%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : AGT031^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 07:44:28 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 229 ( 19 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 789 ( 92 ~; 97 |; 4 &; 596 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 5 con; 0-4 aty)
% Number of variables : 166 ( 53 ^; 113 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_34,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
a1: $i > $i > $o ).
thf(decl_55,type,
a2: $i > $i > $o ).
thf(decl_56,type,
a3: $i > $i > $o ).
thf(decl_57,type,
jan: mu ).
thf(decl_59,type,
cola: mu ).
thf(decl_60,type,
pepsi: mu ).
thf(decl_62,type,
likes: mu > mu > $i > $o ).
thf(decl_63,type,
very_much_likes: mu > mu > $i > $o ).
thf(decl_67,type,
esk3_4: $i > mu > mu > $i > $i ).
thf(decl_68,type,
esk4_4: $i > mu > mu > $i > $i ).
thf(decl_69,type,
esk5_3: $i > mu > mu > $i ).
thf(decl_70,type,
esk6_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mimplies) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mvalid) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mforall_ind) ).
thf(axiom_a2_1,axiom,
mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_a2_1) ).
thf(axiom_a3_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ X1 @ X2 ) @ ( mand @ ( mbox @ a1 @ ( likes @ X1 @ X2 ) ) @ ( mbox @ a2 @ ( likes @ X1 @ X2 ) ) ) ) @ ( very_much_likes @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_a3_4) ).
thf(axiom_a1_1,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_a1_1) ).
thf(axiom_a2_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ X1 @ pepsi ) @ ( likes @ X1 @ cola ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_a2_4) ).
thf(axiom_a3_1,axiom,
mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_a3_1) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',mexists_ind) ).
thf(axiom_user_communication_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ X1 @ X2 ) ) @ ( very_much_likes @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',axiom_user_communication_1) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( very_much_likes @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zCF5QEiPqe/E---3.1_403595.p',conj) ).
thf(c_0_15,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_19,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_20,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_21,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_15,c_0_16]),c_0_17]) ).
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_18,c_0_16]),c_0_17]) ).
thf(c_0_23,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_24,plain,
! [X34: $i,X33: $i] :
( ~ ( a2 @ X34 @ X33 )
| ( likes @ jan @ pepsi @ X33 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a2_1,c_0_19]),c_0_20])]) ).
thf(c_0_25,plain,
! [X56: $i,X55: mu,X54: mu,X53: $i] :
( ~ ( a3 @ X56 @ X53 )
| ~ ~ ( ~ ( likes @ X55 @ X54 @ X53 )
| ~ ~ ( ~ ! [X51: $i] :
( ~ ( a1 @ X53 @ X51 )
| ( likes @ X55 @ X54 @ X51 ) )
| ~ ! [X52: $i] :
( ~ ( a2 @ X53 @ X52 )
| ( likes @ X55 @ X54 @ X52 ) ) ) )
| ( very_much_likes @ X55 @ X54 @ X53 ) ),
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_a3_4]),c_0_21]),c_0_22]),c_0_23]),c_0_19]),c_0_20])]) ).
thf(c_0_26,plain,
! [X22: $i,X21: $i] :
( ~ ( a1 @ X22 @ X21 )
| ( likes @ jan @ cola @ X21 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a1_1,c_0_19]),c_0_20])]) ).
thf(c_0_27,plain,
! [X92: $i,X93: $i] :
( ~ ( a2 @ X92 @ X93 )
| ( likes @ jan @ pepsi @ X93 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_24])]) ).
thf(c_0_28,plain,
! [X110: $i,X111: mu,X112: mu,X113: $i] :
( ( ( a2 @ X113 @ ( esk4_4 @ X110 @ X111 @ X112 @ X113 ) )
| ( a1 @ X113 @ ( esk3_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ X113 )
| ( very_much_likes @ X111 @ X112 @ X113 )
| ~ ( a3 @ X110 @ X113 ) )
& ( ~ ( likes @ X111 @ X112 @ ( esk4_4 @ X110 @ X111 @ X112 @ X113 ) )
| ( a1 @ X113 @ ( esk3_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ X113 )
| ( very_much_likes @ X111 @ X112 @ X113 )
| ~ ( a3 @ X110 @ X113 ) )
& ( ( a2 @ X113 @ ( esk4_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ ( esk3_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ X113 )
| ( very_much_likes @ X111 @ X112 @ X113 )
| ~ ( a3 @ X110 @ X113 ) )
& ( ~ ( likes @ X111 @ X112 @ ( esk4_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ ( esk3_4 @ X110 @ X111 @ X112 @ X113 ) )
| ~ ( likes @ X111 @ X112 @ X113 )
| ( very_much_likes @ X111 @ X112 @ X113 )
| ~ ( a3 @ X110 @ X113 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
thf(c_0_29,plain,
! [X41: $i,X40: mu,X39: $i] :
( ~ ( a2 @ X41 @ X39 )
| ~ ( likes @ X40 @ pepsi @ X39 )
| ( likes @ X40 @ cola @ X39 ) ),
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_a2_4]),c_0_22]),c_0_23]),c_0_19]),c_0_20])]) ).
thf(c_0_30,plain,
! [X80: $i,X81: $i] :
( ~ ( a1 @ X80 @ X81 )
| ( likes @ jan @ cola @ X81 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
thf(c_0_31,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ pepsi @ X14 )
| ~ ( a2 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
! [X1: mu,X14: $i,X2: mu,X3: $i] :
( ( a2 @ X3 @ ( esk4_4 @ X14 @ X1 @ X2 @ X3 ) )
| ( a1 @ X3 @ ( esk3_4 @ X14 @ X1 @ X2 @ X3 ) )
| ( very_much_likes @ X1 @ X2 @ X3 )
| ~ ( likes @ X1 @ X2 @ X3 )
| ~ ( a3 @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,plain,
! [X46: $i,X45: $i] :
( ~ ( a3 @ X46 @ X45 )
| ( likes @ jan @ cola @ X45 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_a3_1,c_0_19]),c_0_20])]) ).
thf(c_0_34,plain,
! [X98: $i,X99: mu,X100: $i] :
( ~ ( a2 @ X98 @ X100 )
| ~ ( likes @ X99 @ pepsi @ X100 )
| ( likes @ X99 @ cola @ X100 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
thf(c_0_35,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ X14 )
| ~ ( a1 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
! [X2: mu,X3: $i,X1: mu,X14: $i] :
( ( likes @ jan @ pepsi @ ( esk4_4 @ X3 @ X1 @ X2 @ X14 ) )
| ( a1 @ X14 @ ( esk3_4 @ X3 @ X1 @ X2 @ X14 ) )
| ( very_much_likes @ X1 @ X2 @ X14 )
| ~ ( likes @ X1 @ X2 @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,plain,
! [X104: $i,X105: $i] :
( ~ ( a3 @ X104 @ X105 )
| ( likes @ jan @ cola @ X105 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
thf(c_0_38,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( likes @ X1 @ cola @ X14 )
| ~ ( a2 @ X3 @ X14 )
| ~ ( likes @ X1 @ pepsi @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_39,plain,
! [X1: mu,X14: $i,X2: mu,X3: $i] :
( ( a2 @ X3 @ ( esk4_4 @ X14 @ X1 @ X2 @ X3 ) )
| ( very_much_likes @ X1 @ X2 @ X3 )
| ~ ( likes @ X1 @ X2 @ ( esk3_4 @ X14 @ X1 @ X2 @ X3 ) )
| ~ ( likes @ X1 @ X2 @ X3 )
| ~ ( a3 @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_40,plain,
! [X2: mu,X3: $i,X1: mu,X14: $i] :
( ( likes @ jan @ pepsi @ ( esk4_4 @ X3 @ X1 @ X2 @ X14 ) )
| ( likes @ jan @ cola @ ( esk3_4 @ X3 @ X1 @ X2 @ X14 ) )
| ( very_much_likes @ X1 @ X2 @ X14 )
| ~ ( likes @ X1 @ X2 @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,plain,
! [X1: mu,X2: mu,X18: mu,X3: $i,X14: $i] :
( ( likes @ X1 @ cola @ ( esk4_4 @ X3 @ X2 @ X18 @ X14 ) )
| ( a1 @ X14 @ ( esk3_4 @ X3 @ X2 @ X18 @ X14 ) )
| ( very_much_likes @ X2 @ X18 @ X14 )
| ~ ( likes @ X1 @ pepsi @ ( esk4_4 @ X3 @ X2 @ X18 @ X14 ) )
| ~ ( likes @ X2 @ X18 @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
thf(c_0_43,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ pepsi @ ( esk4_4 @ X3 @ jan @ cola @ X14 ) )
| ( very_much_likes @ jan @ cola @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_31]) ).
thf(c_0_44,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ ( esk4_4 @ X3 @ jan @ cola @ X14 ) )
| ( a1 @ X14 @ ( esk3_4 @ X3 @ jan @ cola @ X14 ) )
| ( very_much_likes @ jan @ cola @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_41]) ).
thf(c_0_45,plain,
! [X2: mu,X3: $i,X1: mu,X14: $i] :
( ( a1 @ X14 @ ( esk3_4 @ X3 @ X1 @ X2 @ X14 ) )
| ( very_much_likes @ X1 @ X2 @ X14 )
| ~ ( likes @ X1 @ X2 @ ( esk4_4 @ X3 @ X1 @ X2 @ X14 ) )
| ~ ( likes @ X1 @ X2 @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_46,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ ( esk4_4 @ X3 @ jan @ cola @ X14 ) )
| ( likes @ jan @ cola @ ( esk3_4 @ X3 @ jan @ cola @ X14 ) )
| ( very_much_likes @ jan @ cola @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
thf(c_0_47,plain,
! [X3: $i,X14: $i] :
( ( likes @ jan @ cola @ ( esk3_4 @ X3 @ jan @ cola @ X14 ) )
| ( very_much_likes @ jan @ cola @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]),c_0_35]) ).
thf(c_0_48,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_49,plain,
! [X14: $i,X3: $i] :
( ( a2 @ X3 @ ( esk4_4 @ X14 @ jan @ cola @ X3 ) )
| ( very_much_likes @ jan @ cola @ X3 )
| ~ ( a3 @ X14 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_41]) ).
thf(c_0_50,plain,
! [X60: $i,X59: mu,X58: mu] :
( ~ ! [X57: $i] :
( ~ ( a3 @ X60 @ X57 )
| ( very_much_likes @ X59 @ X58 @ X57 ) )
| ( very_much_likes @ X59 @ X58 @ X60 ) ),
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_user_communication_1]),c_0_22]),c_0_23]),c_0_19]),c_0_20])]) ).
thf(c_0_51,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( very_much_likes @ X1 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
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_48,c_0_16]),c_0_23]) ).
thf(c_0_53,plain,
! [X2: mu,X3: $i,X1: mu,X14: $i] :
( ( very_much_likes @ X1 @ X2 @ X14 )
| ~ ( likes @ X1 @ X2 @ ( esk4_4 @ X3 @ X1 @ X2 @ X14 ) )
| ~ ( likes @ X1 @ X2 @ ( esk3_4 @ X3 @ X1 @ X2 @ X14 ) )
| ~ ( likes @ X1 @ X2 @ X14 )
| ~ ( a3 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_54,plain,
! [X3: $i,X1: mu,X14: $i] :
( ( likes @ X1 @ cola @ ( esk4_4 @ X3 @ jan @ cola @ X14 ) )
| ( very_much_likes @ jan @ cola @ X14 )
| ~ ( likes @ X1 @ pepsi @ ( esk4_4 @ X3 @ jan @ cola @ X14 ) )
| ~ ( a3 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
thf(c_0_55,plain,
! [X116: $i,X117: mu,X118: mu] :
( ( ( a3 @ X116 @ ( esk5_3 @ X116 @ X117 @ X118 ) )
| ( very_much_likes @ X117 @ X118 @ X116 ) )
& ( ~ ( very_much_likes @ X117 @ X118 @ ( esk5_3 @ X116 @ X117 @ X118 ) )
| ( very_much_likes @ X117 @ X118 @ X116 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])]) ).
thf(c_0_56,negated_conjecture,
~ ! [X79: $i] :
~ ! [X78: mu] :
~ ~ ! [X77: mu] :
~ ( very_much_likes @ X78 @ X77 @ X79 ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_51]),c_0_52]),c_0_20])]) ).
thf(c_0_57,plain,
! [X14: $i,X3: $i] :
( ( very_much_likes @ jan @ cola @ X3 )
| ~ ( a3 @ X14 @ X3 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_41]),c_0_43]),c_0_47]) ).
thf(c_0_58,plain,
! [X1: mu,X2: mu,X3: $i] :
( ( a3 @ X3 @ ( esk5_3 @ X3 @ X1 @ X2 ) )
| ( very_much_likes @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_59,negated_conjecture,
! [X137: mu,X138: mu] :
~ ( very_much_likes @ X137 @ X138 @ esk6_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
thf(c_0_60,plain,
! [X1: mu,X3: $i,X2: mu] :
( ( very_much_likes @ X1 @ X2 @ X3 )
| ~ ( very_much_likes @ X1 @ X2 @ ( esk5_3 @ X3 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_61,plain,
! [X1: mu,X2: mu,X3: $i] :
( ( very_much_likes @ jan @ cola @ ( esk5_3 @ X3 @ X1 @ X2 ) )
| ( very_much_likes @ X1 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_62,negated_conjecture,
! [X1: mu,X2: mu] :
~ ( very_much_likes @ X1 @ X2 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_63,plain,
! [X3: $i] : ( very_much_likes @ jan @ cola @ X3 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_62,c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT031^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:30:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.zCF5QEiPqe/E---3.1_403595.p
% 0.20/0.27 % Version: 3.5.1-ho
% 0.20/0.27 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.20/0.27 % Starting new_ho_12 with 300s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.27 % post_as_ho3 with pid 403624 completed with status 0
% 0.20/0.27 % Result found by post_as_ho3
% 0.20/0.27 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.20/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.27 % No SInE strategy applied
% 0.20/0.27 % Search class: HGUNM-FFMF32-SHSSMFNN
% 0.20/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.27 % SubtermCWHack with pid 403632 completed with status 0
% 0.20/0.27 % Result found by SubtermCWHack
% 0.20/0.27 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.20/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.27 % No SInE strategy applied
% 0.20/0.27 % Search class: HGUNM-FFMF32-SHSSMFNN
% 0.20/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.27 % Preprocessing time : 0.001 s
% 0.20/0.27
% 0.20/0.27 % Proof found!
% 0.20/0.27 % SZS status Theorem
% 0.20/0.27 % SZS output start CNFRefutation
% See solution above
% 0.20/0.27 % Parsed axioms : 93
% 0.20/0.27 % Removed by relevancy pruning/SinE : 0
% 0.20/0.27 % Initial clauses : 68
% 0.20/0.27 % Removed in clause preprocessing : 43
% 0.20/0.27 % Initial clauses in saturation : 25
% 0.20/0.27 % Processed clauses : 123
% 0.20/0.27 % ...of these trivial : 3
% 0.20/0.27 % ...subsumed : 29
% 0.20/0.27 % ...remaining for further processing : 91
% 0.20/0.27 % Other redundant clauses eliminated : 0
% 0.20/0.27 % Clauses deleted for lack of memory : 0
% 0.20/0.27 % Backward-subsumed : 26
% 0.20/0.27 % Backward-rewritten : 17
% 0.20/0.27 % Generated clauses : 235
% 0.20/0.27 % ...of the previous two non-redundant : 133
% 0.20/0.27 % ...aggressively subsumed : 0
% 0.20/0.27 % Contextual simplify-reflections : 23
% 0.20/0.27 % Paramodulations : 235
% 0.20/0.27 % Factorizations : 0
% 0.20/0.27 % NegExts : 0
% 0.20/0.27 % Equation resolutions : 0
% 0.20/0.27 % Disequality decompositions : 0
% 0.20/0.27 % Total rewrite steps : 120
% 0.20/0.27 % ...of those cached : 103
% 0.20/0.27 % Propositional unsat checks : 0
% 0.20/0.27 % Propositional check models : 0
% 0.20/0.27 % Propositional check unsatisfiable : 0
% 0.20/0.27 % Propositional clauses : 0
% 0.20/0.27 % Propositional clauses after purity: 0
% 0.20/0.27 % Propositional unsat core size : 0
% 0.20/0.27 % Propositional preprocessing time : 0.000
% 0.20/0.27 % Propositional encoding time : 0.000
% 0.20/0.27 % Propositional solver time : 0.000
% 0.20/0.27 % Success case prop preproc time : 0.000
% 0.20/0.27 % Success case prop encoding time : 0.000
% 0.20/0.27 % Success case prop solver time : 0.000
% 0.20/0.27 % Current number of processed clauses : 48
% 0.20/0.27 % Positive orientable unit clauses : 14
% 0.20/0.27 % Positive unorientable unit clauses: 0
% 0.20/0.27 % Negative unit clauses : 1
% 0.20/0.27 % Non-unit-clauses : 33
% 0.20/0.27 % Current number of unprocessed clauses: 21
% 0.20/0.27 % ...number of literals in the above : 115
% 0.20/0.27 % Current number of archived formulas : 0
% 0.20/0.27 % Current number of archived clauses : 43
% 0.20/0.27 % Clause-clause subsumption calls (NU) : 568
% 0.20/0.27 % Rec. Clause-clause subsumption calls : 248
% 0.20/0.27 % Non-unit clause-clause subsumptions : 78
% 0.20/0.27 % Unit Clause-clause subsumption calls : 13
% 0.20/0.27 % Rewrite failures with RHS unbound : 0
% 0.20/0.27 % BW rewrite match attempts : 21
% 0.20/0.27 % BW rewrite match successes : 13
% 0.20/0.27 % Condensation attempts : 0
% 0.20/0.27 % Condensation successes : 0
% 0.20/0.27 % Termbank termtop insertions : 11379
% 0.20/0.27 % Search garbage collected termcells : 2646
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.011 s
% 0.20/0.27 % System time : 0.004 s
% 0.20/0.27 % Total time : 0.016 s
% 0.20/0.27 % Maximum resident set size: 4232 pages
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.012 s
% 0.20/0.27 % System time : 0.007 s
% 0.20/0.27 % Total time : 0.019 s
% 0.20/0.27 % Maximum resident set size: 4864 pages
% 0.20/0.27 % E exiting
%------------------------------------------------------------------------------