%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : PHI004^4 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:20:10 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 2 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 550 ( 66 ~; 56 |; 11 &; 402 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-5 aty)
% Number of variables : 156 ( 37 ^; 119 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
qML_mu: $tType ).
thf(decl_sort2,type,
qML_i: $tType ).
thf(decl_23,type,
scott_G: qML_mu > qML_i > $o ).
thf(decl_25,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(decl_26,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(decl_27,type,
epred1_2: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_29,type,
epred2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_30,type,
esk2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_i ).
thf(decl_31,type,
esk3_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu ).
thf(decl_32,type,
esk4_3: qML_i > ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf(decl_33,type,
esk5_3: qML_i > ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(decl_37,type,
esk8_0: qML_i ).
thf(decl_38,type,
esk9_0: qML_mu ).
thf(fact_5_A1b,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X7 @ X4 )
=> ( scott_P
@ ^ [X12: qML_mu,X13: qML_i] :
~ ( X7 @ X12 @ X13 )
@ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_5_A1b) ).
thf(fact_0_G__def,axiom,
( scott_G
= ( ^ [X1: qML_mu,X2: qML_i] :
! [X3: qML_mu > qML_i > $o] :
( ( scott_P @ X3 @ X2 )
=> ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_0_G__def) ).
thf(fact_2_A4,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ( scott_P @ X7 @ X4 )
=> ! [X8: qML_i] : ( scott_P @ X7 @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_2_A4) ).
thf(conj_0,conjecture,
! [X19: qML_i,X6: qML_mu] :
( ~ ( scott_G @ X6 @ X19 )
| ( scott_ess_QML_mu @ scott_G @ X6 @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',conj_0) ).
thf(fact_4_ess__def,axiom,
( scott_ess_QML_mu
= ( ^ [X9: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ( X9 @ X1 @ X2 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X9 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_4_ess__def) ).
thf(fact_6_A2,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o,X14: qML_mu > qML_i > $o] :
( ( ( scott_P @ X7 @ X4 )
& ! [X15: qML_i,X16: qML_mu] :
( ( X7 @ X16 @ X15 )
=> ( X14 @ X16 @ X15 ) ) )
=> ( scott_P @ X14 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_6_A2) ).
thf(fact_8_A1a,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [X17: qML_mu,X18: qML_i] :
~ ( X7 @ X17 @ X18 )
@ X4 )
=> ~ ( scott_P @ X7 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qkso1GE78n/E---3.1_1257490.p',fact_8_A1a) ).
thf(c_0_7,plain,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X7 @ X4 )
=> ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X7 @ Z0 @ Z1 )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_5_A1b])]) ).
thf(c_0_8,plain,
! [X39: qML_mu,X40: qML_i] :
( ( scott_G @ X39 @ X40 )
<=> ! [X3: qML_mu > qML_i > $o] :
( ( scott_P @ X3 @ X40 )
=> ( X3 @ X39 @ X40 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_0_G__def])]) ).
thf(c_0_9,plain,
! [X54: qML_i,X55: qML_mu > qML_i > $o,X56: qML_i] :
( ~ ( scott_P @ X55 @ X54 )
| ( scott_P @ X55 @ X56 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_A4])])])]) ).
thf(c_0_10,plain,
! [X70: qML_i,X71: qML_mu > qML_i > $o] :
( ( scott_P @ X71 @ X70 )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X71 @ Z0 @ Z1 )
@ X70 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
thf(c_0_11,negated_conjecture,
~ ! [X19: qML_i,X6: qML_mu] :
( ~ ( scott_G @ X6 @ X19 )
| ( scott_ess_QML_mu @ scott_G @ X6 @ X19 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_12,plain,
! [X46: qML_mu,X47: qML_i,X48: qML_mu > qML_i > $o,X49: qML_mu,X50: qML_i] :
( ( ~ ( scott_G @ X46 @ X47 )
| ~ ( scott_P @ X48 @ X47 )
| ( X48 @ X46 @ X47 ) )
& ( ( scott_P @ ( epred1_2 @ X49 @ X50 ) @ X50 )
| ( scott_G @ X49 @ X50 ) )
& ( ~ ( epred1_2 @ X49 @ X50 @ X49 @ X50 )
| ( scott_G @ X49 @ X50 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])])]) ).
thf(c_0_13,plain,
! [X4: qML_i,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X4 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X2 )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ! [X19: qML_i,X6: qML_mu] :
( ~ ( scott_G @ X6 @ X19 )
| ( scott_ess_QML_mu @ scott_G @ X6 @ X19 ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ X1 @ X2 )
| ~ ( scott_G @ X1 @ X2 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X2: qML_i,X3: qML_mu > qML_i > $o,X4: qML_i] :
( ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 )
| ( scott_P @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( scott_G @ esk9_0 @ esk8_0 )
& ~ ( scott_ess_QML_mu @ scott_G @ esk9_0 @ esk8_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_19,plain,
! [X41: qML_mu > qML_i > $o,X42: qML_mu,X43: qML_i] :
( ( scott_ess_QML_mu @ X41 @ X42 @ X43 )
<=> ( ( X41 @ X42 @ X43 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X42 @ X43 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X41 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_4_ess__def])]) ).
thf(c_0_20,plain,
! [X2: qML_i,X1: qML_mu,X3: qML_mu > qML_i > $o,X4: qML_i] :
( ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 )
| ( X3 @ X1 @ X4 )
| ~ ( scott_G @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
scott_G @ esk9_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
! [X58: qML_mu > qML_i > $o,X59: qML_mu,X60: qML_i,X61: qML_mu > qML_i > $o,X62: qML_i,X63: qML_mu,X64: qML_mu > qML_i > $o,X65: qML_mu,X66: qML_i] :
( ( ( X58 @ X59 @ X60 )
| ~ ( scott_ess_QML_mu @ X58 @ X59 @ X60 ) )
& ( ~ ( X61 @ X59 @ X60 )
| ~ ( X58 @ X63 @ X62 )
| ( X61 @ X63 @ X62 )
| ~ ( scott_ess_QML_mu @ X58 @ X59 @ X60 ) )
& ( ( epred2_3 @ X64 @ X65 @ X66 @ X65 @ X66 )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) )
& ( ( X64 @ ( esk3_3 @ X64 @ X65 @ X66 ) @ ( esk2_3 @ X64 @ X65 @ X66 ) )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) )
& ( ~ ( epred2_3 @ X64 @ X65 @ X66 @ ( esk3_3 @ X64 @ X65 @ X66 ) @ ( esk2_3 @ X64 @ X65 @ X66 ) )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])]) ).
thf(c_0_23,plain,
! [X72: qML_i,X73: qML_mu > qML_i > $o,X74: qML_mu > qML_i > $o] :
( ( ( X73 @ ( esk5_3 @ X72 @ X73 @ X74 ) @ ( esk4_3 @ X72 @ X73 @ X74 ) )
| ~ ( scott_P @ X73 @ X72 )
| ( scott_P @ X74 @ X72 ) )
& ( ~ ( X74 @ ( esk5_3 @ X72 @ X73 @ X74 ) @ ( esk4_3 @ X72 @ X73 @ X74 ) )
| ~ ( scott_P @ X73 @ X72 )
| ( scott_P @ X74 @ X72 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_A2])])])])]) ).
thf(c_0_24,negated_conjecture,
! [X2: qML_i,X3: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 )
| ( X3 @ esk9_0 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ X1 @ X2 )
| ~ ( scott_ess_QML_mu @ X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,plain,
! [X7: qML_mu > qML_i > $o,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk5_3 @ X2 @ X3 @ X7 ) @ ( esk4_3 @ X2 @ X3 @ X7 ) )
| ( scott_P @ X7 @ X2 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ esk9_0 @ esk8_0 )
| ~ ( scott_G @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24])]) ).
thf(c_0_28,plain,
! [X7: qML_mu > qML_i > $o,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk5_3 @ X2 @ ( scott_ess_QML_mu @ X3 ) @ X7 ) @ ( esk4_3 @ X2 @ ( scott_ess_QML_mu @ X3 ) @ X7 ) )
| ( scott_P @ X7 @ X2 )
| ~ ( scott_P @ ( scott_ess_QML_mu @ X3 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X7: qML_mu > qML_i > $o,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ esk9_0 @ esk8_0 )
| ( scott_P @ X7 @ X2 )
| ~ ( X3 @ ( esk5_3 @ X2 @ ( scott_ess_QML_mu @ scott_G ) @ X7 ) @ ( esk4_3 @ X2 @ ( scott_ess_QML_mu @ scott_G ) @ X7 ) )
| ~ ( scott_P @ ( scott_ess_QML_mu @ scott_G ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_30,negated_conjecture,
~ ( scott_ess_QML_mu @ scott_G @ esk9_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_31,negated_conjecture,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X2 )
| ~ ( scott_P @ ( scott_ess_QML_mu @ scott_G ) @ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_30]) ).
thf(c_0_32,plain,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X7 @ Z0 @ Z1 )
@ X4 )
=> ~ ( scott_P @ X7 @ X4 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_8_A1a])]) ).
thf(c_0_33,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk3_3 @ X3 @ X1 @ X2 ) @ ( esk2_3 @ X3 @ X1 @ X2 ) )
| ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_34,negated_conjecture,
! [X2: qML_i,X3: qML_mu > qML_i > $o,X4: qML_i] :
( ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( scott_ess_QML_mu @ scott_G @ Z0 @ Z1 )
@ X2 )
| ( scott_P @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
thf(c_0_35,plain,
! [X78: qML_i,X79: qML_mu > qML_i > $o] :
( ~ ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X79 @ Z0 @ Z1 )
@ X78 )
| ~ ( scott_P @ X79 @ X78 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
thf(c_0_36,plain,
! [X1: qML_mu,X4: qML_i,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk3_3 @ scott_G @ X1 @ X2 ) @ ( esk2_3 @ scott_G @ X1 @ X2 ) )
| ( scott_ess_QML_mu @ scott_G @ X1 @ X2 )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X4 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
thf(c_0_37,negated_conjecture,
! [X2: qML_i] :
( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( scott_ess_QML_mu @ scott_G @ Z0 @ Z1 )
@ X2 ),
inference(ef,[status(thm)],[c_0_34]) ).
thf(c_0_38,plain,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ~ ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_39,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( epred2_3 @ X3 @ X1 @ X2 @ ( esk3_3 @ X3 @ X1 @ X2 ) @ ( esk2_3 @ X3 @ X1 @ X2 ) )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_40,negated_conjecture,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk3_3 @ scott_G @ esk9_0 @ esk8_0 ) @ ( esk2_3 @ scott_G @ esk9_0 @ esk8_0 ) )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_30]) ).
thf(c_0_41,negated_conjecture,
! [X1: qML_mu,X2: qML_i] :
~ ( scott_ess_QML_mu @ scott_G @ X1 @ X2 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_37])]),c_0_25]) ).
thf(c_0_42,negated_conjecture,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ esk9_0 @ esk8_0 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_24]) ).
thf(c_0_43,negated_conjecture,
! [X2: qML_i] :
( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( epred2_3 @ scott_G @ esk9_0 @ esk8_0 @ Z0 @ Z1 )
@ X2 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_21])]),c_0_41]) ).
thf(c_0_44,negated_conjecture,
~ ( epred2_3 @ scott_G @ esk9_0 @ esk8_0 @ esk9_0 @ esk8_0 ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_45,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( epred2_3 @ X3 @ X1 @ X2 @ X1 @ X2 )
| ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_21])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI004^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:20:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.Qkso1GE78n/E---3.1_1257490.p
% 0.22/0.36 % Version: 3.5.1-ho
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.36 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.36 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.22/0.36 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.22/0.36 % ehoh_best_nonlift_rwall with pid 1257524 completed with status 0
% 0.22/0.36 % Result found by ehoh_best_nonlift_rwall
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.36 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.36 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.22/0.36 % No SInE strategy applied
% 0.22/0.36 % Search class: HGHNS-FFSF32-MHSFFSBN
% 0.22/0.36 % partial match(2): HGHNS-FFMF32-SHSFFSBN
% 0.22/0.36 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.36 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.36 % SubtermCWHack with pid 1257531 completed with status 0
% 0.22/0.36 % Result found by SubtermCWHack
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSMNHSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.36 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.36 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.22/0.36 % No SInE strategy applied
% 0.22/0.36 % Search class: HGHNS-FFSF32-MHSFFSBN
% 0.22/0.36 % partial match(2): HGHNS-FFMF32-SHSFFSBN
% 0.22/0.36 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.36 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.36 % Preprocessing time : 0.002 s
% 0.22/0.36
% 0.22/0.36 % Proof found!
% 0.22/0.36 % SZS status Theorem
% 0.22/0.36 % SZS output start CNFRefutation
% See solution above
% 0.22/0.36 % Parsed axioms : 17
% 0.22/0.36 % Removed by relevancy pruning/SinE : 0
% 0.22/0.36 % Initial clauses : 27
% 0.22/0.36 % Removed in clause preprocessing : 6
% 0.22/0.36 % Initial clauses in saturation : 21
% 0.22/0.36 % Processed clauses : 805
% 0.22/0.36 % ...of these trivial : 45
% 0.22/0.36 % ...subsumed : 465
% 0.22/0.36 % ...remaining for further processing : 295
% 0.22/0.36 % Other redundant clauses eliminated : 0
% 0.22/0.36 % Clauses deleted for lack of memory : 0
% 0.22/0.36 % Backward-subsumed : 13
% 0.22/0.36 % Backward-rewritten : 2
% 0.22/0.36 % Generated clauses : 2331
% 0.22/0.36 % ...of the previous two non-redundant : 2031
% 0.22/0.36 % ...aggressively subsumed : 0
% 0.22/0.36 % Contextual simplify-reflections : 2
% 0.22/0.36 % Paramodulations : 2329
% 0.22/0.36 % Factorizations : 2
% 0.22/0.36 % NegExts : 0
% 0.22/0.36 % Equation resolutions : 0
% 0.22/0.36 % Disequality decompositions : 0
% 0.22/0.36 % Total rewrite steps : 635
% 0.22/0.36 % ...of those cached : 588
% 0.22/0.36 % Propositional unsat checks : 0
% 0.22/0.36 % Propositional check models : 0
% 0.22/0.36 % Propositional check unsatisfiable : 0
% 0.22/0.36 % Propositional clauses : 0
% 0.22/0.36 % Propositional clauses after purity: 0
% 0.22/0.36 % Propositional unsat core size : 0
% 0.22/0.36 % Propositional preprocessing time : 0.000
% 0.22/0.36 % Propositional encoding time : 0.000
% 0.22/0.36 % Propositional solver time : 0.000
% 0.22/0.36 % Success case prop preproc time : 0.000
% 0.22/0.36 % Success case prop encoding time : 0.000
% 0.22/0.36 % Success case prop solver time : 0.000
% 0.22/0.36 % Current number of processed clauses : 280
% 0.22/0.36 % Positive orientable unit clauses : 22
% 0.22/0.36 % Positive unorientable unit clauses: 0
% 0.22/0.36 % Negative unit clauses : 51
% 0.22/0.36 % Non-unit-clauses : 207
% 0.22/0.36 % Current number of unprocessed clauses: 1199
% 0.22/0.36 % ...number of literals in the above : 3436
% 0.22/0.36 % Current number of archived formulas : 0
% 0.22/0.36 % Current number of archived clauses : 15
% 0.22/0.36 % Clause-clause subsumption calls (NU) : 7511
% 0.22/0.36 % Rec. Clause-clause subsumption calls : 5964
% 0.22/0.36 % Non-unit clause-clause subsumptions : 360
% 0.22/0.36 % Unit Clause-clause subsumption calls : 316
% 0.22/0.36 % Rewrite failures with RHS unbound : 0
% 0.22/0.36 % BW rewrite match attempts : 196
% 0.22/0.36 % BW rewrite match successes : 2
% 0.22/0.36 % Condensation attempts : 0
% 0.22/0.36 % Condensation successes : 0
% 0.22/0.36 % Termbank termtop insertions : 106286
% 0.22/0.36 % Search garbage collected termcells : 600
% 0.22/0.36
% 0.22/0.36 % -------------------------------------------------
% 0.22/0.36 % User time : 0.094 s
% 0.22/0.36 % System time : 0.006 s
% 0.22/0.36 % Total time : 0.100 s
% 0.22/0.36 % Maximum resident set size: 3652 pages
% 0.22/0.36
% 0.22/0.36 % -------------------------------------------------
% 0.22/0.36 % User time : 0.097 s
% 0.22/0.36 % System time : 0.009 s
% 0.22/0.36 % Total time : 0.106 s
% 0.22/0.36 % Maximum resident set size: 4864 pages
% 0.22/0.36 % E exiting
%------------------------------------------------------------------------------