TSTP Solution File: AGT027^2 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : AGT027^2 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 17:57:44 EDT 2024
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 40
% Syntax : Number of formulae : 99 ( 38 unt; 23 typ; 0 def)
% Number of atoms : 212 ( 24 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 609 ( 104 ~; 89 |; 4 &; 412 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-3 aty)
% Number of variables : 187 ( 62 ^ 125 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_33,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_37,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_49,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
a1: $i > $i > $o ).
thf(decl_54,type,
a2: $i > $i > $o ).
thf(decl_55,type,
a: mu ).
thf(decl_57,type,
p: mu > $i > $o ).
thf(decl_58,type,
q: mu > $i > $o ).
thf(decl_59,type,
r: mu > $i > $o ).
thf(decl_60,type,
s: mu > $i > $o ).
thf(decl_61,type,
esk1_1: $i > $i ).
thf(decl_62,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(decl_65,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_67,type,
esk7_0: $i ).
thf(decl_68,type,
esk8_1: mu > $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(axiom_I_for_a2_a1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ a2 @ X6 ) @ ( mbox @ a1 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_a2_a1) ).
thf(axiom_a4,axiom,
mvalid @ ( mdia @ a1 @ ( s @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a4) ).
thf(axiom_4s_for_a2_a1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ a2 @ X6 ) @ ( mbox @ a1 @ ( mbox @ a2 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_a2_a1) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(axiom_a3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X1 ) @ ( mbox @ a1 @ ( r @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3) ).
thf(axiom_a2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X1 ) @ ( s @ X1 ) ) @ ( q @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(axiom_a1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X1 ) ) @ ( p @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] : ( mbox @ a1 @ ( p @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(c_0_17,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_18,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_19,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_20,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X20: $i] :
( ~ ( Z0 @ Z2 @ X20 )
| ~ ( Z1 @ X20 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_21,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_22,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
thf(c_0_23,plain,
( mforall_prop
= ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_prop]) ).
thf(c_0_24,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_25,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X20: $i] :
( ~ ( Z0 @ Z2 @ X20 )
| ~ ( Z1 @ X20 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
thf(c_0_26,plain,
! [X37: $i,X36: $i > $o] :
( ~ ! [X34: $i] :
( ~ ( a2 @ X37 @ X34 )
| ( X36 @ X34 ) )
| ! [X35: $i] :
( ~ ( a1 @ X37 @ X35 )
| ( X36 @ X35 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_I_for_a2_a1]),c_0_22]),c_0_23]),c_0_21]),c_0_24])]) ).
thf(c_0_27,plain,
! [X33: $i] :
~ ! [X32: $i] :
( ~ ( a1 @ X33 @ X32 )
| ~ ( s @ a @ X32 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a4,c_0_25]),c_0_24])]) ).
thf(c_0_28,plain,
! [X52: $i,X51: $i > $o] :
( ~ ! [X48: $i] :
( ~ ( a2 @ X52 @ X48 )
| ( X51 @ X48 ) )
| ! [X50: $i] :
( ~ ( a1 @ X52 @ X50 )
| ! [X49: $i] :
( ~ ( a2 @ X50 @ X49 )
| ( X51 @ X49 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_4s_for_a2_a1]),c_0_22]),c_0_23]),c_0_21]),c_0_24])]) ).
thf(c_0_29,plain,
! [X74: $i,X75: $i > $o,X77: $i] :
( ( ( a2 @ X74 @ ( esk2_2 @ X74 @ X75 ) )
| ~ ( a1 @ X74 @ X77 )
| ( X75 @ X77 ) )
& ( ~ ( X75 @ ( esk2_2 @ X74 @ X75 ) )
| ~ ( a1 @ X74 @ X77 )
| ( X75 @ X77 ) ) ),
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_26])])])])])]) ).
thf(c_0_30,plain,
! [X72: $i] :
( ( a1 @ X72 @ ( esk1_1 @ X72 ) )
& ( s @ a @ ( esk1_1 @ X72 ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
thf(c_0_31,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_32,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_33,plain,
! [X88: $i,X89: $i > $o,X91: $i,X92: $i] :
( ( ( a2 @ X88 @ ( esk5_2 @ X88 @ X89 ) )
| ~ ( a1 @ X88 @ X91 )
| ~ ( a2 @ X91 @ X92 )
| ( X89 @ X92 ) )
& ( ~ ( X89 @ ( esk5_2 @ X88 @ X89 ) )
| ~ ( a1 @ X88 @ X91 )
| ~ ( a2 @ X91 @ X92 )
| ( X89 @ X92 ) ) ),
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_34,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk2_2 @ X3 @ X4 ) )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,plain,
! [X3: $i] : ( a1 @ X3 @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( a2 @ X3 @ ( esk2_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_37,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_18]),c_0_19]) ).
thf(c_0_38,plain,
! [X31: $i,X30: mu,X29: $i] :
( ~ ( a1 @ X31 @ X29 )
| ~ ( s @ X30 @ X29 )
| ! [X28: $i] :
( ~ ( a1 @ X29 @ X28 )
| ( r @ X30 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_a3]),c_0_22]),c_0_32]),c_0_21]),c_0_24])]) ).
thf(c_0_39,plain,
! [X14: $i,X4: $i > $o,X3: $i,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk5_2 @ X3 @ X4 ) )
| ~ ( a1 @ X3 @ X14 )
| ~ ( a2 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_40,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ ( esk1_1 @ X3 ) )
| ~ ( X4 @ ( esk2_2 @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_41,plain,
! [X4: $i > $o,X3: $i] :
( ( a2 @ X3 @ ( esk2_2 @ X3 @ X4 ) )
| ( X4 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
thf(c_0_42,plain,
! [X14: $i,X4: $i > $o,X3: $i,X15: $i] :
( ( a2 @ X3 @ ( esk5_2 @ X3 @ X4 ) )
| ( X4 @ X15 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( a2 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_43,plain,
! [X27: $i,X26: mu,X25: $i] :
( ~ ( a1 @ X27 @ X25 )
| ~ ~ ( ~ ( r @ X26 @ X25 )
| ~ ( s @ X26 @ X25 ) )
| ( q @ X26 @ X25 ) ),
inference(fof_simplification,[status(thm)],[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)],[inference(fof_simplification,[status(thm)],[axiom_a2]),c_0_37]),c_0_22]),c_0_32]),c_0_21]),c_0_24])]) ).
thf(c_0_44,plain,
! [X68: $i,X69: mu,X70: $i,X71: $i] :
( ~ ( a1 @ X68 @ X70 )
| ~ ( s @ X69 @ X70 )
| ~ ( a1 @ X70 @ X71 )
| ( r @ X69 @ X71 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])])]) ).
thf(c_0_45,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_46,plain,
! [X24: $i,X23: mu,X22: $i] :
( ~ ( a2 @ X24 @ X22 )
| ~ ~ ! [X21: $i] :
( ~ ( a2 @ X22 @ X21 )
| ~ ( q @ X23 @ X21 ) )
| ( p @ X23 @ X22 ) ),
inference(fof_simplification,[status(thm)],[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)],[inference(fof_simplification,[status(thm)],[axiom_a1]),c_0_22]),c_0_32]),c_0_21]),c_0_25]),c_0_24])]) ).
thf(c_0_47,plain,
! [X14: $i,X3: $i,X4: $i > $o] :
( ( X4 @ X3 )
| ~ ( a2 @ ( esk1_1 @ X14 ) @ X3 )
| ~ ( X4 @ ( esk5_2 @ X14 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
thf(c_0_48,plain,
! [X3: $i] : ( a2 @ X3 @ ( esk1_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_49,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( a2 @ X3 @ ( esk5_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a2 @ ( esk1_1 @ X3 ) @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
thf(c_0_50,plain,
! [X65: $i,X66: mu,X67: $i] :
( ~ ( a1 @ X65 @ X67 )
| ~ ( r @ X66 @ X67 )
| ~ ( s @ X66 @ X67 )
| ( q @ X66 @ X67 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
thf(c_0_51,plain,
! [X14: $i,X3: $i,X1: mu,X15: $i] :
( ( r @ X1 @ X15 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( s @ X1 @ X14 )
| ~ ( a1 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_52,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45,c_0_18]),c_0_32]) ).
thf(c_0_53,plain,
! [X61: $i,X62: mu,X63: $i,X64: $i] :
( ~ ( a2 @ X61 @ X63 )
| ~ ( a2 @ X63 @ X64 )
| ~ ( q @ X62 @ X64 )
| ( p @ X62 @ X63 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
thf(c_0_54,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( X4 @ ( esk5_2 @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_55,plain,
! [X4: $i > $o,X3: $i] :
( ( a2 @ X3 @ ( esk5_2 @ X3 @ X4 ) )
| ( X4 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
thf(c_0_56,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( q @ X1 @ X14 )
| ~ ( a1 @ X3 @ X14 )
| ~ ( r @ X1 @ X14 )
| ~ ( s @ X1 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_57,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a1 @ X14 @ X3 )
| ~ ( s @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_35]) ).
thf(c_0_58,negated_conjecture,
~ ! [X60: $i] :
~ ! [X59: mu] :
~ ! [X58: $i] :
( ~ ( a1 @ X60 @ X58 )
| ( p @ X59 @ X58 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_52]),c_0_21]),c_0_24])]) ).
thf(c_0_59,plain,
! [X14: $i,X1: mu,X3: $i,X15: $i] :
( ( p @ X1 @ X14 )
| ~ ( a2 @ X3 @ X14 )
| ~ ( a2 @ X14 @ X15 )
| ~ ( q @ X1 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_60,plain,
! [X3: $i] : ( a2 @ X3 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_61,plain,
! [X1: mu,X3: $i] :
( ( q @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( r @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
thf(c_0_62,plain,
! [X1: mu,X3: $i] :
( ( r @ X1 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_57,c_0_35]) ).
thf(c_0_63,negated_conjecture,
! [X99: mu] :
( ( a1 @ esk7_0 @ ( esk8_1 @ X99 ) )
& ~ ( p @ X99 @ ( esk8_1 @ X99 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
thf(c_0_64,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( p @ X1 @ X3 )
| ~ ( q @ X1 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_65,plain,
! [X1: mu,X3: $i] :
( ( q @ X1 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( s @ X1 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_66,negated_conjecture,
! [X1: mu] : ( a1 @ esk7_0 @ ( esk8_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_67,plain,
! [X14: $i,X1: mu,X3: $i] :
( ( p @ X1 @ X3 )
| ~ ( s @ X1 @ ( esk1_1 @ ( esk1_1 @ X3 ) ) )
| ~ ( s @ X1 @ ( esk1_1 @ X3 ) )
| ~ ( a2 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_68,plain,
! [X3: $i] : ( s @ a @ ( esk1_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_69,negated_conjecture,
! [X1: mu,X4: $i > $o] :
( ( X4 @ ( esk8_1 @ X1 ) )
| ~ ( X4 @ ( esk2_2 @ esk7_0 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_66]) ).
thf(c_0_70,negated_conjecture,
! [X4: $i > $o,X1: mu] :
( ( a2 @ esk7_0 @ ( esk2_2 @ esk7_0 @ X4 ) )
| ( X4 @ ( esk8_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
thf(c_0_71,plain,
! [X14: $i,X3: $i] :
( ( p @ a @ X3 )
| ~ ( a2 @ X14 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_68])]) ).
thf(c_0_72,negated_conjecture,
! [X1: mu] : ( a2 @ esk7_0 @ ( esk8_1 @ X1 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70])]) ).
thf(c_0_73,negated_conjecture,
! [X1: mu] :
~ ( p @ X1 @ ( esk8_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_74,negated_conjecture,
! [X1: mu] : ( p @ a @ ( esk8_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_73,c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : AGT027^2 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.09 % Command : run_E %s %d THM
% 0.09/0.28 % Computer : n010.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sat May 18 18:55:07 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.12/0.38 Running higher-order theorem proving
% 0.12/0.38 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/benchmark/theBenchmark.p
% 0.12/0.45 # Version: 3.1.0-ho
% 0.12/0.45 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.12/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.12/0.45 # Starting post_as_ho3 with 300s (1) cores
% 0.12/0.45 # Starting new_ho_12 with 300s (1) cores
% 0.12/0.45 # Starting new_bool_2 with 300s (1) cores
% 0.12/0.45 # new_bool_2 with pid 10465 completed with status 8
% 0.12/0.45 # new_ho_10_cnf2 with pid 10462 completed with status 0
% 0.12/0.45 # Result found by new_ho_10_cnf2
% 0.12/0.45 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.12/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.12/0.45 # No SInE strategy applied
% 0.12/0.45 # Search class: HGUNS-FFSF21-SHSSMMBN
% 0.12/0.45 # partial match(2): HGUNF-FFSF22-SHSSMMBN
% 0.12/0.45 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 # Starting new_ho_10 with 811s (1) cores
% 0.12/0.45 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.12/0.45 # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.12/0.45 # Starting lpo1_def_fix with 136s (1) cores
% 0.12/0.45 # Starting ehoh_best8_lambda with 136s (1) cores
% 0.12/0.45 # new_ho_10_cnf2 with pid 10469 completed with status 0
% 0.12/0.45 # Result found by new_ho_10_cnf2
% 0.12/0.45 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.12/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.12/0.45 # No SInE strategy applied
% 0.12/0.45 # Search class: HGUNS-FFSF21-SHSSMMBN
% 0.12/0.45 # partial match(2): HGUNF-FFSF22-SHSSMMBN
% 0.12/0.45 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 # Starting new_ho_10 with 811s (1) cores
% 0.12/0.45 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.12/0.45 # Preprocessing time : 0.001 s
% 0.12/0.45 # Presaturation interreduction done
% 0.12/0.45
% 0.12/0.45 # Proof found!
% 0.12/0.45 # SZS status Theorem
% 0.12/0.45 # SZS output start CNFRefutation
% See solution above
% 0.12/0.45 # Parsed axioms : 81
% 0.12/0.45 # Removed by relevancy pruning/SinE : 0
% 0.12/0.45 # Initial clauses : 57
% 0.12/0.45 # Removed in clause preprocessing : 40
% 0.12/0.45 # Initial clauses in saturation : 17
% 0.12/0.45 # Processed clauses : 278
% 0.12/0.45 # ...of these trivial : 7
% 0.12/0.45 # ...subsumed : 24
% 0.12/0.45 # ...remaining for further processing : 247
% 0.12/0.45 # Other redundant clauses eliminated : 0
% 0.12/0.45 # Clauses deleted for lack of memory : 0
% 0.12/0.45 # Backward-subsumed : 1
% 0.12/0.45 # Backward-rewritten : 2
% 0.12/0.45 # Generated clauses : 3150
% 0.12/0.45 # ...of the previous two non-redundant : 2909
% 0.12/0.45 # ...aggressively subsumed : 0
% 0.12/0.45 # Contextual simplify-reflections : 0
% 0.12/0.45 # Paramodulations : 3146
% 0.12/0.45 # Factorizations : 4
% 0.12/0.45 # NegExts : 0
% 0.12/0.45 # Equation resolutions : 0
% 0.12/0.45 # Disequality decompositions : 0
% 0.12/0.45 # Total rewrite steps : 291
% 0.12/0.45 # ...of those cached : 271
% 0.12/0.45 # Propositional unsat checks : 0
% 0.12/0.45 # Propositional check models : 0
% 0.12/0.45 # Propositional check unsatisfiable : 0
% 0.12/0.45 # Propositional clauses : 0
% 0.12/0.45 # Propositional clauses after purity: 0
% 0.12/0.45 # Propositional unsat core size : 0
% 0.12/0.45 # Propositional preprocessing time : 0.000
% 0.12/0.45 # Propositional encoding time : 0.000
% 0.12/0.45 # Propositional solver time : 0.000
% 0.12/0.45 # Success case prop preproc time : 0.000
% 0.12/0.45 # Success case prop encoding time : 0.000
% 0.12/0.45 # Success case prop solver time : 0.000
% 0.12/0.45 # Current number of processed clauses : 227
% 0.12/0.45 # Positive orientable unit clauses : 11
% 0.12/0.45 # Positive unorientable unit clauses: 0
% 0.12/0.45 # Negative unit clauses : 1
% 0.12/0.45 # Non-unit-clauses : 215
% 0.12/0.45 # Current number of unprocessed clauses: 2664
% 0.12/0.45 # ...number of literals in the above : 10731
% 0.12/0.45 # Current number of archived formulas : 0
% 0.12/0.45 # Current number of archived clauses : 20
% 0.12/0.45 # Clause-clause subsumption calls (NU) : 5516
% 0.12/0.45 # Rec. Clause-clause subsumption calls : 4049
% 0.12/0.45 # Non-unit clause-clause subsumptions : 25
% 0.12/0.45 # Unit Clause-clause subsumption calls : 11
% 0.12/0.45 # Rewrite failures with RHS unbound : 0
% 0.12/0.45 # BW rewrite match attempts : 4
% 0.12/0.45 # BW rewrite match successes : 3
% 0.12/0.45 # Condensation attempts : 278
% 0.12/0.45 # Condensation successes : 3
% 0.12/0.45 # Termbank termtop insertions : 74102
% 0.12/0.45 # Search garbage collected termcells : 1976
% 0.12/0.45
% 0.12/0.45 # -------------------------------------------------
% 0.12/0.45 # User time : 0.058 s
% 0.12/0.45 # System time : 0.004 s
% 0.12/0.45 # Total time : 0.061 s
% 0.12/0.45 # Maximum resident set size: 2200 pages
% 0.12/0.45
% 0.12/0.45 # -------------------------------------------------
% 0.12/0.45 # User time : 0.292 s
% 0.12/0.45 # System time : 0.038 s
% 0.12/0.45 # Total time : 0.329 s
% 0.12/0.45 # Maximum resident set size: 1804 pages
% 0.12/0.45 % E---3.1 exiting
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------