TSTP Solution File: LCL114-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LCL114-2 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n113.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:27:10 EDT 2014
% Result : Unsatisfiable 1.36s
% Output : Refutation 1.36s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LCL114-2 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n113.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 00:43:13 CDT 2014
% % CPUTime : 1.36
% Processing problem /tmp/CiME_24663_n113.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " y,x,truth : constant; not : 1; implies : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% implies(truth,X) = X;
% implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth;
% implies(implies(X,Y),Y) = implies(implies(Y,X),X);
% implies(implies(not(X),not(Y)),implies(Y,X)) = truth;
% ";
%
% let s1 = status F "
% y lr_lex;
% x lr_lex;
% not lr_lex;
% implies lr_lex;
% truth lr_lex;
% ";
%
% let p1 = precedence F "
% implies > not > truth > x > y";
%
% let s2 = status F "
% y mul;
% x mul;
% not mul;
% implies mul;
% truth mul;
% ";
%
% let p2 = precedence F "
% implies > not > truth = x = y";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " implies(implies(x,y),implies(not(y),not(x))) = truth;"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { implies(truth,X) = X,
% implies(implies(X,Y),implies(implies(Y,Z),
% implies(X,Z))) = truth,
% implies(implies(X,Y),Y) =
% implies(implies(Y,X),X),
% implies(implies(not(X),not(Y)),implies(Y,X)) =
% truth } (4 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { implies(implies(x,y),implies(not(y),not(x)))
% = truth } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] implies(truth,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] implies(implies(not(X),not(Y)),implies(Y,X)) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] implies(implies(X,truth),truth) -> implies(X,X)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] implies(implies(not(X),not(truth)),X) -> truth
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] implies(X,implies(implies(X,Y),Y)) -> truth
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] implies(implies(X,not(not(X))),truth) -> truth
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 10
% Rule [5] implies(implies(X,truth),truth) -> implies(X,X) is composed into
% [5] implies(implies(X,truth),truth) -> truth
% New rule produced : [11] implies(X,X) -> truth
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] implies(X,implies(implies(Y,X),X)) -> truth
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] implies(X,truth) -> truth
% Rule [5] implies(implies(X,truth),truth) -> truth collapsed.
% Rule [8] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% collapsed.
% Rule [9] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% collapsed.
% Rule [10] implies(implies(X,not(not(X))),truth) -> truth collapsed.
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [14] implies(Y,implies(X,Y)) -> truth
% Rule [12] implies(X,implies(implies(Y,X),X)) -> truth collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [15] implies(implies(X,Y),implies(X,implies(Z,Y))) -> truth
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [16] implies(implies(implies(X,Y),Z),implies(Y,Z)) -> truth
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [17] implies(X,implies(Y,implies(Z,X))) -> truth
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [18] implies(X,implies(Y,implies(implies(X,Z),Z))) -> truth
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [19] implies(implies(not(X),not(truth)),implies(Y,X)) -> truth
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [20] implies(not(X),implies(X,Y)) -> truth
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [21] implies(not(truth),X) -> truth
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [22] implies(X,implies(implies(X,Y),implies(Z,Y))) -> truth
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [23] implies(X,implies(implies(implies(Y,X),Z),Z)) -> truth
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [24] implies(X,implies(Y,implies(Z,implies(V_3,X)))) -> truth
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [25] not(not(truth)) -> truth
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [26] implies(implies(X,not(truth)),not(truth)) -> X
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [27] implies(not(X),implies(Y,implies(X,Z))) -> truth
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [28] implies(implies(X,not(truth)),implies(X,Y)) -> truth
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [29] implies(implies(implies(X,Y),Z),implies(not(X),Z)) -> truth
% Current number of equations to process: 89
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [30] implies(implies(X,not(Y)),implies(X,implies(Y,Z))) -> truth
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [31] implies(not(implies(X,Y)),implies(implies(Y,X),X)) -> truth
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [32] implies(not(implies(X,not(truth))),X) -> truth
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [33] implies(X,implies(implies(X,not(truth)),Y)) -> truth
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [34] implies(not(implies(X,not(truth))),implies(Y,X)) -> truth
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [35] implies(not(implies(X,Y)),implies(not(X),Z)) -> truth
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [36] implies(not(X),implies(implies(implies(X,Y),Z),Z)) -> truth
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [37] implies(not(X),implies(Y,implies(Z,implies(X,V_3)))) -> truth
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [38] implies(implies(X,not(truth)),implies(Y,implies(X,Z))) -> truth
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [39] implies(not(not(X)),implies(Y,X)) -> truth
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [40] implies(not(not(X)),X) -> truth
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [41] implies(not(implies(X,Y)),implies(Y,Z)) -> truth
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [42] implies(X,implies(not(X),not(truth))) -> truth
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [43] implies(implies(implies(X,Y),Y),implies(not(Y),X)) -> truth
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [44] implies(implies(not(not(X)),not(truth)),implies(X,Y)) -> truth
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [45] implies(not(implies(implies(X,Y),Y)),implies(X,Y)) -> truth
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [46] implies(not(implies(not(X),not(truth))),implies(X,Y)) -> truth
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [47] implies(X,implies(Y,implies(implies(X,not(truth)),Z))) -> truth
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [48] implies(X,implies(implies(implies(Y,X),not(truth)),Z)) -> truth
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [49] implies(not(X),implies(not(implies(X,not(truth))),Y)) -> truth
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [50] implies(not(X),implies(implies(implies(Y,X),X),Y)) -> truth
% Current number of equations to process: 163
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [51] implies(X,not(not(X))) -> truth
% Current number of equations to process: 186
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [52] implies(not(not(not(X))),implies(X,Y)) -> truth
% Current number of equations to process: 186
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [53] implies(not(not(X)),implies(implies(X,Y),Y)) -> truth
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [54] implies(not(not(X)),implies(Y,implies(Z,X))) -> truth
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [55] implies(implies(X,Y),implies(not(not(X)),Y)) -> truth
% Current number of equations to process: 182
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [56] implies(implies(X,not(not(Y))),implies(X,Y)) -> truth
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [57] not(not(X)) -> X
% Rule [25] not(not(truth)) -> truth collapsed.
% Rule [39] implies(not(not(X)),implies(Y,X)) -> truth collapsed.
% Rule [40] implies(not(not(X)),X) -> truth collapsed.
% Rule [44] implies(implies(not(not(X)),not(truth)),implies(X,Y)) -> truth
% collapsed.
% Rule [51] implies(X,not(not(X))) -> truth collapsed.
% Rule [52] implies(not(not(not(X))),implies(X,Y)) -> truth collapsed.
% Rule [53] implies(not(not(X)),implies(implies(X,Y),Y)) -> truth collapsed.
% Rule [54] implies(not(not(X)),implies(Y,implies(Z,X))) -> truth collapsed.
% Rule [55] implies(implies(X,Y),implies(not(not(X)),Y)) -> truth collapsed.
% Rule [56] implies(implies(X,not(not(Y))),implies(X,Y)) -> truth collapsed.
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [58] implies(not(X),not(truth)) -> X
% Rule [6] implies(implies(not(X),not(truth)),X) -> truth collapsed.
% Rule [19] implies(implies(not(X),not(truth)),implies(Y,X)) -> truth
% collapsed.
% Rule [42] implies(X,implies(not(X),not(truth))) -> truth collapsed.
% Rule [46] implies(not(implies(not(X),not(truth))),implies(X,Y)) -> truth
% collapsed.
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [59] implies(not(implies(X,implies(Y,not(truth)))),Y) -> truth
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [60] implies(not(implies(implies(X,Y),Y)),implies(X,Z)) -> truth
% Rule [45] implies(not(implies(implies(X,Y),Y)),implies(X,Y)) -> truth
% collapsed.
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [61] implies(not(implies(X,Y)),implies(Z,implies(Y,V_3))) -> truth
% Current number of equations to process: 188
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [62] implies(X,implies(not(X),Y)) -> truth
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [63] implies(not(implies(X,Y)),implies(not(Y),X)) -> truth
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [64] implies(X,implies(Y,implies(not(X),Z))) -> truth
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [65] implies(implies(X,not(Y)),implies(Y,not(X))) -> truth
% Current number of equations to process: 223
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [66] implies(implies(not(X),Y),implies(not(Y),X)) -> truth
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [67] implies(not(implies(not(X),Y)),implies(X,Z)) -> truth
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [68] implies(not(implies(X,not(Y))),Y) -> truth
% Current number of equations to process: 229
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [69] implies(X,not(truth)) -> not(X)
% Rule [26] implies(implies(X,not(truth)),not(truth)) -> X collapsed.
% Rule [28] implies(implies(X,not(truth)),implies(X,Y)) -> truth collapsed.
% Rule [32] implies(not(implies(X,not(truth))),X) -> truth collapsed.
% Rule [33] implies(X,implies(implies(X,not(truth)),Y)) -> truth collapsed.
% Rule [34] implies(not(implies(X,not(truth))),implies(Y,X)) -> truth
% collapsed.
% Rule [38] implies(implies(X,not(truth)),implies(Y,implies(X,Z))) -> truth
% collapsed.
% Rule [47] implies(X,implies(Y,implies(implies(X,not(truth)),Z))) -> truth
% collapsed.
% Rule [48] implies(X,implies(implies(implies(Y,X),not(truth)),Z)) -> truth
% collapsed.
% Rule [49] implies(not(X),implies(not(implies(X,not(truth))),Y)) -> truth
% collapsed.
% Rule [58] implies(not(X),not(truth)) -> X collapsed.
% Rule [59] implies(not(implies(X,implies(Y,not(truth)))),Y) -> truth
% collapsed.
% Current number of equations to process: 232
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [70] implies(X,implies(not(implies(Y,X)),Z)) -> truth
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [71] implies(implies(implies(not(X),Y),Z),implies(X,Z)) -> truth
% Current number of equations to process: 233
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [72] implies(implies(X,Y),implies(X,implies(not(Y),Z))) -> truth
% Current number of equations to process: 232
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [73] implies(X,implies(implies(implies(not(X),Y),Z),Z)) -> truth
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [74] implies(X,implies(Y,implies(Z,implies(not(X),V_3)))) -> truth
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [75] implies(not(implies(X,implies(Y,Z))),implies(Z,V_3)) -> truth
% Current number of equations to process: 254
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [76] implies(not(X),implies(not(implies(X,Y)),Z)) -> truth
% Current number of equations to process: 264
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [77] implies(not(implies(X,not(Y))),implies(Y,X)) -> truth
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [78] implies(X,not(Y)) <-> implies(Y,not(X))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 281
% Current number of ordered equations: 0
% Current number of rules: 47
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [1]
% implies(truth,X) -> X; trace = in the starting set
% [2] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X); trace = in the starting set
% [3] implies(implies(not(X),not(Y)),implies(Y,X)) -> truth; trace = in the starting set
% [4] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) -> truth; trace = in the starting set
% [6] implies(implies(not(X),not(truth)),X) -> truth; trace = Cp of 3 and 1
% [14] implies(Y,implies(X,Y)) -> truth; trace = Cp of 4 and 1
% [16] implies(implies(implies(X,Y),Z),implies(Y,Z)) -> truth; trace = Cp of 14 and 4
% [20] implies(not(X),implies(X,Y)) -> truth; trace = Cp of 16 and 3
% [29] implies(implies(implies(X,Y),Z),implies(not(X),Z)) -> truth; trace = Cp of 20 and 4
% [40] implies(not(not(X)),X) -> truth; trace = Cp of 29 and 6
% [57] not(not(X)) -> X; trace = Cp of 40 and 2
% [65] implies(implies(X,not(Y)),implies(Y,not(X))) -> truth; trace = Cp of 57 and 3
% [78] implies(X,not(Y)) <-> implies(Y,not(X)); trace = Cp of 65 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.250000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------