TSTP Solution File: SYN551+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 06:03:42 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 1
% Syntax : Number of formulae : 58 ( 8 unt; 0 def)
% Number of atoms : 186 ( 185 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 189 ( 61 ~; 111 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% 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 : 48 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ? [X1] :
( X1 = f(g(X1))
& ! [X2] :
( X2 = f(g(X2))
=> X2 = X1 ) )
<=> ? [X1] :
( X1 = g(f(X1))
& ! [X2] :
( X2 = g(f(X2))
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_this_cute_thing) ).
fof(c_0_1,negated_conjecture,
~ ( ? [X1] :
( X1 = f(g(X1))
& ! [X2] :
( X2 = f(g(X2))
=> X2 = X1 ) )
<=> ? [X1] :
( X1 = g(f(X1))
& ! [X2] :
( X2 = g(f(X2))
=> X2 = X1 ) ) ),
inference(assume_negation,[status(cth)],[prove_this_cute_thing]) ).
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)) )
& ( esk2_1(X5) != 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))
| esk1_1(X3) != X3
| X3 != f(g(X3)) )
& ( esk2_1(X5) != X5
| X5 != g(f(X5))
| esk1_1(X3) != X3
| X3 != f(g(X3)) )
& ( esk4_0 = g(f(esk4_0))
| esk3_0 = f(g(esk3_0)) )
& ( X10 != g(f(X10))
| X10 = esk4_0
| esk3_0 = f(g(esk3_0)) )
& ( esk4_0 = g(f(esk4_0))
| X8 != f(g(X8))
| X8 = esk3_0 )
& ( X10 != g(f(X10))
| X10 = esk4_0
| X8 != f(g(X8))
| X8 = esk3_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])])]) ).
cnf(c_0_3,negated_conjecture,
( esk1_1(X1) = f(g(esk1_1(X1)))
| esk2_1(X2) = g(f(esk2_1(X2)))
| X1 != f(g(X1))
| X2 != g(f(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( esk3_0 = f(g(esk3_0))
| esk4_0 = g(f(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( g(f(esk2_1(g(esk3_0)))) = esk2_1(g(esk3_0))
| f(g(esk1_1(X1))) = esk1_1(X1)
| g(f(esk4_0)) = esk4_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( X1 = esk3_0
| esk4_0 = g(f(esk4_0))
| 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,
( esk1_1(X1) = f(g(esk1_1(X1)))
| X1 != f(g(X1))
| X2 != g(f(X2))
| esk2_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| g(f(g(esk3_0))) = g(esk3_0)
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| f(g(esk1_1(X1))) = esk1_1(X1)
| g(f(esk4_0)) = esk4_0
| f(g(X1)) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_11]) ).
cnf(c_0_13,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( esk2_1(X2) = g(f(esk2_1(X2)))
| X1 != f(g(X1))
| esk1_1(X1) != X1
| X2 != g(f(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_16,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_14,c_0_15]),c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( X1 != f(g(X1))
| esk1_1(X1) != X1
| X2 != g(f(X2))
| esk2_1(X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_18,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_16]) ).
cnf(c_0_19,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_17,c_0_15]),c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk2_1(X1) = g(esk3_0)
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| g(f(X1)) != X1
| g(esk3_0) != X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
g(f(esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_21,c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( g(f(esk2_1(esk4_0))) = esk2_1(esk4_0)
| f(g(esk1_1(X1))) = esk1_1(X1)
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( esk3_0 = f(g(esk3_0))
| X1 = esk4_0
| X1 != g(f(X1)) ),
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(esk4_0))) = esk2_1(esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| f(g(esk3_0)) = esk3_0
| esk2_1(esk4_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| f(g(esk1_1(X1))) = esk1_1(X1)
| f(g(esk3_0)) = esk3_0
| f(g(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_26]),c_0_22])]) ).
cnf(c_0_28,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| f(g(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( g(esk1_1(f(esk4_0))) = esk4_0
| f(g(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( esk1_1(f(esk4_0)) = f(esk4_0)
| f(g(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( g(f(esk2_1(X1))) = esk2_1(X1)
| f(g(esk3_0)) = esk3_0
| g(f(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_30]),c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
( f(g(esk3_0)) = esk3_0
| g(f(X1)) != X1
| esk2_1(X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_30]),c_0_22])]) ).
cnf(c_0_33,negated_conjecture,
( f(g(esk3_0)) = esk3_0
| esk2_1(X1) = esk4_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( f(g(esk3_0)) = esk3_0
| g(f(X1)) != X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]) ).
cnf(c_0_35,negated_conjecture,
( X1 = esk3_0
| X2 = esk4_0
| X1 != f(g(X1))
| X2 != g(f(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_36,negated_conjecture,
f(g(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( g(esk3_0) = esk4_0
| X1 = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| esk2_1(esk4_0) = esk4_0
| X1 = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_39,negated_conjecture,
( f(esk4_0) = esk3_0
| g(esk3_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_40,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| f(esk2_1(esk4_0)) = esk3_0
| esk2_1(esk4_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_41,negated_conjecture,
g(esk3_0) = esk4_0,
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( f(g(esk1_1(f(esk4_0)))) = esk1_1(f(esk4_0))
| esk2_1(esk4_0) = g(esk3_0)
| esk2_1(esk4_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
f(esk4_0) = esk3_0,
inference(rw,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| esk2_1(esk4_0) = esk4_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41])]),c_0_43]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( f(g(esk1_1(esk3_0))) = esk1_1(esk3_0)
| f(g(esk1_1(X1))) = esk1_1(X1)
| f(g(X1)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_44]),c_0_43]),c_0_41])]) ).
cnf(c_0_46,negated_conjecture,
f(g(esk1_1(esk3_0))) = esk1_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_41]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
( g(esk1_1(esk3_0)) = esk4_0
| X1 = esk3_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( g(esk1_1(esk3_0)) = esk4_0
| esk1_1(esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
esk1_1(esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_48]),c_0_43])]) ).
cnf(c_0_50,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_14,c_0_49]),c_0_41]),c_0_43])]) ).
cnf(c_0_51,negated_conjecture,
( esk2_1(X1) = esk4_0
| X2 = esk3_0
| f(g(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( f(esk2_1(X1)) = esk3_0
| esk2_1(X2) = esk4_0
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( f(esk2_1(X1)) = 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_52,c_0_43]),c_0_41])]) ).
cnf(c_0_54,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_53,c_0_43]),c_0_41])]) ).
cnf(c_0_55,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_17,c_0_49]),c_0_41]),c_0_43])]) ).
cnf(c_0_56,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_50,c_0_54]),c_0_41]),c_0_43]),c_0_41])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n026.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 : Tue Jul 12 07:38:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.013 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 58
% 0.24/1.42 # Proof object clause steps : 55
% 0.24/1.42 # Proof object formula steps : 3
% 0.24/1.42 # Proof object conjectures : 58
% 0.24/1.42 # Proof object clause conjectures : 55
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 8
% 0.24/1.42 # Proof object initial formulas used : 1
% 0.24/1.42 # Proof object generating inferences : 45
% 0.24/1.42 # Proof object simplifying inferences : 39
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 1
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 8
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 8
% 0.24/1.42 # Processed clauses : 138
% 0.24/1.42 # ...of these trivial : 2
% 0.24/1.42 # ...subsumed : 50
% 0.24/1.42 # ...remaining for further processing : 86
% 0.24/1.42 # Other redundant clauses eliminated : 0
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 29
% 0.24/1.42 # Backward-rewritten : 48
% 0.24/1.42 # Generated clauses : 325
% 0.24/1.42 # ...of the previous two non-trivial : 294
% 0.24/1.42 # Contextual simplify-reflections : 76
% 0.24/1.42 # Paramodulations : 324
% 0.24/1.42 # Factorizations : 1
% 0.24/1.42 # Equation resolutions : 0
% 0.24/1.42 # Current number of processed clauses : 9
% 0.24/1.42 # Positive orientable unit clauses : 4
% 0.24/1.42 # Positive unorientable unit clauses: 0
% 0.24/1.42 # Negative unit clauses : 0
% 0.24/1.42 # Non-unit-clauses : 5
% 0.24/1.42 # Current number of unprocessed clauses: 1
% 0.24/1.42 # ...number of literals in the above : 4
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 77
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 723
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 476
% 0.24/1.42 # Non-unit clause-clause subsumptions : 155
% 0.24/1.42 # Unit Clause-clause subsumption calls : 3
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 9
% 0.24/1.42 # BW rewrite match successes : 7
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 8073
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.029 s
% 0.24/1.42 # System time : 0.002 s
% 0.24/1.42 # Total time : 0.031 s
% 0.24/1.42 # Maximum resident set size: 2760 pages
%------------------------------------------------------------------------------