ld(X1,X1) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.6.2.0','0.2.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.11.1.0',plain,
% 0.57/0.99 ( unit = ld(X1,X1) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.57/0.99 [weight('<19,6,2,[1,0,0,2]>')]).
% 0.57/0.99 cnf('0.11.2.0',plain,
% 0.57/0.99 ( ld(X1,X1) = unit ),
% 0.57/0.99 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_11]).
% 0.57/0.99 cnf('0.12.0.0',plain,
% 0.57/0.99 ( X1 = rd(X2,ld(X1,X2)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.12.1.0',plain,
% 0.57/0.99 ( X1 = rd(X2,ld(X1,X2)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.57/0.99 [weight('<41,5,1,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.12.2.0',plain,
% 0.57/0.99 ( rd(X1,ld(X2,X1)) = X2 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_12]).
% 0.57/0.99 cnf('0.13.0.0',plain,
% 0.57/0.99 ( X1 = ld(rd(X2,X1),X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.6.2.0','0.4.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.13.1.0',plain,
% 0.57/0.99 ( X1 = ld(rd(X2,X1),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.57/0.99 [weight('<41,6,4,[1,0,0,2]>')]).
% 0.57/0.99 cnf('0.13.2.0',plain,
% 0.57/0.99 ( ld(rd(X1,X2),X1) = X2 ),
% 0.57/0.99 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_13]).
% 0.57/0.99 cnf('0.14.0.0',plain,
% 0.57/0.99 ( mult(mult(X1,X1),mult(X2,unit)) = mult(X1,mult(X1,X2)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 0.57/0.99 [pos('L','L')]).
% 0.57/0.99 cnf('0.14.0.1',plain,
% 0.57/0.99 ( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.14.0.0','0.2.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.14.1.0',plain,
% 0.57/0.99 ( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.14.0.1']),
% 0.57/0.99 [weight('<65,7,2,[1,0,0,0]>')]).
% 0.57/0.99 cnf('0.14.2.0',plain,
% 0.57/0.99 ( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_14]).
% 0.57/0.99 cnf('0.15.0.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.15.1.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.57/0.99 [weight('<87,14,5,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.15.2.0',plain,
% 0.57/0.99 ( rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_15]).
% 0.57/0.99 cnf('0.16.0.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.15.2.0','0.1.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1.2','L')]).
% 0.57/0.99 cnf('0.16.1.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.57/0.99 [weight('<87,15,1,[1,0,0,3]>')]).
% 0.57/0.99 cnf('0.16.2.0',plain,
% 0.57/0.99 ( rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_16]).
% 0.57/0.99 cnf('0.19.0.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(X2,ld(X1,ld(X1,X2))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.16.2.0','0.1.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.19.1.0',plain,
% 0.57/0.99 ( mult(X1,X1) = rd(X2,ld(X1,ld(X1,X2))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.57/0.99 [weight('<87,16,1,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.19.2.0',plain,
% 0.57/0.99 ( rd(X1,ld(X2,ld(X2,X1))) = mult(X2,X2) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_19]).
% 0.57/0.99 cnf('0.20.0.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,X2)) = ld(mult(X1,X1),X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.13.2.0','0.19.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.20.1.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,X2)) = ld(mult(X1,X1),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.57/0.99 [weight('<65,19,13,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.20.2.0',plain,
% 0.57/0.99 ( ld(mult(X1,X1),X2) = ld(X1,ld(X1,X2)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_20]).
% 0.57/0.99 cnf('0.22.0.0',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X1,X2)),X3) = mult(mult(X1,X1),mult(X2,X3)) ),
% 0.57/0.99 inference(interreduction_right,[status(thm)],['0.7.2.0'])).
% 0.57/0.99 cnf('0.22.0.1',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X1,X2)),X3) = mult(X1,mult(X1,mult(X2,X3))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.22.0.0','0.14.2.0',theory(equality)]),
% 0.57/0.99 [pos('R','L')]).
% 0.57/0.99 cnf('0.22.1.0',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X1,X2)),X3) = mult(X1,mult(X1,mult(X2,X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.22.0.1']),
% 0.57/0.99 [weight('<119,7,14,[0,0,0,0]>')]).
% 0.57/0.99 cnf('0.22.2.0',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X1,X2)),X3) = mult(X1,mult(X1,mult(X2,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_22]).
% 0.57/0.99 cnf('0.28.0.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,mult(ld(X1,X2),X3))) = mult(mult(X1,X2),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.22.2.0','0.1.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1.2','L')]).
% 0.57/0.99 cnf('0.28.1.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,mult(ld(X1,X2),X3))) = mult(mult(X1,X2),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.57/0.99 [weight('<149,22,1,[1,0,0,3]>')]).
% 0.57/0.99 cnf('0.28.2.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,mult(ld(X1,X2),X3))) = mult(mult(X1,X2),X3) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_28]).
% 0.57/0.99 cnf('0.29.0.0',plain,
% 0.57/0.99 ( mult(X1,mult(ld(X1,X2),X3)) = ld(X1,mult(mult(X1,X2),X3)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.6.2.0','0.28.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.29.1.0',plain,
% 0.57/0.99 ( mult(X1,mult(ld(X1,X2),X3)) = ld(X1,mult(mult(X1,X2),X3)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.57/0.99 [weight('<119,28,6,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.29.2.0',plain,
% 0.57/0.99 ( mult(X1,mult(ld(X1,X2),X3)) = ld(X1,mult(mult(X1,X2),X3)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_29]).
% 0.57/0.99 cnf('0.30.0.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,X2)) = rd(mult(X1,mult(X1,mult(X2,X3))),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.5.2.0','0.22.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.30.1.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,X2)) = rd(mult(X1,mult(X1,mult(X2,X3))),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.57/0.99 [weight('<149,22,5,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.30.2.0',plain,
% 0.57/0.99 ( rd(mult(X1,mult(X1,mult(X2,X3))),X3) = mult(X1,mult(X1,X2)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_30]).
% 0.57/0.99 cnf('0.31.0.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,rd(X2,X3))) = rd(mult(X1,mult(X1,X2)),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.30.2.0','0.4.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1.2.2','L')]).
% 0.57/0.99 cnf('0.31.1.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,rd(X2,X3))) = rd(mult(X1,mult(X1,X2)),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.57/0.99 [weight('<119,30,4,[1,0,0,5]>')]).
% 0.57/0.99 cnf('0.31.2.0',plain,
% 0.57/0.99 ( mult(X1,mult(X1,rd(X2,X3))) = rd(mult(X1,mult(X1,X2)),X3) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_31]).
% 0.57/0.99 cnf('0.33.0.0',plain,
% 0.57/0.99 ( mult(ld(X1,X2),X3) = ld(X1,ld(X1,mult(mult(X1,X2),X3))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.6.2.0','0.29.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.33.1.0',plain,
% 0.57/0.99 ( mult(ld(X1,X2),X3) = ld(X1,ld(X1,mult(mult(X1,X2),X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.33.0.0']),
% 0.57/0.99 [weight('<149,29,6,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.33.2.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(ld(X1,X2),X3) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_33]).
% 0.57/0.99 cnf('0.34.0.0',plain,
% 0.57/0.99 ( mult(ld(X1,unit),X2) = ld(X1,ld(X1,mult(X1,X2))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.33.2.0','0.2.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2.2.1','L')]).
% 0.57/0.99 cnf('0.34.0.1',plain,
% 0.57/0.99 ( mult(ld(X1,unit),X2) = ld(X1,X2) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.34.0.0','0.6.2.0',theory(equality)]),
% 0.57/0.99 [pos('R.2','L')]).
% 0.57/0.99 cnf('0.34.1.0',plain,
% 0.57/0.99 ( mult(ld(X1,unit),X2) = ld(X1,X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.34.0.1']),
% 0.57/0.99 [weight('<53,33,2,[1,0,0,5]>')]).
% 0.57/0.99 cnf('0.34.2.0',plain,
% 0.57/0.99 ( mult(ld(X1,unit),X2) = ld(X1,X2) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_34]).
% 0.57/0.99 cnf('0.35.0.0',plain,
% 0.57/0.99 ( ld(X1,unit) = rd(ld(X1,X2),X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.5.2.0','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.35.1.0',plain,
% 0.57/0.99 ( ld(X1,unit) = rd(ld(X1,X2),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.57/0.99 [weight('<53,34,5,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.35.2.0',plain,
% 0.57/0.99 ( rd(ld(X1,X2),X2) = ld(X1,unit) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_35]).
% 0.57/0.99 cnf('0.36.0.0',plain,
% 0.57/0.99 ( ld(X1,unit) = rd(unit,X1) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.35.2.0','0.11.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.36.1.0',plain,
% 0.57/0.99 ( ld(X1,unit) = rd(unit,X1) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.57/0.99 [weight('<27,35,11,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.36.2.0',plain,
% 0.57/0.99 ( rd(unit,X1) = ld(X1,unit) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_36]).
% 0.57/0.99 cnf('0.38.0.0',plain,
% 0.57/0.99 ( ld(rd(unit,X1),X2) = mult(X1,X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.34.2.0','0.13.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.38.1.0',plain,
% 0.57/0.99 ( ld(rd(unit,X1),X2) = mult(X1,X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.57/0.99 [weight('<53,34,13,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.38.1.1',plain,
% 0.57/0.99 ( ld(ld(X1,unit),X2) = mult(X1,X2) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.38.1.0','0.36.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.38.2.0',plain,
% 0.57/0.99 ( ld(ld(X1,unit),X2) = mult(X1,X2) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.38.1.1',theory(equality)]),
% 0.57/0.99 [u,rule_38]).
% 0.57/0.99 cnf('0.56.0.0',plain,
% 0.57/0.99 ( rd(mult(ld(X1,unit),mult(ld(X1,unit),X2)),X3) = mult(ld(X1,unit),ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.31.2.0','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.56.0.1',plain,
% 0.57/0.99 ( rd(ld(X1,mult(ld(X1,unit),X2)),X3) = mult(ld(X1,unit),ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.56.0.0','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.56.0.2',plain,
% 0.57/0.99 ( rd(ld(X1,ld(X1,X2)),X3) = mult(ld(X1,unit),ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.56.0.1','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1.2','L')]).
% 0.57/0.99 cnf('0.56.0.3',plain,
% 0.57/0.99 ( rd(ld(X1,ld(X1,X2)),X3) = ld(X1,ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.56.0.2','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('R','L')]).
% 0.57/0.99 cnf('0.56.1.0',plain,
% 0.57/0.99 ( rd(ld(X1,ld(X1,X2)),X3) = ld(X1,ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.56.0.3']),
% 0.57/0.99 [weight('<119,34,31,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.56.2.0',plain,
% 0.57/0.99 ( rd(ld(X1,ld(X1,X2)),X3) = ld(X1,ld(X1,rd(X2,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_56]).
% 0.57/0.99 cnf('0.57.0.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,rd(X1,X2))) = rd(ld(X1,unit),X2) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.56.2.0','0.11.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1.2','L')]).
% 0.57/0.99 cnf('0.57.1.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,rd(X1,X2))) = rd(ld(X1,unit),X2) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.57/0.99 [weight('<103,56,11,[1,0,0,3]>')]).
% 0.57/0.99 cnf('0.57.2.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,rd(X1,X2))) = rd(ld(X1,unit),X2) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_57]).
% 0.57/0.99 cnf('0.59.0.0',plain,
% 0.57/0.99 ( rd(ld(X1,unit),ld(X2,X1)) = ld(X1,ld(X1,X2)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.57.2.0','0.12.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2.2','L')]).
% 0.57/0.99 cnf('0.59.1.0',plain,
% 0.57/0.99 ( rd(ld(X1,unit),ld(X2,X1)) = ld(X1,ld(X1,X2)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.59.0.0']),
% 0.57/0.99 [weight('<103,57,12,[1,0,0,4]>')]).
% 0.57/0.99 cnf('0.59.2.0',plain,
% 0.57/0.99 ( rd(ld(X1,unit),ld(X2,X1)) = ld(X1,ld(X1,X2)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_59]).
% 0.57/0.99 cnf('0.61.0.0',plain,
% 0.57/0.99 ( ld(mult(X1,X1),ld(mult(X1,X1),X2)) = rd(ld(X1,ld(X1,unit)),ld(X2,mult(X1,X1))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.59.2.0','0.20.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.61.0.1',plain,
% 0.57/0.99 ( ld(X1,ld(X1,ld(mult(X1,X1),X2))) = rd(ld(X1,ld(X1,unit)),ld(X2,mult(X1,X1))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.61.0.0','0.20.2.0',theory(equality)]),
% 0.57/0.99 [pos('L','L')]).
% 0.57/0.99 cnf('0.61.0.2',plain,
% 0.57/0.99 ( ld(X1,ld(X1,ld(X1,ld(X1,X2)))) = rd(ld(X1,ld(X1,unit)),ld(X2,mult(X1,X1))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.61.0.1','0.20.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2.2','L')]).
% 0.57/0.99 cnf('0.61.0.3',plain,
% 0.57/0.99 ( ld(X1,ld(X1,ld(X1,ld(X1,X2)))) = ld(X1,ld(X1,rd(unit,ld(X2,mult(X1,X1))))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.61.0.2','0.56.2.0',theory(equality)]),
% 0.57/0.99 [pos('R','L')]).
% 0.57/0.99 cnf('0.61.0.4',plain,
% 0.57/0.99 ( ld(X1,ld(X1,ld(X1,ld(X1,X2)))) = ld(X1,ld(X1,ld(ld(X2,mult(X1,X1)),unit))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.61.0.3','0.36.2.0',theory(equality)]),
% 0.57/0.99 [pos('R.2.2','L')]).
% 0.57/0.99 cnf('0.61.1.0',plain,
% 0.57/0.99 ( ld(X1,ld(X1,X2)) = ld(ld(X2,mult(X1,X1)),unit) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.61.0.4']),
% 0.57/0.99 [weight('<103,59,20,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.61.2.0',plain,
% 0.57/0.99 ( ld(ld(X1,mult(X2,X2)),unit) = ld(X2,ld(X2,X1)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_61]).
% 0.57/0.99 cnf('0.64.0.0',plain,
% 0.57/0.99 ( ld(X1,mult(X2,X2)) = rd(unit,ld(X2,ld(X2,X1))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.12.2.0','0.61.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.64.0.1',plain,
% 0.57/0.99 ( ld(X1,mult(X2,X2)) = ld(ld(X2,ld(X2,X1)),unit) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.64.0.0','0.36.2.0',theory(equality)]),
% 0.57/0.99 [pos('R','L')]).
% 0.57/0.99 cnf('0.64.1.0',plain,
% 0.57/0.99 ( ld(X1,mult(X2,X2)) = ld(ld(X2,ld(X2,X1)),unit) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.64.0.1']),
% 0.57/0.99 [weight('<103,61,12,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.64.2.0',plain,
% 0.57/0.99 ( ld(ld(X1,ld(X1,X2)),unit) = ld(X2,mult(X1,X1)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_64]).
% 0.57/0.99 cnf('0.88.0.0',plain,
% 0.57/0.99 ( ld(ld(X1,ld(X1,X2)),X3) = mult(ld(X2,mult(X1,X1)),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.34.2.0','0.64.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.88.1.0',plain,
% 0.57/0.99 ( ld(ld(X1,ld(X1,X2)),X3) = mult(ld(X2,mult(X1,X1)),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.88.0.0']),
% 0.57/0.99 [weight('<119,64,34,[0,0,0,1]>')]).
% 0.57/0.99 cnf('0.88.2.0',plain,
% 0.57/0.99 ( mult(ld(X1,mult(X2,X2)),X3) = ld(ld(X2,ld(X2,X1)),X3) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.88.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_88]).
% 0.57/0.99 cnf('0.107.0.0',plain,
% 0.57/0.99 ( mult(ld(X1,X2),ld(mult(X1,X2),X3)) = ld(X1,ld(X1,X3)) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.33.2.0','0.1.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2.2','L')]).
% 0.57/0.99 cnf('0.107.1.0',plain,
% 0.57/0.99 ( mult(ld(X1,X2),ld(mult(X1,X2),X3)) = ld(X1,ld(X1,X3)) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.107.0.0']),
% 0.57/0.99 [weight('<149,33,1,[1,0,0,4]>')]).
% 0.57/0.99 cnf('0.107.2.0',plain,
% 0.57/0.99 ( mult(ld(X1,X2),ld(mult(X1,X2),X3)) = ld(X1,ld(X1,X3)) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_107]).
% 0.57/0.99 cnf('0.123.0.0',plain,
% 0.57/0.99 ( ld(mult(X1,X2),X3) = ld(ld(X1,X2),ld(X1,ld(X1,X3))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.6.2.0','0.107.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.123.1.0',plain,
% 0.57/0.99 ( ld(mult(X1,X2),X3) = ld(ld(X1,X2),ld(X1,ld(X1,X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.123.0.0']),
% 0.57/0.99 [weight('<149,107,6,[0,0,0,2]>')]).
% 0.57/0.99 cnf('0.123.2.0',plain,
% 0.57/0.99 ( ld(ld(X1,X2),ld(X1,ld(X1,X3))) = ld(mult(X1,X2),X3) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.123.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_123]).
% 0.57/0.99 cnf('0.124.0.0',plain,
% 0.57/0.99 ( ld(mult(X1,mult(X1,X2)),X3) = ld(X2,ld(X1,ld(X1,X3))) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.123.2.0','0.6.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.124.1.0',plain,
% 0.57/0.99 ( ld(mult(X1,mult(X1,X2)),X3) = ld(X2,ld(X1,ld(X1,X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.124.0.0']),
% 0.57/0.99 [weight('<119,123,6,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.124.2.0',plain,
% 0.57/0.99 ( ld(mult(X1,mult(X1,X2)),X3) = ld(X2,ld(X1,ld(X1,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_124]).
% 0.57/0.99 cnf('0.126.0.0',plain,
% 0.57/0.99 ( ld(X1,ld(ld(X2,unit),ld(ld(X2,unit),X3))) = ld(ld(X2,mult(ld(X2,unit),X1)),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.124.2.0','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.126.0.1',plain,
% 0.57/0.99 ( ld(X1,mult(X2,ld(ld(X2,unit),X3))) = ld(ld(X2,mult(ld(X2,unit),X1)),X3) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.126.0.0','0.38.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2','L')]).
% 0.57/0.99 cnf('0.126.0.2',plain,
% 0.57/0.99 ( ld(X1,mult(X2,mult(X2,X3))) = ld(ld(X2,mult(ld(X2,unit),X1)),X3) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.126.0.1','0.38.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.2.2','L')]).
% 0.57/0.99 cnf('0.126.0.3',plain,
% 0.57/0.99 ( ld(X1,mult(X2,mult(X2,X3))) = ld(ld(X2,ld(X2,X1)),X3) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.126.0.2','0.34.2.0',theory(equality)]),
% 0.57/0.99 [pos('R.1.2','L')]).
% 0.57/0.99 cnf('0.126.1.0',plain,
% 0.57/0.99 ( ld(X1,mult(X2,mult(X2,X3))) = ld(ld(X2,ld(X2,X1)),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.126.0.3']),
% 0.57/0.99 [weight('<119,124,34,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.126.2.0',plain,
% 0.57/0.99 ( ld(ld(X1,ld(X1,X2)),X3) = ld(X2,mult(X1,mult(X1,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_126]).
% 0.57/0.99 cnf('0.127.0.0',plain,
% 0.57/0.99 ( mult(ld(X1,mult(X2,X2)),X3) = ld(ld(X2,ld(X2,X1)),X3) ),
% 0.57/0.99 inference(interreduction_right,[status(thm)],['0.88.2.0'])).
% 0.57/0.99 cnf('0.127.0.1',plain,
% 0.57/0.99 ( mult(ld(X1,mult(X2,X2)),X3) = ld(X1,mult(X2,mult(X2,X3))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.127.0.0','0.126.2.0',theory(equality)]),
% 0.57/0.99 [pos('R','L')]).
% 0.57/0.99 cnf('0.127.1.0',plain,
% 0.57/0.99 ( mult(ld(X1,mult(X2,X2)),X3) = ld(X1,mult(X2,mult(X2,X3))) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.127.0.1']),
% 0.57/0.99 [weight('<119,88,126,[0,0,0,0]>')]).
% 0.57/0.99 cnf('0.127.2.0',plain,
% 0.57/0.99 ( mult(ld(X1,mult(X2,X2)),X3) = ld(X1,mult(X2,mult(X2,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.127.1.0',theory(equality)]),
% 0.57/0.99 [u,rule_127]).
% 0.57/0.99 cnf('0.128.0.0',plain,
% 0.57/0.99 ( ld(ld(X1,unit),mult(X2,mult(X2,X3))) = mult(mult(X1,mult(X2,X2)),X3) ),
% 0.57/0.99 inference(cp,[status(thm)],['0.127.2.0','0.38.2.0',theory(equality)]),
% 0.57/0.99 [pos('L.1','L')]).
% 0.57/0.99 cnf('0.128.0.1',plain,
% 0.57/0.99 ( mult(X1,mult(X2,mult(X2,X3))) = mult(mult(X1,mult(X2,X2)),X3) ),
% 0.57/0.99 inference(reduction,[status(thm)],['0.128.0.0','0.38.2.0',theory(equality)]),
% 0.57/0.99 [pos('L','L')]).
% 0.57/0.99 cnf('0.128.1.0',plain,
% 0.57/0.99 ( mult(X1,mult(X2,mult(X2,X3))) = mult(mult(X1,mult(X2,X2)),X3) ),
% 0.57/0.99 inference(weigh,[status(thm)],['0.128.0.1']),
% 0.57/0.99 [weight('<119,127,38,[1,0,0,1]>')]).
% 0.57/0.99 cnf('0.128.2.0',plain,
% 0.57/0.99 ( mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))) ),
% 0.57/0.99 inference(orient,[status(thm)],['0.128.1.0',theory(equality)]),
% 0.57/0.99 [x,rule_128]).
% 0.57/0.99 cnf('1.0.0.0',conjecture,
% 0.57/0.99 ( mult(mult(a,mult(b,b)),c) = mult(a,mult(b,mult(b,c))) ),
% 0.57/0.99 file('/tmp/WALDMEISTER_8001_n027',conjecture_1)).
% 0.57/0.99 cnf('1.0.0.1',plain,
% 0.57/0.99 ( mult(a,mult(b,mult(b,c))) = mult(a,mult(b,mult(b,c))) ),
% 0.57/0.99 inference(reduction,[status(thm)],['1.0.0.0','0.128.2.0',theory(equality)]),
% 0.57/0.99 [pos('L','L')]).
% 0.57/0.99 cnf('1.0.0.2',plain,
% 0.57/0.99 ( $true ),
% 0.57/0.99 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.57/0.99 [conjecture_1]).
% 0.57/0.99
% 0.57/0.99 Proved Goals:
% 0.57/0.99 No. 1: mult(mult(a,mult(b,b)),c) ?= mult(a,mult(b,mult(b,c))) joined, current: mult(a,mult(b,mult(b,c))) = mult(a,mult(b,mult(b,c)))
% 0.57/0.99 1 goal was specified, which was proved.
% 0.57/0.99 % SZS output end CNFRefutation
% 0.57/0.99 #END OF PROOF
% 0.57/0.99
% 0.57/0.99 Problem WALDMEISTER_8001_n027
% 0.57/0.99 CPs.gen 5220
% 0.57/0.99 CPs.reexp 0
% 0.57/0.99 Select 360
% 0.57/0.99 R 128
% 0.57/0.99 E 0
% 0.57/0.99 vsize 6.5M
% 0.57/0.99 rss 3.8M
% 0.57/0.99 process.time 0.036s
% 0.57/0.99 wallclock.time 0.036s
% 0.57/0.99 status S
% 0.57/0.99
% 0.57/0.99
% 0.57/0.99 Waldmeister states: Goal proved.
% 0.57/0.99 % SZS status Unsatisfiable
%------------------------------------------------------------------------------