%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEG002^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Wed Sep 30 07:49:18 AM UTC 2026
% Result : Theorem 1.91s 0.56s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 370 ( 19 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 1193 ( 122 ~; 120 |; 84 &; 814 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 8 con; 0-2 aty)
% Number of variables : 176 ( 38 ^; 112 !; 26 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_23,type,
c: reg > reg > $o ).
thf(decl_24,type,
dc: reg > reg > $o ).
thf(decl_25,type,
p: reg > reg > $o ).
thf(decl_27,type,
o: reg > reg > $o ).
thf(decl_29,type,
ec: reg > reg > $o ).
thf(decl_30,type,
pp: reg > reg > $o ).
thf(decl_31,type,
tpp: reg > reg > $o ).
thf(decl_32,type,
ntpp: reg > reg > $o ).
thf(decl_33,type,
catalunya: reg ).
thf(decl_34,type,
france: reg ).
thf(decl_35,type,
spain: reg ).
thf(decl_36,type,
paris: reg ).
thf(decl_37,type,
esk1_0: reg ).
thf(decl_38,type,
esk2_0: reg ).
thf(decl_39,type,
esk3_1: reg > reg ).
thf(decl_40,type,
esk4_1: reg > reg ).
thf(decl_41,type,
esk5_1: reg > reg ).
thf(decl_42,type,
esk6_1: reg > reg ).
thf(decl_43,type,
esk7_1: reg > reg ).
thf(decl_44,type,
esk8_1: reg > reg ).
thf(decl_45,type,
esk9_0: reg ).
thf(decl_46,type,
esk10_1: reg > reg ).
thf(decl_47,type,
esk11_1: reg > reg ).
thf(o,axiom,
( o
= ( ^ [X1: reg,X2: reg] :
? [X3: reg] :
( ( p @ X3 @ X1 )
& ( p @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',o) ).
thf(p,axiom,
( p
= ( ^ [X1: reg,X2: reg] :
! [X3: reg] :
( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',p) ).
thf(ec,axiom,
( ec
= ( ^ [X1: reg,X2: reg] :
( ( c @ X1 @ X2 )
& ~ ( o @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',ec) ).
thf(pp,axiom,
( pp
= ( ^ [X1: reg,X2: reg] :
( ( p @ X1 @ X2 )
& ~ ( p @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',pp) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X1: reg,X2: reg] :
( ( pp @ X1 @ X2 )
& ~ ? [X3: reg] :
( ( ec @ X3 @ X1 )
& ( ec @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',ntpp) ).
thf(tpp,axiom,
( tpp
= ( ^ [X1: reg,X2: reg] :
( ( pp @ X1 @ X2 )
& ? [X3: reg] :
( ( ec @ X3 @ X1 )
& ( ec @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',tpp) ).
thf(con,conjecture,
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',con) ).
thf(dc,axiom,
( dc
= ( ^ [X1: reg,X2: reg] :
~ ( c @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',dc) ).
thf(ax3,axiom,
ntpp @ paris @ france,
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',ax3) ).
thf(ax2,axiom,
ec @ spain @ france,
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',ax2) ).
thf(ax1,axiom,
tpp @ catalunya @ spain,
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',ax1) ).
thf(c_symmetric,axiom,
! [X1: reg,X2: reg] :
( ( c @ X1 @ X2 )
=> ( c @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p',c_symmetric) ).
thf(c_0_12,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X3: reg] :
( ! [X9: reg] :
( ( c @ X9 @ X3 )
=> ( c @ X9 @ Z0 ) )
& ! [X10: reg] :
( ( c @ X10 @ X3 )
=> ( c @ X10 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[o]) ).
thf(c_0_13,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X3: reg] :
( ( c @ X3 @ Z0 )
=> ( c @ X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_14,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X16: reg] :
( ! [X17: reg] :
( ( c @ X17 @ X16 )
=> ( c @ X17 @ Z0 ) )
& ! [X18: reg] :
( ( c @ X18 @ X16 )
=> ( c @ X18 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_15,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X3: reg] :
( ! [X9: reg] :
( ( c @ X9 @ X3 )
=> ( c @ X9 @ Z0 ) )
& ! [X10: reg] :
( ( c @ X10 @ X3 )
=> ( c @ X10 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X19: reg] :
( ( c @ X19 @ Z0 )
=> ( c @ X19 @ Z1 ) )
& ~ ! [X20: reg] :
( ( c @ X20 @ Z1 )
=> ( c @ X20 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_17,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X29: reg] :
( ( c @ X29 @ Z0 )
=> ( c @ X29 @ Z1 ) )
& ~ ! [X30: reg] :
( ( c @ X30 @ Z1 )
=> ( c @ X30 @ Z0 ) )
& ~ ? [X3: reg] :
( ( c @ X3 @ Z0 )
& ~ ? [X31: reg] :
( ! [X32: reg] :
( ( c @ X32 @ X31 )
=> ( c @ X32 @ X3 ) )
& ! [X33: reg] :
( ( c @ X33 @ X31 )
=> ( c @ X33 @ Z0 ) ) )
& ( c @ X3 @ Z1 )
& ~ ? [X34: reg] :
( ! [X35: reg] :
( ( c @ X35 @ X34 )
=> ( c @ X35 @ X3 ) )
& ! [X36: reg] :
( ( c @ X36 @ X34 )
=> ( c @ X36 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ntpp]) ).
thf(c_0_18,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X16: reg] :
( ! [X17: reg] :
( ( c @ X17 @ X16 )
=> ( c @ X17 @ Z0 ) )
& ! [X18: reg] :
( ( c @ X18 @ X16 )
=> ( c @ X18 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X19: reg] :
( ( c @ X19 @ Z0 )
=> ( c @ X19 @ Z1 ) )
& ~ ! [X20: reg] :
( ( c @ X20 @ Z1 )
=> ( c @ X20 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_13]) ).
thf(c_0_20,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X29: reg] :
( ( c @ X29 @ Z0 )
=> ( c @ X29 @ Z1 ) )
& ~ ! [X30: reg] :
( ( c @ X30 @ Z1 )
=> ( c @ X30 @ Z0 ) )
& ~ ? [X3: reg] :
( ( c @ X3 @ Z0 )
& ~ ? [X31: reg] :
( ! [X32: reg] :
( ( c @ X32 @ X31 )
=> ( c @ X32 @ X3 ) )
& ! [X33: reg] :
( ( c @ X33 @ X31 )
=> ( c @ X33 @ Z0 ) ) )
& ( c @ X3 @ Z1 )
& ~ ? [X34: reg] :
( ! [X35: reg] :
( ( c @ X35 @ X34 )
=> ( c @ X35 @ X3 ) )
& ! [X36: reg] :
( ( c @ X36 @ X34 )
=> ( c @ X36 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
thf(c_0_21,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X21: reg] :
( ( c @ X21 @ Z0 )
=> ( c @ X21 @ Z1 ) )
& ~ ! [X22: reg] :
( ( c @ X22 @ Z1 )
=> ( c @ X22 @ Z0 ) )
& ? [X3: reg] :
( ( c @ X3 @ Z0 )
& ~ ? [X23: reg] :
( ! [X24: reg] :
( ( c @ X24 @ X23 )
=> ( c @ X24 @ X3 ) )
& ! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ Z0 ) ) )
& ( c @ X3 @ Z1 )
& ~ ? [X26: reg] :
( ! [X27: reg] :
( ( c @ X27 @ X26 )
=> ( c @ X27 @ X3 ) )
& ! [X28: reg] :
( ( c @ X28 @ X26 )
=> ( c @ X28 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[tpp]) ).
thf(c_0_22,negated_conjecture,
~ ( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_23,plain,
( dc
= ( ^ [Z0: reg,Z1: reg] :
~ ( c @ Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[dc]) ).
thf(c_0_24,plain,
( ! [X49: reg] :
( ( c @ X49 @ paris )
=> ( c @ X49 @ france ) )
& ~ ! [X50: reg] :
( ( c @ X50 @ france )
=> ( c @ X50 @ paris ) )
& ~ ? [X51: reg] :
( ( c @ X51 @ paris )
& ~ ? [X52: reg] :
( ! [X53: reg] :
( ( c @ X53 @ X52 )
=> ( c @ X53 @ X51 ) )
& ! [X54: reg] :
( ( c @ X54 @ X52 )
=> ( c @ X54 @ paris ) ) )
& ( c @ X51 @ france )
& ~ ? [X55: reg] :
( ! [X56: reg] :
( ( c @ X56 @ X55 )
=> ( c @ X56 @ X51 ) )
& ! [X57: reg] :
( ( c @ X57 @ X55 )
=> ( c @ X57 @ france ) ) ) ) ),
inference(apply_def,[status(thm)],[ax3,c_0_20]) ).
thf(c_0_25,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X21: reg] :
( ( c @ X21 @ Z0 )
=> ( c @ X21 @ Z1 ) )
& ~ ! [X22: reg] :
( ( c @ X22 @ Z1 )
=> ( c @ X22 @ Z0 ) )
& ? [X3: reg] :
( ( c @ X3 @ Z0 )
& ~ ? [X23: reg] :
( ! [X24: reg] :
( ( c @ X24 @ X23 )
=> ( c @ X24 @ X3 ) )
& ! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ Z0 ) ) )
& ( c @ X3 @ Z1 )
& ~ ? [X26: reg] :
( ! [X27: reg] :
( ( c @ X27 @ X26 )
=> ( c @ X27 @ X3 ) )
& ! [X28: reg] :
( ( c @ X28 @ X26 )
=> ( c @ X28 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_18]),c_0_19]) ).
thf(c_0_26,negated_conjecture,
~ ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_27,plain,
! [X73: reg,X75: reg,X77: reg,X78: reg,X80: reg,X81: reg] :
( ( ~ ( c @ X73 @ paris )
| ( c @ X73 @ france ) )
& ( c @ esk9_0 @ france )
& ~ ( c @ esk9_0 @ paris )
& ( ~ ( c @ X80 @ ( esk11_1 @ X75 ) )
| ( c @ X80 @ X75 )
| ~ ( c @ X75 @ france )
| ~ ( c @ X77 @ ( esk10_1 @ X75 ) )
| ( c @ X77 @ X75 )
| ~ ( c @ X75 @ paris ) )
& ( ~ ( c @ X81 @ ( esk11_1 @ X75 ) )
| ( c @ X81 @ france )
| ~ ( c @ X75 @ france )
| ~ ( c @ X77 @ ( esk10_1 @ X75 ) )
| ( c @ X77 @ X75 )
| ~ ( c @ X75 @ paris ) )
& ( ~ ( c @ X80 @ ( esk11_1 @ X75 ) )
| ( c @ X80 @ X75 )
| ~ ( c @ X75 @ france )
| ~ ( c @ X78 @ ( esk10_1 @ X75 ) )
| ( c @ X78 @ paris )
| ~ ( c @ X75 @ paris ) )
& ( ~ ( c @ X81 @ ( esk11_1 @ X75 ) )
| ( c @ X81 @ france )
| ~ ( c @ X75 @ france )
| ~ ( c @ X78 @ ( esk10_1 @ X75 ) )
| ( c @ X78 @ paris )
| ~ ( c @ X75 @ paris ) ) ),
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_24])])])])])]) ).
thf(c_0_28,plain,
( ( c @ spain @ france )
& ~ ? [X46: reg] :
( ! [X47: reg] :
( ( c @ X47 @ X46 )
=> ( c @ X47 @ spain ) )
& ! [X48: reg] :
( ( c @ X48 @ X46 )
=> ( c @ X48 @ france ) ) ) ),
inference(apply_def,[status(thm)],[ax2,c_0_18]) ).
thf(c_0_29,plain,
( ! [X37: reg] :
( ( c @ X37 @ catalunya )
=> ( c @ X37 @ spain ) )
& ~ ! [X38: reg] :
( ( c @ X38 @ spain )
=> ( c @ X38 @ catalunya ) )
& ? [X39: reg] :
( ( c @ X39 @ catalunya )
& ~ ? [X40: reg] :
( ! [X41: reg] :
( ( c @ X41 @ X40 )
=> ( c @ X41 @ X39 ) )
& ! [X42: reg] :
( ( c @ X42 @ X40 )
=> ( c @ X42 @ catalunya ) ) )
& ( c @ X39 @ spain )
& ~ ? [X43: reg] :
( ! [X44: reg] :
( ( c @ X44 @ X43 )
=> ( c @ X44 @ X39 ) )
& ! [X45: reg] :
( ( c @ X45 @ X43 )
=> ( c @ X45 @ spain ) ) ) ) ),
inference(apply_def,[status(thm)],[ax1,c_0_25]) ).
thf(c_0_30,plain,
! [X59: reg,X60: reg] :
( ~ ( c @ X59 @ X60 )
| ( c @ X60 @ X59 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])])]) ).
thf(c_0_31,negated_conjecture,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
thf(c_0_32,plain,
! [X1: reg,X3: reg,X2: reg] :
( ( c @ X1 @ france )
| ( c @ X3 @ paris )
| ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
| ~ ( c @ X2 @ france )
| ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
| ~ ( c @ X2 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_33,plain,
! [X1: reg] :
( ( c @ X1 @ france )
| ~ ( c @ X1 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,plain,
! [X70: reg] :
( ( c @ spain @ france )
& ( ( c @ ( esk8_1 @ X70 ) @ X70 )
| ( c @ ( esk7_1 @ X70 ) @ X70 ) )
& ( ~ ( c @ ( esk8_1 @ X70 ) @ france )
| ( c @ ( esk7_1 @ X70 ) @ X70 ) )
& ( ( c @ ( esk8_1 @ X70 ) @ X70 )
| ~ ( c @ ( esk7_1 @ X70 ) @ spain ) )
& ( ~ ( c @ ( esk8_1 @ X70 ) @ france )
| ~ ( c @ ( esk7_1 @ X70 ) @ spain ) ) ),
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_28])])])])])]) ).
thf(c_0_35,plain,
! [X61: reg,X64: reg,X67: reg] :
( ( ~ ( c @ X61 @ catalunya )
| ( c @ X61 @ spain ) )
& ( c @ esk1_0 @ spain )
& ~ ( c @ esk1_0 @ catalunya )
& ( c @ esk2_0 @ catalunya )
& ( ( c @ ( esk4_1 @ X64 ) @ X64 )
| ( c @ ( esk3_1 @ X64 ) @ X64 ) )
& ( ~ ( c @ ( esk4_1 @ X64 ) @ catalunya )
| ( c @ ( esk3_1 @ X64 ) @ X64 ) )
& ( ( c @ ( esk4_1 @ X64 ) @ X64 )
| ~ ( c @ ( esk3_1 @ X64 ) @ esk2_0 ) )
& ( ~ ( c @ ( esk4_1 @ X64 ) @ catalunya )
| ~ ( c @ ( esk3_1 @ X64 ) @ esk2_0 ) )
& ( c @ esk2_0 @ spain )
& ( ( c @ ( esk6_1 @ X67 ) @ X67 )
| ( c @ ( esk5_1 @ X67 ) @ X67 ) )
& ( ~ ( c @ ( esk6_1 @ X67 ) @ spain )
| ( c @ ( esk5_1 @ X67 ) @ X67 ) )
& ( ( c @ ( esk6_1 @ X67 ) @ X67 )
| ~ ( c @ ( esk5_1 @ X67 ) @ esk2_0 ) )
& ( ~ ( c @ ( esk6_1 @ X67 ) @ spain )
| ~ ( c @ ( esk5_1 @ X67 ) @ esk2_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_29])])])])])]) ).
thf(c_0_36,plain,
! [X1: reg,X2: reg] :
( ( c @ X2 @ X1 )
| ~ ( c @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,negated_conjecture,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_38,plain,
! [X1: reg,X2: reg,X3: reg] :
( ( c @ X1 @ france )
| ( c @ X2 @ paris )
| ~ ( c @ X2 @ ( esk10_1 @ X3 ) )
| ~ ( c @ X1 @ ( esk11_1 @ X3 ) )
| ~ ( c @ X3 @ paris ) ),
inference(csr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_39,plain,
! [X1: reg] :
( ( c @ ( esk8_1 @ X1 ) @ X1 )
| ( c @ ( esk7_1 @ X1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_40,plain,
! [X1: reg] :
( ( c @ X1 @ spain )
| ~ ( c @ X1 @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_41,negated_conjecture,
( ( c @ spain @ paris )
| ( c @ paris @ catalunya ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_42,plain,
! [X1: reg,X3: reg,X2: reg] :
( ( c @ X1 @ X2 )
| ( c @ X3 @ paris )
| ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
| ~ ( c @ X2 @ france )
| ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
| ~ ( c @ X2 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_43,plain,
! [X2: reg,X1: reg] :
( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ( c @ X2 @ france )
| ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
| ~ ( c @ X1 @ paris ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_44,plain,
! [X1: reg] :
( ( c @ ( esk7_1 @ X1 ) @ X1 )
| ~ ( c @ ( esk8_1 @ X1 ) @ france ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_45,negated_conjecture,
c @ paris @ spain,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36]) ).
thf(c_0_46,plain,
! [X1: reg,X2: reg,X3: reg] :
( ( c @ X1 @ paris )
| ( c @ X2 @ X3 )
| ~ ( c @ X1 @ ( esk10_1 @ X3 ) )
| ~ ( c @ X2 @ ( esk11_1 @ X3 ) )
| ~ ( c @ X3 @ paris ) ),
inference(csr,[status(thm)],[c_0_42,c_0_33]) ).
thf(c_0_47,plain,
! [X1: reg] :
( ( c @ ( esk7_1 @ ( esk11_1 @ X1 ) ) @ ( esk11_1 @ X1 ) )
| ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ~ ( c @ X1 @ paris ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]) ).
thf(c_0_48,negated_conjecture,
c @ spain @ paris,
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
thf(c_0_49,plain,
! [X1: reg] :
( ( c @ ( esk8_1 @ X1 ) @ X1 )
| ~ ( c @ ( esk7_1 @ X1 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_50,plain,
! [X1: reg] :
( ~ ( c @ ( esk8_1 @ X1 ) @ france )
| ~ ( c @ ( esk7_1 @ X1 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_51,plain,
! [X2: reg,X1: reg] :
( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ( c @ X2 @ X1 )
| ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
| ~ ( c @ X1 @ paris ) ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
thf(c_0_52,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
| ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_53,plain,
! [X1: reg] :
( ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ ( esk10_1 @ X1 ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ~ ( c @ ( esk7_1 @ ( esk11_1 @ X1 ) ) @ spain )
| ~ ( c @ X1 @ paris ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_49]),c_0_50]) ).
thf(c_0_54,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
| ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain )
| ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48])]) ).
thf(c_0_55,plain,
! [X1: reg,X3: reg,X2: reg] :
( ( c @ X1 @ france )
| ( c @ X3 @ X2 )
| ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
| ~ ( c @ X2 @ france )
| ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
| ~ ( c @ X2 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_56,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48])]) ).
thf(c_0_57,plain,
! [X1: reg,X3: reg,X2: reg] :
( ( c @ X1 @ X2 )
| ( c @ X3 @ X2 )
| ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
| ~ ( c @ X2 @ france )
| ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
| ~ ( c @ X2 @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_58,plain,
! [X1: reg,X2: reg,X3: reg] :
( ( c @ X1 @ france )
| ( c @ X2 @ X3 )
| ~ ( c @ X2 @ ( esk10_1 @ X3 ) )
| ~ ( c @ X1 @ ( esk11_1 @ X3 ) )
| ~ ( c @ X3 @ paris ) ),
inference(csr,[status(thm)],[c_0_55,c_0_33]) ).
thf(c_0_59,negated_conjecture,
c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ ( esk10_1 @ spain ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_56]),c_0_44]) ).
thf(c_0_60,plain,
! [X1: reg,X3: reg,X2: reg] :
( ( c @ X1 @ X2 )
| ( c @ X3 @ X2 )
| ~ ( c @ X3 @ ( esk10_1 @ X2 ) )
| ~ ( c @ X1 @ ( esk11_1 @ X2 ) )
| ~ ( c @ X2 @ paris ) ),
inference(csr,[status(thm)],[c_0_57,c_0_33]) ).
thf(c_0_61,negated_conjecture,
! [X1: reg] :
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
| ( c @ X1 @ france )
| ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48])]) ).
thf(c_0_62,negated_conjecture,
! [X1: reg] :
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
| ( c @ X1 @ spain )
| ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_48])]) ).
thf(c_0_63,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_39]),c_0_44]) ).
thf(c_0_64,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain )
| ~ ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_49]),c_0_50]) ).
thf(c_0_65,plain,
! [X2: reg,X1: reg] :
( ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ( c @ X2 @ france )
| ~ ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ spain )
| ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
| ~ ( c @ X1 @ paris ) ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
thf(c_0_66,negated_conjecture,
c @ ( esk7_1 @ ( esk10_1 @ spain ) ) @ spain,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
thf(c_0_67,plain,
! [X2: reg,X1: reg] :
( ( c @ ( esk8_1 @ ( esk10_1 @ X1 ) ) @ paris )
| ( c @ X2 @ X1 )
| ~ ( c @ ( esk7_1 @ ( esk10_1 @ X1 ) ) @ spain )
| ~ ( c @ X2 @ ( esk11_1 @ X1 ) )
| ~ ( c @ X1 @ paris ) ),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
thf(c_0_68,negated_conjecture,
! [X1: reg] :
( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
| ( c @ X1 @ france )
| ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_48])]) ).
thf(c_0_69,negated_conjecture,
! [X1: reg] :
( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
| ( c @ X1 @ spain )
| ~ ( c @ X1 @ ( esk11_1 @ spain ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_48])]) ).
thf(c_0_70,negated_conjecture,
( ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ ( esk11_1 @ spain ) )
| ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_39]),c_0_44]) ).
thf(c_0_71,negated_conjecture,
( ( c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris )
| ~ ( c @ ( esk7_1 @ ( esk11_1 @ spain ) ) @ spain ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_49]),c_0_50]) ).
thf(c_0_72,negated_conjecture,
c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ paris,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
thf(c_0_73,negated_conjecture,
c @ ( esk8_1 @ ( esk10_1 @ spain ) ) @ france,
inference(spm,[status(thm)],[c_0_33,c_0_72]) ).
thf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_73]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG002^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n016.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 18:38:49 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.YtSyDQmsFE/E---3.1_740051.p
% 1.91/0.56 % Version: 3.5.1-ho
% 1.91/0.56 % partial match(1): HSSSSMSSSLSNSFN
% 1.91/0.56 % Preprocessing class: HSSSSMSSMLSNSFN.
% 1.91/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.91/0.56 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.91/0.56 % Starting post_as_ho5 with 300s (1) cores
% 1.91/0.56 % Starting sh4l with 300s (1) cores
% 1.91/0.56 % Starting ho_unfolding_2 with 300s (1) cores
% 1.91/0.56 % post_as_ho5 with pid 740082 completed with status 9
% 1.91/0.56 % ho_unfolding_3 with pid 740080 completed with status 0
% 1.91/0.56 % Result found by ho_unfolding_3
% 1.91/0.56 % partial match(1): HSSSSMSSSLSNSFN
% 1.91/0.56 % Preprocessing class: HSSSSMSSMLSNSFN.
% 1.91/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.91/0.56 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.91/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.91/0.56 % No SInE strategy applied
% 1.91/0.56 % Search class: HGHNF-FFMM11-SSFSMFNN
% 1.91/0.56 % partial match(3): HGHNF-FFMF11-SHSSMFNN
% 1.91/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.91/0.56 % Starting SubtermCWHack with 136s (1) cores
% 1.91/0.56 % Starting ho_unfolding_3 with 151s (1) cores
% 1.91/0.56 % Starting post_as_ho11 with 136s (1) cores
% 1.91/0.56 % Starting new_ho_9 with 136s (1) cores
% 1.91/0.56 % Starting post_as_ho4 with 136s (1) cores
% 1.91/0.56 % ho_unfolding_3 with pid 740094 completed with status 0
% 1.91/0.56 % Result found by ho_unfolding_3
% 1.91/0.56 % partial match(1): HSSSSMSSSLSNSFN
% 1.91/0.56 % Preprocessing class: HSSSSMSSMLSNSFN.
% 1.91/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.91/0.56 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.91/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.91/0.56 % No SInE strategy applied
% 1.91/0.56 % Search class: HGHNF-FFMM11-SSFSMFNN
% 1.91/0.56 % partial match(3): HGHNF-FFMF11-SHSSMFNN
% 1.91/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.91/0.56 % Starting SubtermCWHack with 136s (1) cores
% 1.91/0.56 % Starting ho_unfolding_3 with 151s (1) cores
% 1.91/0.56 % Preprocessing time : 0.002 s
% 1.91/0.56 % Presaturation interreduction done
% 1.91/0.56
% 1.91/0.56 % Proof found!
% 1.91/0.56 % SZS status Theorem
% 1.91/0.56 % SZS output start CNFRefutation
% See solution above
% 1.91/0.56 % Parsed axioms : 30
% 1.91/0.56 % Removed by relevancy pruning/SinE : 0
% 1.91/0.56 % Initial clauses : 43
% 1.91/0.56 % Removed in clause preprocessing : 15
% 1.91/0.56 % Initial clauses in saturation : 28
% 1.91/0.56 % Processed clauses : 871
% 1.91/0.56 % ...of these trivial : 7
% 1.91/0.56 % ...subsumed : 263
% 1.91/0.56 % ...remaining for further processing : 601
% 1.91/0.56 % Other redundant clauses eliminated : 0
% 1.91/0.56 % Clauses deleted for lack of memory : 0
% 1.91/0.56 % Backward-subsumed : 57
% 1.91/0.56 % Backward-rewritten : 77
% 1.91/0.56 % Generated clauses : 4390
% 1.91/0.56 % ...of the previous two non-redundant : 2533
% 1.91/0.56 % ...aggressively subsumed : 0
% 1.91/0.56 % Contextual simplify-reflections : 59
% 1.91/0.56 % Paramodulations : 4390
% 1.91/0.56 % Factorizations : 0
% 1.91/0.56 % NegExts : 0
% 1.91/0.56 % Equation resolutions : 0
% 1.91/0.56 % Disequality decompositions : 0
% 1.91/0.56 % Total rewrite steps : 3560
% 1.91/0.56 % ...of those cached : 3518
% 1.91/0.56 % Propositional unsat checks : 0
% 1.91/0.56 % Propositional check models : 0
% 1.91/0.56 % Propositional check unsatisfiable : 0
% 1.91/0.56 % Propositional clauses : 0
% 1.91/0.56 % Propositional clauses after purity: 0
% 1.91/0.56 % Propositional unsat core size : 0
% 1.91/0.56 % Propositional preprocessing time : 0.000
% 1.91/0.56 % Propositional encoding time : 0.000
% 1.91/0.56 % Propositional solver time : 0.000
% 1.91/0.56 % Success case prop preproc time : 0.000
% 1.91/0.56 % Success case prop encoding time : 0.000
% 1.91/0.56 % Success case prop solver time : 0.000
% 1.91/0.56 % Current number of processed clauses : 439
% 1.91/0.56 % Positive orientable unit clauses : 50
% 1.91/0.56 % Positive unorientable unit clauses: 0
% 1.91/0.56 % Negative unit clauses : 7
% 1.91/0.56 % Non-unit-clauses : 382
% 1.91/0.56 % Current number of unprocessed clauses: 1659
% 1.91/0.56 % ...number of literals in the above : 7565
% 1.91/0.56 % Current number of archived formulas : 0
% 1.91/0.56 % Current number of archived clauses : 162
% 1.91/0.56 % Clause-clause subsumption calls (NU) : 41858
% 1.91/0.56 % Rec. Clause-clause subsumption calls : 16331
% 1.91/0.56 % Non-unit clause-clause subsumptions : 369
% 1.91/0.56 % Unit Clause-clause subsumption calls : 2803
% 1.91/0.56 % Rewrite failures with RHS unbound : 0
% 1.91/0.56 % BW rewrite match attempts : 23
% 1.91/0.56 % BW rewrite match successes : 7
% 1.91/0.56 % Condensation attempts : 871
% 1.91/0.56 % Condensation successes : 0
% 1.91/0.56 % Termbank termtop insertions : 106494
% 1.91/0.56 % Search garbage collected termcells : 785
% 1.91/0.56
% 1.91/0.56 % -------------------------------------------------
% 1.91/0.56 % User time : 0.235 s
% 1.91/0.56 % System time : 0.019 s
% 1.91/0.56 % Total time : 0.254 s
% 1.91/0.56 % Maximum resident set size: 3592 pages
% 1.91/0.56
% 1.91/0.56 % -------------------------------------------------
% 1.91/0.56 % User time : 1.345 s
% 1.91/0.56 % System time : 0.072 s
% 1.91/0.56 % Total time : 1.418 s
% 1.91/0.56 % Maximum resident set size: 4608 pages
% 1.91/0.56 % E exiting
%------------------------------------------------------------------------------