%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU653^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:24:53 AM UTC 2026
% Result : Theorem 0.12s 0.26s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 90 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 624 ( 22 ~; 39 |; 6 &; 524 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
secondinupair: $o ).
thf(decl_27,type,
upairset2E: $o ).
thf(decl_28,type,
setukpairinjL2: $o ).
thf(decl_29,type,
setukpairinjR1: $o ).
thf(decl_30,type,
upairequniteq: $o ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(setukpairinjR2,conjecture,
( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',setukpairinjR2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',secondinupair) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X3 = X1 )
| ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',upairset2E) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',setukpairinjL2) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p',upairequniteq) ).
thf(c_0_6,negated_conjecture,
~ ( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setukpairinjR2]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X25: $i,X26: $i] : ( in @ X26 @ ( setadjoin @ X25 @ ( setadjoin @ X26 @ emptyset ) ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ ( setadjoin @ X27 @ ( setadjoin @ X28 @ emptyset ) ) )
=> ( ( X29 = X27 )
| ( X29 = X28 ) ) )
=> ( ! [X30: $i,X31: $i,X32: $i,X33: $i] :
( ( ( setadjoin @ ( setadjoin @ X30 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X30 @ ( setadjoin @ X31 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X32 @ ( setadjoin @ X33 @ emptyset ) ) @ emptyset ) ) )
=> ( X30 = X32 ) )
=> ( ! [X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ( setadjoin @ ( setadjoin @ X34 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X34 @ ( setadjoin @ X35 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X36 @ ( setadjoin @ X37 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X36 = X37 )
=> ( X35 = X37 ) ) )
=> ( ! [X38: $i,X39: $i,X40: $i] :
( ( ( setadjoin @ X38 @ ( setadjoin @ X39 @ emptyset ) )
= ( setadjoin @ X40 @ emptyset ) )
=> ( X38 = X39 ) )
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,secondinupair]),upairset2E]),setukpairinjL2]),setukpairinjR1]),upairequniteq]) ).
thf(c_0_8,negated_conjecture,
! [X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i] :
( ( in @ X42 @ ( setadjoin @ X41 @ ( setadjoin @ X42 @ emptyset ) ) )
& ( ~ ( in @ X45 @ ( setadjoin @ X43 @ ( setadjoin @ X44 @ emptyset ) ) )
| ( X45 = X43 )
| ( X45 = X44 ) )
& ( ( ( setadjoin @ ( setadjoin @ X46 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X46 @ ( setadjoin @ X47 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X48 @ ( setadjoin @ X49 @ emptyset ) ) @ emptyset ) ) )
| ( X46 = X48 ) )
& ( ( ( setadjoin @ ( setadjoin @ X50 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X50 @ ( setadjoin @ X51 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X52 @ ( setadjoin @ X53 @ emptyset ) ) @ emptyset ) ) )
| ( X52 != X53 )
| ( X51 = X53 ) )
& ( ( ( setadjoin @ X54 @ ( setadjoin @ X55 @ emptyset ) )
!= ( setadjoin @ X56 @ emptyset ) )
| ( X54 = X55 ) )
& ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) )
& ( esk2_0 != esk4_0 ) ),
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_7])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
in @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) )
| ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( in @ esk2_0 @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
thf(c_0_15,negated_conjecture,
esk2_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
!= ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( esk2_0 = esk3_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ( esk2_0 = esk3_0 )
| ( esk2_0 = esk1_0 )
| ( ( setadjoin @ esk3_0 @ emptyset )
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( X1 = esk2_0 )
| ( X1 = esk1_0 )
| ~ ( in @ X1 @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_21,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ( esk2_0 = esk3_0 ) ),
inference(er,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( esk1_0 = esk4_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_9]),c_0_15]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i] :
( ( esk2_0 = esk3_0 )
| ( X1 = esk1_0 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
thf(c_0_24,negated_conjecture,
( ( ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ) ) )
| ( esk2_0 = esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
thf(c_0_25,negated_conjecture,
( ( esk2_0 = esk3_0 )
| ( esk1_0 != esk3_0 ) ),
inference(ef,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( esk1_0 = esk4_0 )
| ( esk2_0 = esk1_0 )
| ( ( setadjoin @ esk3_0 @ emptyset )
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i] :
( ( X1
= ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) )
| ( X1
= ( setadjoin @ esk1_0 @ emptyset ) )
| ~ ( in @ X1 @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
thf(c_0_28,negated_conjecture,
esk2_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = esk1_0 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
thf(c_0_30,negated_conjecture,
( ( esk2_0 = esk1_0 )
| ( esk1_0 = esk4_0 ) ),
inference(er,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) )
| ( ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) )
= ( setadjoin @ esk1_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_9]) ).
thf(c_0_32,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk3_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( esk1_0 = esk4_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
thf(c_0_33,negated_conjecture,
esk1_0 = esk3_0,
inference(er,[status(thm)],[c_0_29]) ).
thf(c_0_34,negated_conjecture,
esk4_0 != esk3_0,
inference(rw,[status(thm)],[c_0_15,c_0_28]) ).
thf(c_0_35,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk1_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) )
| ( esk1_0 = esk4_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
thf(c_0_36,negated_conjecture,
( ( ( setadjoin @ esk1_0 @ ( setadjoin @ esk3_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) )
| ( ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) )
= ( setadjoin @ esk1_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
thf(c_0_37,negated_conjecture,
( ( setadjoin @ esk3_0 @ ( setadjoin @ esk3_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]),c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( esk1_0 = esk4_0 )
| ( X1 = esk1_0 )
| ~ ( in @ X1 @ ( setadjoin @ esk3_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_35]) ).
thf(c_0_39,negated_conjecture,
( ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_33]),c_0_33]),c_0_37])]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i] :
( ( X1 = esk3_0 )
| ~ ( in @ X1 @ ( setadjoin @ esk3_0 @ emptyset ) ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_33]),c_0_33]),c_0_34]) ).
thf(c_0_41,negated_conjecture,
in @ esk4_0 @ ( setadjoin @ esk3_0 @ emptyset ),
inference(spm,[status(thm)],[c_0_9,c_0_39]) ).
thf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU653^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n006.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 14:02:39 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running higher-order theorem proving
% 0.12/0.23 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.8VsUTSwIAe/E---3.1_764811.p
% 0.12/0.26 % Version: 3.5.1-ho
% 0.12/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.12/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.12/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.12/0.26 % post_as_ho2 with pid 764845 completed with status 0
% 0.12/0.26 % Result found by post_as_ho2
% 0.12/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.12/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.12/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.12/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.26 % No SInE strategy applied
% 0.12/0.26 % Search class: HGUSF-FFSF22-MFFFMFNN
% 0.12/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.26 % SubtermCWHack with pid 764853 completed with status 0
% 0.12/0.26 % Result found by SubtermCWHack
% 0.12/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.12/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.12/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.12/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.12/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.26 % No SInE strategy applied
% 0.12/0.26 % Search class: HGUSF-FFSF22-MFFFMFNN
% 0.12/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.26 % Preprocessing time : 0.001 s
% 0.12/0.26
% 0.12/0.26 % Proof found!
% 0.12/0.26 % SZS status Theorem
% 0.12/0.26 % SZS output start CNFRefutation
% See solution above
% 0.12/0.26 % Parsed axioms : 14
% 0.12/0.26 % Removed by relevancy pruning/SinE : 0
% 0.12/0.26 % Initial clauses : 15
% 0.12/0.26 % Removed in clause preprocessing : 8
% 0.12/0.26 % Initial clauses in saturation : 7
% 0.12/0.26 % Processed clauses : 151
% 0.12/0.26 % ...of these trivial : 11
% 0.12/0.26 % ...subsumed : 50
% 0.12/0.26 % ...remaining for further processing : 90
% 0.12/0.26 % Other redundant clauses eliminated : 1
% 0.12/0.26 % Clauses deleted for lack of memory : 0
% 0.12/0.26 % Backward-subsumed : 21
% 0.12/0.26 % Backward-rewritten : 48
% 0.12/0.26 % Generated clauses : 326
% 0.12/0.26 % ...of the previous two non-redundant : 315
% 0.12/0.26 % ...aggressively subsumed : 0
% 0.12/0.26 % Contextual simplify-reflections : 5
% 0.12/0.26 % Paramodulations : 312
% 0.12/0.26 % Factorizations : 4
% 0.12/0.26 % NegExts : 0
% 0.12/0.26 % Equation resolutions : 6
% 0.12/0.26 % Disequality decompositions : 0
% 0.12/0.26 % Total rewrite steps : 132
% 0.12/0.26 % ...of those cached : 121
% 0.12/0.26 % Propositional unsat checks : 0
% 0.12/0.26 % Propositional check models : 0
% 0.12/0.26 % Propositional check unsatisfiable : 0
% 0.12/0.26 % Propositional clauses : 0
% 0.12/0.26 % Propositional clauses after purity: 0
% 0.12/0.26 % Propositional unsat core size : 0
% 0.12/0.26 % Propositional preprocessing time : 0.000
% 0.12/0.26 % Propositional encoding time : 0.000
% 0.12/0.26 % Propositional solver time : 0.000
% 0.12/0.26 % Success case prop preproc time : 0.000
% 0.12/0.26 % Success case prop encoding time : 0.000
% 0.12/0.26 % Success case prop solver time : 0.000
% 0.12/0.26 % Current number of processed clauses : 16
% 0.12/0.26 % Positive orientable unit clauses : 11
% 0.12/0.26 % Positive unorientable unit clauses: 0
% 0.12/0.26 % Negative unit clauses : 1
% 0.12/0.26 % Non-unit-clauses : 4
% 0.12/0.26 % Current number of unprocessed clauses: 145
% 0.12/0.26 % ...number of literals in the above : 435
% 0.12/0.26 % Current number of archived formulas : 0
% 0.12/0.26 % Current number of archived clauses : 73
% 0.12/0.26 % Clause-clause subsumption calls (NU) : 449
% 0.12/0.26 % Rec. Clause-clause subsumption calls : 385
% 0.12/0.26 % Non-unit clause-clause subsumptions : 63
% 0.12/0.26 % Unit Clause-clause subsumption calls : 27
% 0.12/0.26 % Rewrite failures with RHS unbound : 0
% 0.12/0.26 % BW rewrite match attempts : 7
% 0.12/0.26 % BW rewrite match successes : 6
% 0.12/0.26 % Condensation attempts : 0
% 0.12/0.26 % Condensation successes : 0
% 0.12/0.26 % Termbank termtop insertions : 8454
% 0.12/0.26 % Search garbage collected termcells : 407
% 0.12/0.26
% 0.12/0.26 % -------------------------------------------------
% 0.12/0.26 % User time : 0.010 s
% 0.12/0.26 % System time : 0.001 s
% 0.12/0.26 % Total time : 0.011 s
% 0.12/0.26 % Maximum resident set size: 3640 pages
% 0.12/0.26
% 0.12/0.26 % -------------------------------------------------
% 0.12/0.26 % User time : 0.011 s
% 0.12/0.26 % System time : 0.006 s
% 0.12/0.26 % Total time : 0.016 s
% 0.12/0.26 % Maximum resident set size: 4864 pages
% 0.12/0.26 % E exiting
%------------------------------------------------------------------------------