TSTP Solution File: LCL119-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL119-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : Thu Aug 31 06:52:23 EDT 2023
% Result : Unsatisfiable 3.10s 3.14s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 36 unt; 5 typ; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 126 ( 64 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 240 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equivalent: ( $i * $i ) > $i ).
tff(decl_23,type,
is_a_theorem: $i > $o ).
tff(decl_24,type,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(xgj,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X1)),equivalent(X2,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xgj) ).
cnf(prove_wo,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(b,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wo) ).
cnf(c_0_3,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment ).
cnf(c_0_4,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X1)),equivalent(X2,X3)))),
xgj ).
cnf(c_0_5,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),X1))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_9,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,equivalent(X3,X1)))
| ~ is_a_theorem(equivalent(X2,X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_10,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,equivalent(X1,equivalent(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_11,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_12,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,X1))))
| ~ is_a_theorem(equivalent(X2,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_13,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(X2,X2))) ),
inference(spm,[status(thm)],[c_0_3,c_0_11]) ).
cnf(c_0_14,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(X2,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_15,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(X2,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_16,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,equivalent(X1,equivalent(X3,X3)))) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_17,plain,
is_a_theorem(equivalent(X1,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_18,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_4]) ).
cnf(c_0_19,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_12]) ).
cnf(c_0_21,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_22,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X2,equivalent(X3,X1))),X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_23,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X3))),equivalent(X1,X2))),
inference(spm,[status(thm)],[c_0_21,c_0_4]) ).
cnf(c_0_25,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,equivalent(X3,X1)))
| ~ is_a_theorem(equivalent(X3,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(X3,equivalent(X1,equivalent(X2,equivalent(X4,X4))))) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_27,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,equivalent(X3,equivalent(X3,X1)))) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_28,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_29,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_4]) ).
cnf(c_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X1),X3)),
inference(spm,[status(thm)],[c_0_26,c_0_4]) ).
cnf(c_0_31,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X2,X1)),X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X2,X1)))),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_33,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_34,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X2,equivalent(X3,equivalent(X3,X1)))))),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_35,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_37,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(X1,X2)),X3))
| ~ is_a_theorem(equivalent(X3,X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_38,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X1)),equivalent(X2,X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_4]) ).
cnf(c_0_39,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X2,X3))))
| ~ is_a_theorem(equivalent(X3,X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_34]) ).
cnf(c_0_40,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2))) ),
inference(spm,[status(thm)],[c_0_3,c_0_35]) ).
cnf(c_0_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X3,X4)))),equivalent(X1,X2)),X4)),
inference(spm,[status(thm)],[c_0_36,c_0_4]) ).
cnf(c_0_42,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X1),X3),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_28]) ).
cnf(c_0_43,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,X2)),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_4]) ).
cnf(c_0_44,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X2,X3))))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_45,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,equivalent(X3,equivalent(equivalent(X3,X2),X1)))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X3,equivalent(equivalent(X4,X4),equivalent(X1,X2))))))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X1),X3))
| ~ is_a_theorem(equivalent(X2,X3)) ),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_48,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,equivalent(X4,equivalent(X4,X1)))),equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_49,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_44]) ).
cnf(c_0_50,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),equivalent(X2,X1)))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),X3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_30]) ).
cnf(c_0_52,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),equivalent(X3,equivalent(X3,X4)))),X1),X4)),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
cnf(c_0_53,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X4,X4),equivalent(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X3),equivalent(X4,equivalent(X4,X2))))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X3,X2),X3))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X1),equivalent(equivalent(X3,X3),X2))),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_57,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),X1),equivalent(X3,X2))),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_58,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(equivalent(X3,X1),X3)),X2))),
inference(spm,[status(thm)],[c_0_27,c_0_57]) ).
cnf(c_0_59,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)),X1)),
inference(spm,[status(thm)],[c_0_10,c_0_58]) ).
cnf(c_0_60,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,equivalent(X2,X1)),X3),equivalent(equivalent(X4,X3),X4)))),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_61,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,equivalent(X2,X1))) ),
inference(spm,[status(thm)],[c_0_3,c_0_18]) ).
cnf(c_0_62,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3)))
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X4,X3),X4))) ),
inference(spm,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_63,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X1,X2)),X3),equivalent(X2,X3))),
inference(spm,[status(thm)],[c_0_10,c_0_60]) ).
cnf(c_0_64,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X2,X3)),X1),X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_37]) ).
cnf(c_0_65,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(X1,equivalent(X2,X3))),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_18]) ).
cnf(c_0_66,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X1,equivalent(X2,X3))),X2),equivalent(equivalent(X4,X4),X3))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(X1,X2)),equivalent(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X4,X1),X3),X4)) ),
inference(spm,[status(thm)],[c_0_62,c_0_12]) ).
cnf(c_0_69,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X1,equivalent(X2,equivalent(X3,X4)))),X2),equivalent(X4,X3))),
inference(spm,[status(thm)],[c_0_53,c_0_66]) ).
cnf(c_0_70,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X3,X1))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_67]) ).
cnf(c_0_71,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,X1))),equivalent(equivalent(X4,X4),X3))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X2,X3),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_70]) ).
cnf(c_0_73,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X4),equivalent(X2,X1))),equivalent(X4,X3))),
inference(spm,[status(thm)],[c_0_53,c_0_71]) ).
cnf(c_0_74,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X4)))
| ~ is_a_theorem(equivalent(equivalent(X2,X1),equivalent(X4,X3))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X4),equivalent(X3,equivalent(X4,equivalent(X2,X1)))))),
inference(spm,[status(thm)],[c_0_74,c_0_4]) ).
cnf(c_0_76,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X4)))
| ~ is_a_theorem(equivalent(X3,equivalent(X4,equivalent(X2,X1)))) ),
inference(spm,[status(thm)],[c_0_6,c_0_75]) ).
cnf(c_0_77,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,equivalent(X2,equivalent(X1,X3))))),
inference(spm,[status(thm)],[c_0_76,c_0_4]) ).
cnf(c_0_78,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X3),X2))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(b,a)))),
prove_wo ).
cnf(c_0_80,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,equivalent(X2,X1)))),
inference(spm,[status(thm)],[c_0_74,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL119-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 06:06:55 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 3.10/3.14 % Version : CSE_E---1.5
% 3.10/3.14 % Problem : theBenchmark.p
% 3.10/3.14 % Proof found
% 3.10/3.14 % SZS status Theorem for theBenchmark.p
% 3.10/3.14 % SZS output start Proof
% See solution above
% 3.10/3.14 % Total time : 2.576000 s
% 3.10/3.14 % SZS output end Proof
% 3.10/3.14 % Total time : 2.579000 s
%------------------------------------------------------------------------------