%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% 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 : Thu Jul 21 04:55:34 EDT 2022
% Result : Theorem 7.50s 2.42s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 5 unt; 0 def)
% Number of atoms : 271 ( 135 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 275 ( 91 ~; 176 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_3,negated_conjecture,
( esk3_0 = X1
| g(f(X2)) = X2
| esk4_0 != X2
| f(g(X1)) != X1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_3) ).
cnf(i_0_4,negated_conjecture,
( esk3_0 = X1
| esk4_0 = X2
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_4) ).
cnf(i_0_1,negated_conjecture,
( f(g(X1)) = X1
| g(f(X2)) = X2
| esk3_0 != X1
| esk4_0 != X2 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_1) ).
cnf(i_0_2,negated_conjecture,
( esk4_0 = X1
| f(g(X2)) = X2
| esk3_0 != X2
| g(f(X1)) != X1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_2) ).
cnf(i_0_7,negated_conjecture,
( esk2_1(X1) = X1
| g(f(esk2_1(X1))) = esk2_1(X1)
| esk1_1(X2) != X2
| f(g(esk1_1(X2))) != esk1_1(X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_7) ).
cnf(i_0_8,negated_conjecture,
( esk1_1(X1) != X1
| esk2_1(X2) != X2
| f(g(esk1_1(X1))) != esk1_1(X1)
| g(f(esk2_1(X2))) != esk2_1(X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_8) ).
cnf(i_0_6,negated_conjecture,
( esk1_1(X1) = X1
| f(g(esk1_1(X1))) = esk1_1(X1)
| esk2_1(X2) != X2
| g(f(esk2_1(X2))) != esk2_1(X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_6) ).
cnf(i_0_5,negated_conjecture,
( esk1_1(X1) = X1
| esk2_1(X2) = X2
| f(g(esk1_1(X1))) = esk1_1(X1)
| g(f(esk2_1(X2))) = esk2_1(X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-wvo3obdx/input.p',i_0_5) ).
fof(c_0_17,plain,
( ~ epred4_0
<=> ! [X1] :
( esk4_0 = X1
| g(f(X1)) != X1 ) ),
introduced(definition) ).
fof(c_0_18,plain,
( ~ epred6_0
<=> ! [X2] :
( esk2_1(X2) = X2
| g(f(esk2_1(X2))) = esk2_1(X2) ) ),
introduced(definition) ).
cnf(c_0_19,negated_conjecture,
( esk4_0 = X1
| epred4_0
| g(f(X1)) != X1 ),
inference(split_equiv,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( g(f(esk2_1(X1))) = esk2_1(X1)
| esk2_1(X1) = X1
| epred6_0 ),
inference(split_equiv,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
( ~ epred3_0
<=> ! [X1] :
( esk3_0 = X1
| f(g(X1)) != X1 ) ),
introduced(definition) ).
cnf(c_0_22,negated_conjecture,
( esk4_0 = esk2_1(X1)
| esk2_1(X1) = X1
| epred6_0
| epred4_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( esk3_0 = X1
| epred3_0
| f(g(X1)) != X1 ),
inference(split_equiv,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
( ~ epred7_0
<=> ! [X2] :
( esk2_1(X2) != X2
| g(f(esk2_1(X2))) != esk2_1(X2) ) ),
introduced(definition) ).
cnf(c_0_25,negated_conjecture,
( esk2_1(X1) = X1
| epred6_0
| epred4_0
| esk4_0 != X1 ),
inference(ef,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
( ~ epred2_0
<=> ! [X2] :
( g(f(X2)) = X2
| esk4_0 != X2 ) ),
introduced(definition) ).
cnf(c_0_27,negated_conjecture,
( esk3_0 = f(esk2_1(X1))
| esk2_1(X1) = X1
| epred6_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( epred7_0
| g(f(esk2_1(X1))) != esk2_1(X1)
| esk2_1(X1) != X1 ),
inference(split_equiv,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( esk2_1(esk4_0) = esk4_0
| epred6_0
| epred4_0 ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( g(f(X1)) = X1
| epred2_0
| esk4_0 != X1 ),
inference(split_equiv,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
( ~ epred5_0
<=> ! [X1] :
( esk1_1(X1) = X1
| f(g(esk1_1(X1))) = esk1_1(X1) ) ),
introduced(definition) ).
cnf(c_0_32,negated_conjecture,
( g(esk3_0) = esk2_1(X1)
| esk2_1(X1) = X1
| epred6_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( esk3_0 = X1
| g(f(X2)) = X2
| esk4_0 != X2
| f(g(X1)) != X1 ),
i_0_3 ).
cnf(c_0_34,negated_conjecture,
( epred7_0
| epred6_0
| epred4_0
| g(f(esk4_0)) != esk4_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| epred2_0 ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( esk3_0 = X1
| esk4_0 = X2
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
i_0_4 ).
cnf(c_0_37,negated_conjecture,
( f(g(esk1_1(X1))) = esk1_1(X1)
| esk1_1(X1) = X1
| epred5_0 ),
inference(split_equiv,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( esk2_1(X1) = X1
| epred6_0
| epred3_0
| g(esk3_0) != X1 ),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ epred3_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_26]),c_0_21]) ).
cnf(c_0_40,negated_conjecture,
( epred7_0
| epred6_0
| epred4_0
| epred2_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,c_0_17]),c_0_21]) ).
fof(c_0_42,plain,
( ~ epred1_0
<=> ! [X1] :
( f(g(X1)) = X1
| esk3_0 != X1 ) ),
introduced(definition) ).
cnf(c_0_43,negated_conjecture,
( esk3_0 = esk1_1(X1)
| esk1_1(X1) = X1
| epred5_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( esk2_1(g(esk3_0)) = g(esk3_0)
| epred6_0
| epred3_0 ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( epred7_0
| epred6_0
| ~ epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( f(g(X1)) = X1
| epred1_0
| esk3_0 != X1 ),
inference(split_equiv,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( esk4_0 = g(esk1_1(X1))
| esk1_1(X1) = X1
| epred5_0
| epred4_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
fof(c_0_48,plain,
( ~ epred8_0
<=> ! [X2] :
( esk1_1(X2) != X2
| f(g(esk1_1(X2))) != esk1_1(X2) ) ),
introduced(definition) ).
cnf(c_0_49,negated_conjecture,
( esk1_1(X1) = X1
| epred5_0
| epred3_0
| esk3_0 != X1 ),
inference(ef,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( f(esk4_0) = esk3_0
| epred3_0
| epred2_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_51,negated_conjecture,
( f(g(X1)) = X1
| g(f(X2)) = X2
| esk3_0 != X1
| esk4_0 != X2 ),
i_0_1 ).
cnf(c_0_52,negated_conjecture,
( epred7_0
| epred6_0
| g(f(g(esk3_0))) != g(esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( f(g(esk3_0)) = esk3_0
| epred1_0 ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( esk4_0 = X1
| f(g(X2)) = X2
| esk3_0 != X2
| g(f(X1)) != X1 ),
i_0_2 ).
cnf(c_0_55,negated_conjecture,
( f(esk4_0) = esk1_1(X1)
| esk1_1(X1) = X1
| epred5_0
| epred4_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( epred8_0
| f(g(esk1_1(X1))) != esk1_1(X1)
| esk1_1(X1) != X1 ),
inference(split_equiv,[status(thm)],[c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( esk1_1(esk3_0) = esk3_0
| epred5_0
| epred3_0 ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( esk4_0 = g(esk3_0)
| epred3_0
| epred2_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_51,c_0_42]),c_0_26]) ).
cnf(c_0_60,negated_conjecture,
( epred7_0
| epred6_0
| epred1_0 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( ~ epred4_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54,c_0_42]),c_0_17]) ).
cnf(c_0_62,negated_conjecture,
( esk1_1(X1) = X1
| epred5_0
| epred4_0
| f(esk4_0) != X1 ),
inference(ef,[status(thm)],[c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( esk4_0 = g(esk3_0)
| epred4_0
| epred1_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( epred8_0
| epred5_0
| epred3_0
| f(g(esk3_0)) != esk3_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( f(g(esk3_0)) = esk3_0
| epred3_0
| epred2_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( esk2_1(X1) = X1
| g(f(esk2_1(X1))) = esk2_1(X1)
| esk1_1(X2) != X2
| f(g(esk1_1(X2))) != esk1_1(X2) ),
i_0_7 ).
cnf(c_0_67,negated_conjecture,
( epred7_0
| epred6_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( epred7_0
| epred6_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( esk1_1(X1) != X1
| esk2_1(X2) != X2
| f(g(esk1_1(X1))) != esk1_1(X1)
| g(f(esk2_1(X2))) != esk2_1(X2) ),
i_0_8 ).
cnf(c_0_70,negated_conjecture,
( esk1_1(X1) = X1
| epred5_0
| epred4_0
| epred1_0
| f(g(esk3_0)) != X1 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( epred8_0
| epred5_0
| epred3_0
| epred1_0 ),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_72,negated_conjecture,
( epred8_0
| epred5_0
| epred3_0
| epred2_0 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( ~ epred8_0
| ~ epred6_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_66,c_0_18]),c_0_48]) ).
cnf(c_0_74,negated_conjecture,
( epred7_0
| epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_40]),c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( ~ epred8_0
| ~ epred7_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_69,c_0_24]),c_0_48]) ).
cnf(c_0_76,negated_conjecture,
( esk1_1(X1) = X1
| epred5_0
| epred4_0
| epred1_0
| esk3_0 != X1 ),
inference(spm,[status(thm)],[c_0_70,c_0_53]) ).
cnf(c_0_77,negated_conjecture,
( epred8_0
| epred5_0
| epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_71]),c_0_72]) ).
cnf(c_0_78,negated_conjecture,
~ epred8_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( esk1_1(esk3_0) = esk3_0
| epred5_0
| epred4_0
| epred1_0 ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_80,negated_conjecture,
( epred8_0
| epred5_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( epred5_0
| epred3_0 ),
inference(sr,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( epred8_0
| epred5_0
| epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_79]),c_0_53]),c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( esk1_1(f(esk4_0)) = f(esk4_0)
| epred5_0
| epred4_0 ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_84,negated_conjecture,
( epred5_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( epred5_0
| epred1_0 ),
inference(sr,[status(thm)],[c_0_82,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( esk1_1(X1) = X1
| f(g(esk1_1(X1))) = esk1_1(X1)
| esk2_1(X2) != X2
| g(f(esk2_1(X2))) != esk2_1(X2) ),
i_0_6 ).
cnf(c_0_87,negated_conjecture,
( epred5_0
| f(g(f(esk4_0))) != f(esk4_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_83]),c_0_78]),c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( epred5_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_59,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( esk1_1(X1) = X1
| esk2_1(X2) = X2
| f(g(esk1_1(X1))) = esk1_1(X1)
| g(f(esk2_1(X2))) = esk2_1(X2) ),
i_0_5 ).
cnf(c_0_90,negated_conjecture,
( ~ epred7_0
| ~ epred5_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_86,c_0_31]),c_0_24]) ).
cnf(c_0_91,negated_conjecture,
epred5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_35]),c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( ~ epred6_0
| ~ epred5_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_89,c_0_31]),c_0_18]) ).
cnf(c_0_93,negated_conjecture,
~ epred7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_94,negated_conjecture,
~ epred6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_91])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_74,c_0_93]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 13:34:50 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected complete mode:
% 7.50/2.42 # ENIGMATIC: Solved by autoschedule:
% 7.50/2.42 # No SInE strategy applied
% 7.50/2.42 # Trying AutoSched0 for 150 seconds
% 7.50/2.42 # AutoSched0-Mode selected heuristic G_N___023_B07_F1_SP_PI_Q7_CS_SP_CO_S0Y
% 7.50/2.42 # and selection function SelectMaxLComplexAvoidPosPred.
% 7.50/2.42 #
% 7.50/2.42 # Preprocessing time : 0.014 s
% 7.50/2.42
% 7.50/2.42 # Proof found!
% 7.50/2.42 # SZS status Theorem
% 7.50/2.42 # SZS output start CNFRefutation
% See solution above
% 7.50/2.42 # Training examples: 0 positive, 0 negative
% 7.50/2.42
% 7.50/2.42 # -------------------------------------------------
% 7.50/2.42 # User time : 0.020 s
% 7.50/2.42 # System time : 0.002 s
% 7.50/2.42 # Total time : 0.023 s
% 7.50/2.42 # Maximum resident set size: 7124 pages
% 7.50/2.42
%------------------------------------------------------------------------------