TSTP Solution File: SYN417+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 : Fri Sep 1 01:51:41 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 6 unt; 6 typ; 0 def)
% Number of atoms : 210 ( 209 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 216 ( 67 ~; 132 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 54 ( 0 sgn; 8 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
g: $i > $i ).
tff(decl_23,type,
f: $i > $i ).
tff(decl_24,type,
esk1_1: $i > $i ).
tff(decl_25,type,
esk2_1: $i > $i ).
tff(decl_26,type,
esk3_0: $i ).
tff(decl_27,type,
esk4_0: $i ).
fof(cute,conjecture,
( ? [X1] :
( X1 = f(g(X1))
& ! [X2] :
( X2 = f(g(X2))
=> X1 = X2 ) )
<=> ? [X1] :
( X1 = g(f(X1))
& ! [X2] :
( X2 = g(f(X2))
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).
fof(c_0_1,negated_conjecture,
~ ( ? [X1] :
( X1 = f(g(X1))
& ! [X2] :
( X2 = f(g(X2))
=> X1 = X2 ) )
<=> ? [X1] :
( X1 = g(f(X1))
& ! [X2] :
( X2 = g(f(X2))
=> X1 = X2 ) ) ),
inference(assume_negation,[status(cth)],[cute]) ).
fof(c_0_2,negated_conjecture,
! [X3,X5,X8,X10] :
( ( esk2_1(X5) = g(f(esk2_1(X5)))
| X5 != g(f(X5))
| esk1_1(X3) = f(g(esk1_1(X3)))
| X3 != f(g(X3)) )
& ( X5 != esk2_1(X5)
| X5 != g(f(X5))
| esk1_1(X3) = f(g(esk1_1(X3)))
| X3 != f(g(X3)) )
& ( esk2_1(X5) = g(f(esk2_1(X5)))
| X5 != g(f(X5))
| X3 != esk1_1(X3)
| X3 != f(g(X3)) )
& ( X5 != esk2_1(X5)
| X5 != g(f(X5))
| X3 != esk1_1(X3)
| X3 != f(g(X3)) )
& ( esk4_0 = g(f(esk4_0))
| esk3_0 = f(g(esk3_0)) )
& ( X10 != g(f(X10))
| esk4_0 = X10
| esk3_0 = f(g(esk3_0)) )
& ( esk4_0 = g(f(esk4_0))
| X8 != f(g(X8))
| esk3_0 = X8 )
& ( X10 != g(f(X10))
| esk4_0 = X10
| X8 != f(g(X8))
| esk3_0 = X8 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( esk2_1(X1) = g(f(esk2_1(X1)))
| esk1_1(X2) = f(g(esk1_1(X2)))
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( esk4_0 = g(f(esk4_0))
| esk3_0 = f(g(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| g(f(esk2_1(X1))) = esk2_1(X1)
| g(f(esk4_0)) = esk4_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( esk4_0 = g(f(esk4_0))
| esk3_0 = X1
| X1 != f(g(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( g(f(esk2_1(g(esk3_0)))) = esk2_1(g(esk3_0))
| f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| f(esk2_1(g(esk3_0))) = esk3_0
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| esk2_1(g(esk3_0)) = g(esk3_0)
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,negated_conjecture,
( esk2_1(g(esk3_0)) = g(esk3_0)
| g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( esk1_1(X2) = f(g(esk1_1(X2)))
| X1 != esk2_1(X1)
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
( g(f(g(esk3_0))) = g(esk3_0)
| g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( f(g(esk1_1(X1))) = esk1_1(X1)
| g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0
| f(g(X1)) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0
| esk1_1(X1) = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
( esk2_1(X1) = g(f(esk2_1(X1)))
| X1 != g(f(X1))
| X2 != esk1_1(X2)
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_16,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( g(f(esk2_1(X1))) = esk2_1(X1)
| g(f(esk4_0)) = esk4_0
| g(f(X1)) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_4]) ).
cnf(c_0_18,negated_conjecture,
( X1 != esk2_1(X1)
| X1 != g(f(X1))
| X2 != esk1_1(X2)
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_19,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(esk2_1(X1)) = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| g(f(X1)) != X1
| esk2_1(X1) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_4]) ).
cnf(c_0_21,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk2_1(X1) = g(esk3_0)
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| g(f(g(esk3_0))) != g(esk3_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_23,negated_conjecture,
g(f(esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_22,c_0_4]) ).
cnf(c_0_24,negated_conjecture,
( esk4_0 = X1
| esk3_0 = X2
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_25,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| g(f(esk2_1(X1))) = esk2_1(X1)
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( f(esk4_0) = esk3_0
| esk4_0 = X1
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| g(f(esk2_1(esk4_0))) = esk2_1(esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| g(esk1_1(f(esk4_0))) = esk4_0
| f(esk4_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| esk1_1(f(esk4_0)) = f(esk4_0)
| f(esk4_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( esk1_1(f(esk4_0)) = f(esk4_0)
| esk2_1(esk4_0) = esk4_0
| f(esk4_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( g(f(esk2_1(X1))) = esk2_1(X1)
| f(esk4_0) = esk3_0
| esk2_1(esk4_0) = esk4_0
| g(f(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
( esk2_1(esk4_0) = esk4_0
| f(esk4_0) = esk3_0
| esk2_1(X1) = esk4_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( f(esk4_0) = esk3_0
| esk2_1(esk4_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( f(g(esk1_1(X1))) = esk1_1(X1)
| f(esk4_0) = esk3_0
| f(g(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_33]),c_0_23])]) ).
cnf(c_0_35,negated_conjecture,
( g(esk1_1(X1)) = esk4_0
| f(esk4_0) = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| esk1_1(f(esk4_0)) = esk3_0
| esk4_0 = X1
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( esk1_1(X1) = f(esk4_0)
| f(esk4_0) = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| g(esk1_1(f(esk4_0))) = esk4_0
| esk1_1(f(esk4_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_39,negated_conjecture,
( f(esk4_0) = esk3_0
| g(f(X1)) != X1
| esk2_1(X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_37])]),c_0_23])]) ).
cnf(c_0_40,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| esk1_1(f(esk4_0)) = f(esk4_0)
| esk1_1(f(esk4_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
f(esk4_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_23])]) ).
cnf(c_0_42,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| esk1_1(esk3_0) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]),c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
( f(esk2_1(esk4_0)) = esk3_0
| esk1_1(esk3_0) = esk3_0
| esk4_0 = X1
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( f(esk2_1(esk4_0)) = esk3_0
| esk2_1(esk4_0) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
g(esk3_0) = esk4_0,
inference(rw,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( esk1_1(esk3_0) = esk3_0
| esk2_1(esk4_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_44]),c_0_45])]) ).
cnf(c_0_47,negated_conjecture,
( f(g(esk1_1(X1))) = esk1_1(X1)
| esk1_1(esk3_0) = esk3_0
| f(g(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_46]),c_0_41]),c_0_45])]) ).
cnf(c_0_48,negated_conjecture,
( esk1_1(esk3_0) = esk3_0
| esk1_1(X1) = esk3_0
| esk4_0 = X2
| g(f(X2)) != X2
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
( g(esk1_1(X1)) = esk4_0
| esk1_1(esk3_0) = esk3_0
| esk1_1(X2) = esk3_0
| f(g(X2)) != X2
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( g(esk1_1(X1)) = esk4_0
| esk1_1(esk3_0) = esk3_0
| f(g(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_45]),c_0_41])]) ).
cnf(c_0_51,negated_conjecture,
( esk1_1(esk3_0) = esk3_0
| esk1_1(X1) = esk3_0
| f(g(X1)) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_41]) ).
cnf(c_0_52,negated_conjecture,
esk1_1(esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_41])]) ).
cnf(c_0_53,negated_conjecture,
( g(f(esk2_1(X1))) = esk2_1(X1)
| g(f(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_52]),c_0_45]),c_0_41])]) ).
cnf(c_0_54,negated_conjecture,
( f(esk2_1(X1)) = esk3_0
| esk4_0 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
( f(esk2_1(X1)) = esk3_0
| esk2_1(X2) = esk4_0
| g(f(X1)) != X1
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( f(esk2_1(esk4_0)) = esk3_0
| esk2_1(X1) = esk4_0
| g(f(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_45])]) ).
cnf(c_0_57,negated_conjecture,
( f(esk2_1(esk4_0)) = esk3_0
| esk2_1(esk4_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_45])]) ).
cnf(c_0_58,negated_conjecture,
( g(f(X1)) != X1
| esk2_1(X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_52]),c_0_45]),c_0_41])]) ).
cnf(c_0_59,negated_conjecture,
esk2_1(esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_57]),c_0_45]),c_0_41]),c_0_45])]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_41]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 20:20:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.015000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.018000 s
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