TSTP Solution File: LCL156-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LCL156-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n094.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 00:27:13 EDT 2014
% Result : Unsatisfiable 1.18s
% Output : Refutation 1.18s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LCL156-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n094.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 02:16:38 CDT 2014
% % CPUTime : 1.18
% Processing problem /tmp/CiME_53770_n094.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " xor : infix commutative; and_star,and,or : AC; x,falsehood,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;
% X or Y = implies(not(X),Y);
% X and Y = not(not(X) or not(Y));
% X xor Y = (X and not(Y)) or (not(X) and Y);
% X and_star Y = not(not(X) or not(Y));
% not(truth) = falsehood;
% ";
%
% let s1 = status F "
% x lr_lex;
% falsehood lr_lex;
% not lr_lex;
% implies lr_lex;
% truth lr_lex;
% and_star mul;
% xor mul;
% and mul;
% or mul;
% ";
%
% let p1 = precedence F "
% xor > implies > not > and_star > or > and > truth > falsehood > x";
%
% let s2 = status F "
% x mul;
% falsehood mul;
% and_star mul;
% xor mul;
% and mul;
% or mul;
% not mul;
% implies mul;
% truth mul;
% ";
%
% let p2 = precedence F "
% xor > implies > not > and_star > or > and > truth = falsehood = x";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " x and_star truth = x;"
% ;
% (*
% 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,
% X or Y = implies(not(X),Y),
% X and Y = not(not(X) or not(Y)),
% X xor Y = (not(X) and Y) or (not(Y) and X),
% X and_star Y = not(not(X) or not(Y)),
% not(truth) = falsehood } (9 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 = { x and_star truth = x } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] not(truth) -> falsehood
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 1
% New rule produced : [2] implies(truth,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 2
% New rule produced : [3] implies(not(X),Y) -> X or Y
% Current number of equations to process: 1
% Current number of ordered equations: 6
% Current number of rules: 3
% New rule produced : [4] not(not(X) or not(Y)) -> X and_star Y
% Current number of equations to process: 1
% Current number of ordered equations: 5
% Current number of rules: 4
% Rule [4] not(not(X) or not(Y)) -> X and_star Y is composed into [4]
% not(not(X) or
% not(Y))
% -> X and Y
% New rule produced : [5] X and_star Y -> X and Y
% The conjecture has been reduced.
% Conjecture is now:
% x and truth = x
%
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 5
% New rule produced : [6] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 6
% New rule produced : [7] implies(not(Y) or X,implies(Y,X)) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] X xor Y -> (not(X) and Y) or (not(Y) and X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced :
% [9] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] implies(falsehood,X) -> truth or X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] not(falsehood or not(X)) -> truth and X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] implies(implies(X,truth),truth) -> implies(X,X)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] implies(falsehood or X,X) -> truth
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] implies(X and Y,Z) -> not(X) or not(Y) or Z
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] implies(implies(Y,not(X)),not(X)) -> implies(X or Y,Y)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] implies(not(not(X)) or Y,X or Y) -> truth
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] not((X and Y) or not(Z)) -> (not(X) or not(Y)) and Z
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] 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: 18
% New rule produced :
% [19] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] implies(implies(X,falsehood),falsehood) -> implies(truth or X,X)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] not(falsehood or falsehood) -> truth and truth
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] implies(not(falsehood) or X,truth or X) -> truth
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] implies(truth or X,truth) -> not(X) or X
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25] implies(falsehood or truth,falsehood or truth) -> truth
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] implies(not(falsehood or X) or X,truth) -> truth
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27] not((truth and X) or falsehood) -> (falsehood or not(X)) and truth
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% implies(implies(X,truth),implies(X,truth)) <-> implies(implies(X,X),truth)
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [29]
% implies(implies(X,X),truth) <-> implies(implies(X,truth),implies(X,truth))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30] implies(implies(X,falsehood or X),falsehood or X) -> X
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31] implies(implies(X,Y),implies(falsehood or X,Y)) -> truth
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [32] implies(implies(X,falsehood or Y),implies(X,Y)) -> truth
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33] not((X and Y) or falsehood) -> (not(X) or not(Y)) and truth
% Rule [27] not((truth and X) or falsehood) -> (falsehood or not(X)) and truth
% collapsed.
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34] implies(truth or not(X),not(X)) -> implies(falsehood or X,falsehood)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35] implies(truth or not(implies(X,truth)),implies(X,X)) -> truth
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36] implies(not(Y) or X,not(Y)) <-> implies(not(X) or Y,not(X))
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 35
% Rule [12] implies(implies(X,truth),truth) -> implies(X,X) is composed into
% [12] implies(implies(X,truth),truth) -> truth
% New rule produced : [37] implies(X,X) -> truth
% Rule [25] implies(falsehood or truth,falsehood or truth) -> truth collapsed.
% Rule
% [28]
% implies(implies(X,truth),implies(X,truth)) <-> implies(implies(X,X),truth)
% collapsed.
% Rule
% [29]
% implies(implies(X,X),truth) <-> implies(implies(X,truth),implies(X,truth))
% collapsed.
% Rule [35] implies(truth or not(implies(X,truth)),implies(X,X)) -> truth
% collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [38] implies(X or Y,Y) or X -> truth
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [39] implies(X,implies(implies(Y,X),X)) -> truth
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [40] not(not(implies(X,truth))) or not(implies(X,truth)) -> truth
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [41] implies(X,truth) -> truth
% Rule [12] implies(implies(X,truth),truth) -> truth collapsed.
% Rule [19] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% collapsed.
% Rule [20] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% collapsed.
% Rule [24] implies(truth or X,truth) -> not(X) or X collapsed.
% Rule [26] implies(not(falsehood or X) or X,truth) -> truth collapsed.
% Rule [40] not(not(implies(X,truth))) or not(implies(X,truth)) -> truth
% collapsed.
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [42] not(X) or X -> truth
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [43] implies(Y,implies(X,Y)) -> truth
% Rule [39] implies(X,implies(implies(Y,X),X)) -> truth collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [44] falsehood or truth -> truth
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [45] falsehood or falsehood -> falsehood
% Rule [22] not(falsehood or falsehood) -> truth and truth collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [46] not(falsehood) -> truth and truth
% Rule [23] implies(not(falsehood) or X,truth or X) -> truth collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [47] falsehood or not(X) -> not(X)
% Rule [11] not(falsehood or not(X)) -> truth and X collapsed.
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [48] not(not(X)) -> truth and X
% Rule [16] implies(not(not(X)) or Y,X or Y) -> truth collapsed.
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [49] implies((truth and X) or Y,X or Y) -> truth
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [50] implies(falsehood or X,implies(implies(X,Y),Y)) -> truth
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [51] implies(not(implies(X,falsehood or X)) or X,X) -> truth
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [52] truth or implies(falsehood or X,falsehood) -> truth
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [53] implies(X,implies(not(X) or Y,Y)) -> truth
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 37
% Rule [21] implies(implies(X,falsehood),falsehood) -> implies(truth or X,X) is composed into
% [21] implies(implies(X,falsehood),falsehood) -> implies(truth,X)
% Rule [10] implies(falsehood,X) -> truth or X is composed into [10]
% implies(falsehood,X)
% -> truth
% New rule produced : [54] truth or X -> truth
% Rule
% [34] implies(truth or not(X),not(X)) -> implies(falsehood or X,falsehood)
% collapsed.
% Rule [44] falsehood or truth -> truth collapsed.
% Rule [52] truth or implies(falsehood or X,falsehood) -> truth collapsed.
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [55] implies(falsehood or X,falsehood) -> not(X)
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [56] implies(X,X or Y) -> truth
% Rule [30] implies(implies(X,falsehood or X),falsehood or X) -> X collapsed.
% Rule [51] implies(not(implies(X,falsehood or X)) or X,X) -> truth collapsed.
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [57] falsehood or X -> X
% Rule [13] implies(falsehood or X,X) -> truth collapsed.
% Rule [31] implies(implies(X,Y),implies(falsehood or X,Y)) -> truth collapsed.
% Rule [32] implies(implies(X,falsehood or Y),implies(X,Y)) -> truth collapsed.
% Rule [33] not((X and Y) or falsehood) -> (not(X) or not(Y)) and truth
% collapsed.
% Rule [45] falsehood or falsehood -> falsehood collapsed.
% Rule [47] falsehood or not(X) -> not(X) collapsed.
% Rule [50] implies(falsehood or X,implies(implies(X,Y),Y)) -> truth collapsed.
% Rule [55] implies(falsehood or X,falsehood) -> not(X) collapsed.
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [58] implies(X,falsehood) -> not(X)
% Rule [21] implies(implies(X,falsehood),falsehood) -> implies(truth,X)
% collapsed.
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 28
% Rule [48] not(not(X)) -> truth and X is composed into [48] not(not(X)) -> X
% Rule [46] not(falsehood) -> truth and truth is composed into [46]
% not(falsehood)
% -> truth
% New rule produced : [59] truth and X -> X
% Rule [49] implies((truth and X) or Y,X or Y) -> truth collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 28
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 6 rules have been used:
% [1]
% not(truth) -> falsehood; trace = in the starting set
% [3] implies(not(X),Y) -> X or Y; trace = in the starting set
% [5] X and_star Y -> X and Y; trace = in the starting set
% [6] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X); trace = in the starting set
% [10] implies(falsehood,X) -> truth or X; trace = Cp of 3 and 1
% [59] truth and X -> X; trace = Cp of 10 and 6
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.090000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------