%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:25:35 PM UTC 2026
% Result : Theorem 0.14s 0.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 114 ( 18 unt; 0 def)
% Number of atoms : 360 ( 276 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 415 ( 169 ~; 208 |; 20 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 82 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ( ! [X2,X3] :
( ( X3 = f(g(X3))
& X2 = f(g(X2)) )
=> X2 = X3 )
& ? [X1] : X1 = f(g(X1)) )
<=> ( ! [X2,X3] :
( ( X3 = g(f(X3))
& X2 = g(f(X2)) )
=> X2 = X3 )
& ? [X1] : X1 = g(f(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(c_0_1,negated_conjecture,
~ ( ( ! [X2,X3] :
( ( X3 = f(g(X3))
& X2 = f(g(X2)) )
=> X2 = X3 )
& ? [X1] : X1 = f(g(X1)) )
<=> ( ! [X2,X3] :
( ( X3 = g(f(X3))
& X2 = g(f(X2)) )
=> X2 = X3 )
& ? [X1] : X1 = g(f(X1)) ) ),
inference(assume_negation,[status(cth)],[prove_this_cute_thing]) ).
fof(c_0_2,plain,
( ~ epred2_0
<=> ! [X1] : g(f(X1)) != X1 ),
introduced(definition) ).
fof(c_0_3,negated_conjecture,
! [X4,X7,X11,X12,X14,X15] :
( ( X11 = X12
| X12 != f(g(X12))
| X11 != f(g(X11))
| X14 = X15
| X15 != g(f(X15))
| X14 != g(f(X14)) )
& ( X11 = X12
| X12 != f(g(X12))
| X11 != f(g(X11))
| esk6_0 = g(f(esk6_0)) )
& ( esk5_0 = f(g(esk5_0))
| X14 = X15
| X15 != g(f(X15))
| X14 != g(f(X14)) )
& ( esk5_0 = f(g(esk5_0))
| esk6_0 = g(f(esk6_0)) )
& ( X4 != f(g(X4))
| esk1_0 != esk2_0
| X7 != g(f(X7))
| esk3_0 != esk4_0 )
& ( X4 != f(g(X4))
| esk1_0 != esk2_0
| X7 != g(f(X7))
| esk4_0 = g(f(esk4_0)) )
& ( X4 != f(g(X4))
| esk1_0 != esk2_0
| X7 != g(f(X7))
| esk3_0 = g(f(esk3_0)) )
& ( X4 != f(g(X4))
| esk2_0 = f(g(esk2_0))
| X7 != g(f(X7))
| esk3_0 != esk4_0 )
& ( X4 != f(g(X4))
| esk2_0 = f(g(esk2_0))
| X7 != g(f(X7))
| esk4_0 = g(f(esk4_0)) )
& ( X4 != f(g(X4))
| esk2_0 = f(g(esk2_0))
| X7 != g(f(X7))
| esk3_0 = g(f(esk3_0)) )
& ( X4 != f(g(X4))
| esk1_0 = f(g(esk1_0))
| X7 != g(f(X7))
| esk3_0 != esk4_0 )
& ( X4 != f(g(X4))
| esk1_0 = f(g(esk1_0))
| X7 != g(f(X7))
| esk4_0 = g(f(esk4_0)) )
& ( X4 != f(g(X4))
| esk1_0 = f(g(esk1_0))
| X7 != g(f(X7))
| esk3_0 = g(f(esk3_0)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_4,negated_conjecture,
( g(f(X1)) != X1
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( esk5_0 = f(g(esk5_0))
| esk6_0 = g(f(esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
( ~ epred4_0
<=> ! [X2] :
( f(g(X2)) != X2
| esk4_0 != esk3_0
| f(g(esk2_0)) = esk2_0 ) ),
introduced(definition) ).
cnf(c_0_7,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk3_0 != esk4_0
| esk2_0 = f(g(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,negated_conjecture,
( epred2_0
| f(g(esk5_0)) = esk5_0 ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
fof(c_0_9,plain,
( ~ epred7_0
<=> ! [X2] :
( f(g(X2)) != X2
| g(f(esk3_0)) = esk3_0
| f(g(esk1_0)) = esk1_0 ) ),
introduced(definition) ).
cnf(c_0_10,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk1_0 = f(g(esk1_0))
| esk3_0 = g(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,negated_conjecture,
( ~ epred2_0
| ~ epred4_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_6]),c_0_2]) ).
cnf(c_0_12,negated_conjecture,
epred2_0,
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
fof(c_0_13,plain,
( ~ epred8_0
<=> ! [X2] :
( f(g(X2)) != X2
| g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk1_0 ) ),
introduced(definition) ).
cnf(c_0_14,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk1_0 = f(g(esk1_0))
| esk4_0 = g(f(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_15,negated_conjecture,
( ~ epred2_0
| ~ epred7_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_9]),c_0_2]) ).
cnf(c_0_16,negated_conjecture,
~ epred4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
( ~ epred2_0
| ~ epred8_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_13]),c_0_2]) ).
cnf(c_0_18,negated_conjecture,
~ epred7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12])]) ).
fof(c_0_19,plain,
( ~ epred12_0
<=> ! [X3,X4] :
( f(g(X4)) != X4
| f(g(X3)) != X3
| X3 = X4 ) ),
introduced(definition) ).
cnf(c_0_20,negated_conjecture,
( esk4_0 != esk3_0
| f(g(X1)) != X1
| f(g(esk2_0)) = esk2_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_6]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ epred8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12])]) ).
fof(c_0_22,plain,
( ~ epred3_0
<=> ! [X2] :
( f(g(X2)) != X2
| esk4_0 != esk3_0
| f(g(esk1_0)) = esk1_0 ) ),
introduced(definition) ).
cnf(c_0_23,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk3_0 != esk4_0
| esk1_0 = f(g(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
( f(g(X1)) != X1
| f(g(esk1_0)) = esk1_0
| g(f(esk3_0)) = esk3_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_9]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( f(g(X2)) != X2
| f(g(X1)) != X1
| epred12_0
| X1 = X2 ),
inference(split_equiv,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( esk4_0 != esk3_0
| f(g(esk2_0)) = esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_5]),c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( f(g(X1)) != X1
| f(g(esk1_0)) = esk1_0
| g(f(esk4_0)) = esk4_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_13]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( ~ epred2_0
| ~ epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_22]),c_0_2]) ).
cnf(c_0_29,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| f(g(esk1_0)) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_5]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( esk4_0 != esk3_0
| f(g(X1)) != X1
| epred12_0
| esk2_0 = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( esk4_0 != esk3_0
| g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
~ epred3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_12])]) ).
cnf(c_0_33,negated_conjecture,
( f(g(X1)) != X1
| epred12_0
| f(esk3_0) = X1
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
fof(c_0_35,plain,
( ~ epred9_0
<=> ! [X2] :
( f(g(X2)) != X2
| g(f(esk3_0)) = esk3_0
| f(g(esk2_0)) = esk2_0 ) ),
introduced(definition) ).
cnf(c_0_36,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk2_0 = f(g(esk2_0))
| esk3_0 = g(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_37,plain,
( ~ epred10_0
<=> ! [X2] :
( f(g(X2)) != X2
| g(f(esk4_0)) = esk4_0
| f(g(esk2_0)) = esk2_0 ) ),
introduced(definition) ).
cnf(c_0_38,negated_conjecture,
( X2 != f(g(X2))
| X1 != g(f(X1))
| esk2_0 = f(g(esk2_0))
| esk4_0 = g(f(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_39,negated_conjecture,
( esk4_0 != esk3_0
| epred12_0
| esk2_0 = f(esk4_0)
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
( esk4_0 != esk3_0
| f(g(X1)) != X1
| f(g(esk1_0)) = esk1_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_22]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( epred12_0
| f(g(esk1_0)) = esk1_0
| f(esk4_0) = f(esk3_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( ~ epred2_0
| ~ epred9_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,c_0_35]),c_0_2]) ).
cnf(c_0_43,negated_conjecture,
( ~ epred2_0
| ~ epred10_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38,c_0_37]),c_0_2]) ).
fof(c_0_44,plain,
( ~ epred5_0
<=> ! [X2] :
( f(g(X2)) != X2
| esk2_0 != esk1_0
| g(f(esk3_0)) = esk3_0 ) ),
introduced(definition) ).
cnf(c_0_45,negated_conjecture,
( X2 != f(g(X2))
| esk1_0 != esk2_0
| X1 != g(f(X1))
| esk3_0 = g(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_46,negated_conjecture,
( esk4_0 != esk3_0
| epred12_0
| f(g(esk1_0)) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( epred12_0
| f(g(esk1_0)) = esk1_0
| esk4_0 = g(f(esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
~ epred9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_12])]) ).
fof(c_0_49,plain,
( ~ epred6_0
<=> ! [X2] :
( f(g(X2)) != X2
| esk2_0 != esk1_0
| g(f(esk4_0)) = esk4_0 ) ),
introduced(definition) ).
cnf(c_0_50,negated_conjecture,
( X2 != f(g(X2))
| esk1_0 != esk2_0
| X1 != g(f(X1))
| esk4_0 = g(f(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_51,negated_conjecture,
~ epred10_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_12])]) ).
cnf(c_0_52,negated_conjecture,
( ~ epred2_0
| ~ epred5_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45,c_0_44]),c_0_2]) ).
cnf(c_0_53,negated_conjecture,
( epred12_0
| f(g(esk1_0)) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_29]) ).
cnf(c_0_54,negated_conjecture,
( f(g(X1)) != X1
| f(g(esk2_0)) = esk2_0
| g(f(esk3_0)) = esk3_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_35]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( ~ epred2_0
| ~ epred6_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_50,c_0_49]),c_0_2]) ).
cnf(c_0_56,negated_conjecture,
( f(g(X1)) != X1
| f(g(esk2_0)) = esk2_0
| g(f(esk4_0)) = esk4_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_37]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
~ epred5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_12])]) ).
cnf(c_0_58,negated_conjecture,
( f(g(X1)) != X1
| epred12_0
| esk1_0 = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| f(g(esk2_0)) = esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_5]),c_0_54]) ).
cnf(c_0_60,negated_conjecture,
~ epred6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_12])]) ).
cnf(c_0_61,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(g(esk2_0)) = esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_5]),c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( esk2_0 != esk1_0
| f(g(X1)) != X1
| g(f(esk3_0)) = esk3_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_44]),c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( epred12_0
| esk2_0 = esk1_0
| g(f(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_64,plain,
( ~ epred11_0
<=> ! [X1,X2] :
( g(f(X2)) != X2
| g(f(X1)) != X1
| X1 = X2 ) ),
introduced(definition) ).
cnf(c_0_65,negated_conjecture,
( esk2_0 != esk1_0
| f(g(X1)) != X1
| g(f(esk4_0)) = esk4_0 ),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_49]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( epred12_0
| esk2_0 = esk1_0
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( f(g(X1)) != X1
| epred12_0
| g(f(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( g(f(X2)) != X2
| g(f(X1)) != X1
| epred11_0
| X1 = X2 ),
inference(split_equiv,[status(thm)],[c_0_64]) ).
fof(c_0_69,plain,
( ~ epred1_0
<=> ! [X2] :
( f(g(X2)) != X2
| esk2_0 != esk1_0
| esk4_0 != esk3_0 ) ),
introduced(definition) ).
cnf(c_0_70,negated_conjecture,
( X2 != f(g(X2))
| esk1_0 != esk2_0
| X1 != g(f(X1))
| esk3_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_71,negated_conjecture,
( f(g(X1)) != X1
| epred12_0
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( epred12_0
| g(f(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( g(f(X1)) != X1
| epred11_0
| esk3_0 = X1
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_74,negated_conjecture,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_70,c_0_69]),c_0_2]) ).
cnf(c_0_75,negated_conjecture,
( epred12_0
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( epred11_0
| esk4_0 = esk3_0
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_77,negated_conjecture,
( esk2_0 != esk1_0
| esk4_0 != esk3_0
| f(g(X1)) != X1
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( esk4_0 != esk3_0
| epred12_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_79,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_12])]) ).
cnf(c_0_80,negated_conjecture,
( epred12_0
| f(esk4_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( epred12_0
| f(esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( f(g(X1)) != X1
| epred11_0
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( esk4_0 != esk3_0
| f(g(X1)) != X1
| epred12_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( epred12_0
| esk4_0 = g(esk1_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( epred12_0
| esk3_0 = g(esk1_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( epred11_0
| f(g(esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_82,c_0_34]) ).
cnf(c_0_87,negated_conjecture,
( X4 != f(g(X4))
| X3 != f(g(X3))
| X2 != g(f(X2))
| X1 != g(f(X1))
| X3 = X4
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_88,negated_conjecture,
( f(g(X1)) != X1
| epred12_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( g(f(X1)) != X1
| epred11_0
| g(esk1_0) = X1 ),
inference(spm,[status(thm)],[c_0_68,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
( epred11_0
| g(f(esk3_0)) = esk3_0
| f(g(esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( ~ epred11_0
| ~ epred12_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_87,c_0_64]),c_0_19]) ).
cnf(c_0_92,negated_conjecture,
epred12_0,
inference(spm,[status(thm)],[c_0_88,c_0_75]) ).
cnf(c_0_93,negated_conjecture,
( epred11_0
| g(esk2_0) = g(esk1_0)
| g(f(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
~ epred11_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_95,negated_conjecture,
( epred11_0
| g(f(esk4_0)) = esk4_0
| f(g(esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_86]) ).
cnf(c_0_96,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| g(esk2_0) = g(esk1_0) ),
inference(sr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_97,negated_conjecture,
f(g(esk1_0)) = esk1_0,
inference(sr,[status(thm)],[c_0_86,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( epred11_0
| g(esk2_0) = g(esk1_0)
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_89,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( esk4_0 != esk3_0
| g(f(X1)) != X1
| epred11_0
| g(esk2_0) = X1 ),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_100,negated_conjecture,
( esk2_0 = esk1_0
| g(f(esk3_0)) = esk3_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_96]),c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| g(esk2_0) = g(esk1_0) ),
inference(sr,[status(thm)],[c_0_98,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
( esk4_0 != esk3_0
| epred11_0
| g(esk2_0) = g(esk1_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_86]) ).
cnf(c_0_103,negated_conjecture,
( f(g(X1)) != X1
| g(f(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( esk2_0 = esk1_0
| g(f(esk4_0)) = esk4_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_101]),c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( esk4_0 != esk3_0
| epred11_0
| esk2_0 = f(g(esk1_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( g(f(X1)) != X1
| g(esk1_0) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_97]),c_0_94]) ).
cnf(c_0_107,negated_conjecture,
g(f(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_103,c_0_59]) ).
cnf(c_0_108,negated_conjecture,
( f(g(X1)) != X1
| g(f(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_65,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( esk4_0 != esk3_0
| epred11_0 ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_105]),c_0_79])]),c_0_86]) ).
cnf(c_0_110,negated_conjecture,
esk3_0 = g(esk1_0),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
g(f(esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_108,c_0_61]) ).
cnf(c_0_112,negated_conjecture,
esk4_0 != g(esk1_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_94]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_111]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.52 % Computer : n010.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Mon Sep 21 11:08:43 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.56 Running first-order theorem proving
% 0.14/0.56 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.60 % Version: 3.5.1
% 0.14/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.60 % Starting sh5l with 300s (1) cores
% 0.14/0.60 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 742436 completed with status 0
% 0.14/0.60 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.60 % No SInE strategy applied
% 0.14/0.60 % Search class: FGHPF-FFMF11-SFFFFFNN
% 0.14/0.60 % partial match(1): FGHNF-FFMF11-SFFFFFNN
% 0.14/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.60 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.14/0.60 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.60 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.14/0.60 % G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with pid 742447 completed with status 0
% 0.14/0.60 % Result found by G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y
% 0.14/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.60 % No SInE strategy applied
% 0.14/0.60 % Search class: FGHPF-FFMF11-SFFFFFNN
% 0.14/0.60 % partial match(1): FGHNF-FFMF11-SFFFFFNN
% 0.14/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.60 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.14/0.60 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.60 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.14/0.60 % Preprocessing time : 0.001 s
% 0.14/0.60
% 0.14/0.60 % Proof found!
% 0.14/0.60 % SZS status Theorem
% 0.14/0.60 % SZS output start CNFRefutation
% See solution above
% 0.14/0.60 % Parsed axioms : 1
% 0.14/0.60 % Removed by relevancy pruning/SinE : 0
% 0.14/0.60 % Initial clauses : 13
% 0.14/0.60 % Removed in clause preprocessing : 0
% 0.14/0.60 % Initial clauses in saturation : 13
% 0.14/0.60 % Processed clauses : 293
% 0.14/0.60 % ...of these trivial : 0
% 0.14/0.60 % ...subsumed : 127
% 0.14/0.60 % ...remaining for further processing : 166
% 0.14/0.60 % Other redundant clauses eliminated : 0
% 0.14/0.60 % Clauses deleted for lack of memory : 0
% 0.14/0.60 % Backward-subsumed : 65
% 0.14/0.60 % Backward-rewritten : 61
% 0.14/0.60 % Generated clauses : 960
% 0.14/0.60 % ...of the previous two non-redundant : 945
% 0.14/0.60 % ...aggressively subsumed : 0
% 0.14/0.60 % Contextual simplify-reflections : 8
% 0.14/0.60 % Paramodulations : 932
% 0.14/0.60 % Factorizations : 0
% 0.14/0.60 % NegExts : 0
% 0.14/0.60 % Equation resolutions : 0
% 0.14/0.60 % Disequality decompositions : 0
% 0.14/0.60 % Total rewrite steps : 88
% 0.14/0.60 % ...of those cached : 82
% 0.14/0.60 % Propositional unsat checks : 0
% 0.14/0.60 % Propositional check models : 0
% 0.14/0.60 % Propositional check unsatisfiable : 0
% 0.14/0.60 % Propositional clauses : 0
% 0.14/0.60 % Propositional clauses after purity: 0
% 0.14/0.60 % Propositional unsat core size : 0
% 0.14/0.60 % Propositional preprocessing time : 0.000
% 0.14/0.60 % Propositional encoding time : 0.000
% 0.14/0.60 % Propositional solver time : 0.000
% 0.14/0.60 % Success case prop preproc time : 0.000
% 0.14/0.60 % Success case prop encoding time : 0.000
% 0.14/0.60 % Success case prop solver time : 0.000
% 0.14/0.60 % Current number of processed clauses : 24
% 0.14/0.60 % Positive orientable unit clauses : 5
% 0.14/0.60 % Positive unorientable unit clauses: 0
% 0.14/0.60 % Negative unit clauses : 11
% 0.14/0.60 % Non-unit-clauses : 8
% 0.14/0.60 % Current number of unprocessed clauses: 280
% 0.14/0.60 % ...number of literals in the above : 1110
% 0.14/0.60 % Current number of archived formulas : 0
% 0.14/0.60 % Current number of archived clauses : 132
% 0.14/0.60 % Clause-clause subsumption calls (NU) : 831
% 0.14/0.60 % Rec. Clause-clause subsumption calls : 653
% 0.14/0.60 % Non-unit clause-clause subsumptions : 197
% 0.14/0.60 % Unit Clause-clause subsumption calls : 114
% 0.14/0.60 % Rewrite failures with RHS unbound : 0
% 0.14/0.60 % BW rewrite match attempts : 6
% 0.14/0.60 % BW rewrite match successes : 6
% 0.14/0.60 % Condensation attempts : 293
% 0.14/0.60 % Condensation successes : 1
% 0.14/0.60 % Termbank termtop insertions : 12318
% 0.14/0.60 % Search garbage collected termcells : 246
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.020 s
% 0.14/0.60 % System time : 0.003 s
% 0.14/0.60 % Total time : 0.023 s
% 0.14/0.60 % Maximum resident set size: 3628 pages
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.103 s
% 0.14/0.60 % System time : 0.011 s
% 0.14/0.60 % Total time : 0.113 s
% 0.14/0.60 % Maximum resident set size: 4864 pages
% 0.14/0.60 % E exiting
%------------------------------------------------------------------------------