%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU362+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 : Tue May 5 05:12:04 PM UTC 2026
% Result : Theorem 3.28s 3.02s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 19 unt; 0 def)
% Number of atoms : 230 ( 12 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 267 ( 110 ~; 108 |; 21 &)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 113 ( 3 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(d13_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( rel_str(X2)
=> ( subrelstr(X2,X1)
<=> ( subset(the_carrier(X2),the_carrier(X1))
& subset(the_InternalRel(X2),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(dt_m1_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> rel_str(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(t60_yellow_0,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X2,X5,X6) )
=> related(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_yellow_0) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(c_0_10,plain,
! [X123,X124] :
( ~ element(X123,X124)
| empty(X124)
| in(X123,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_11,plain,
! [X125,X126] :
( ( ~ element(X125,powerset(X126))
| subset(X125,X126) )
& ( ~ subset(X125,X126)
| element(X125,powerset(X126)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_12,plain,
! [X84,X85] :
( ( subset(the_carrier(X85),the_carrier(X84))
| ~ subrelstr(X85,X84)
| ~ rel_str(X85)
| ~ rel_str(X84) )
& ( subset(the_InternalRel(X85),the_InternalRel(X84))
| ~ subrelstr(X85,X84)
| ~ rel_str(X85)
| ~ rel_str(X84) )
& ( ~ subset(the_carrier(X85),the_carrier(X84))
| ~ subset(the_InternalRel(X85),the_InternalRel(X84))
| subrelstr(X85,X84)
| ~ rel_str(X85)
| ~ rel_str(X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_yellow_0])])])]) ).
fof(c_0_13,plain,
! [X90,X91] :
( ~ rel_str(X90)
| ~ subrelstr(X91,X90)
| rel_str(X91) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_yellow_0])])]) ).
cnf(c_0_14,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subset(the_InternalRel(X1),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( rel_str(X2)
| ~ rel_str(X1)
| ~ subrelstr(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X2,X5,X6) )
=> related(X1,X3,X4) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t60_yellow_0]) ).
fof(c_0_19,plain,
! [X130,X131,X132] :
( ~ in(X130,X131)
| ~ element(X131,powerset(X132))
| ~ empty(X132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_20,plain,
! [X127,X128,X129] :
( ~ in(X127,X128)
| ~ element(X128,powerset(X129))
| element(X127,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_21,plain,
! [X121,X122] :
( ~ in(X121,X122)
| element(X121,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_22,plain,
( empty(powerset(X1))
| in(X2,powerset(X1))
| ~ subset(X2,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( subset(the_InternalRel(X1),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,negated_conjecture,
( rel_str(esk12_0)
& subrelstr(esk13_0,esk12_0)
& element(esk14_0,the_carrier(esk12_0))
& element(esk15_0,the_carrier(esk12_0))
& element(esk16_0,the_carrier(esk13_0))
& element(esk17_0,the_carrier(esk13_0))
& esk16_0 = esk14_0
& esk17_0 = esk15_0
& related(esk13_0,esk16_0,esk17_0)
& ~ related(esk12_0,esk14_0,esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_25,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( empty(powerset(the_InternalRel(X1)))
| in(the_InternalRel(X2),powerset(the_InternalRel(X1)))
| ~ subrelstr(X2,X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
subrelstr(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
fof(c_0_32,plain,
! [X86,X87,X88] :
( ( ~ related(X86,X87,X88)
| in(ordered_pair(X87,X88),the_InternalRel(X86))
| ~ element(X88,the_carrier(X86))
| ~ element(X87,the_carrier(X86))
| ~ rel_str(X86) )
& ( ~ in(ordered_pair(X87,X88),the_InternalRel(X86))
| related(X86,X87,X88)
| ~ element(X88,the_carrier(X86))
| ~ element(X87,the_carrier(X86))
| ~ rel_str(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
cnf(c_0_33,plain,
( element(X1,X2)
| ~ in(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( empty(powerset(the_InternalRel(esk12_0)))
| in(the_InternalRel(esk13_0),powerset(the_InternalRel(esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
( ~ subrelstr(X1,X2)
| ~ rel_str(X2)
| ~ empty(the_InternalRel(X2))
| ~ in(X3,the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_36,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( element(X1,the_InternalRel(esk12_0))
| empty(powerset(the_InternalRel(esk12_0)))
| ~ in(X1,the_InternalRel(esk13_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
rel_str(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_30])]) ).
cnf(c_0_39,plain,
( ~ related(X1,X2,X3)
| ~ subrelstr(X1,X4)
| ~ rel_str(X4)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ empty(the_InternalRel(X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_17]) ).
cnf(c_0_40,negated_conjecture,
element(esk17_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,negated_conjecture,
related(esk13_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_42,negated_conjecture,
esk16_0 = esk14_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_43,negated_conjecture,
element(esk16_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_44,negated_conjecture,
( element(ordered_pair(X1,X2),the_InternalRel(esk12_0))
| empty(powerset(the_InternalRel(esk12_0)))
| ~ related(esk13_0,X1,X2)
| ~ element(X2,the_carrier(esk13_0))
| ~ element(X1,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_38])]) ).
cnf(c_0_45,negated_conjecture,
( ~ related(esk13_0,X1,esk17_0)
| ~ subrelstr(esk13_0,X2)
| ~ rel_str(X2)
| ~ element(X1,the_carrier(esk13_0))
| ~ empty(the_InternalRel(X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
related(esk13_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
element(esk14_0,the_carrier(esk13_0)),
inference(rw,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( element(ordered_pair(X1,esk17_0),the_InternalRel(esk12_0))
| empty(powerset(the_InternalRel(esk12_0)))
| ~ related(esk13_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk13_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( ~ subrelstr(esk13_0,X1)
| ~ rel_str(X1)
| ~ empty(the_InternalRel(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_50,negated_conjecture,
( element(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0))
| empty(powerset(the_InternalRel(esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_47])]) ).
cnf(c_0_51,negated_conjecture,
~ empty(the_InternalRel(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_29]),c_0_30])]) ).
cnf(c_0_52,negated_conjecture,
element(esk15_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_53,negated_conjecture,
esk17_0 = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_54,negated_conjecture,
~ related(esk12_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_55,plain,
! [X139] :
( ~ empty(X139)
| X139 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_56,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_57,negated_conjecture,
( empty(powerset(the_InternalRel(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_50]),c_0_51]) ).
cnf(c_0_58,negated_conjecture,
element(esk17_0,the_carrier(esk12_0)),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_60,negated_conjecture,
~ related(esk12_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_61,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,negated_conjecture,
empty(powerset(the_InternalRel(esk12_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_30]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
powerset(the_InternalRel(esk12_0)) = empty_set,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
( element(X1,empty_set)
| ~ subset(X1,the_InternalRel(esk12_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_63]) ).
cnf(c_0_65,negated_conjecture,
( element(X1,the_InternalRel(esk12_0))
| ~ element(X2,empty_set)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( element(the_InternalRel(X1),empty_set)
| ~ subrelstr(X1,esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_23]),c_0_30])]) ).
cnf(c_0_67,negated_conjecture,
( element(X1,the_InternalRel(esk12_0))
| ~ subrelstr(X2,esk12_0)
| ~ in(X1,the_InternalRel(X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,negated_conjecture,
( element(ordered_pair(X1,X2),the_InternalRel(esk12_0))
| ~ related(X3,X1,X2)
| ~ subrelstr(X3,esk12_0)
| ~ rel_str(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_36]) ).
cnf(c_0_69,negated_conjecture,
( element(ordered_pair(X1,esk17_0),the_InternalRel(esk12_0))
| ~ related(esk13_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_40]),c_0_29]),c_0_38])]) ).
cnf(c_0_70,negated_conjecture,
( in(ordered_pair(X1,esk17_0),the_InternalRel(esk12_0))
| ~ related(esk13_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk13_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_69]),c_0_51]) ).
cnf(c_0_71,negated_conjecture,
( related(esk12_0,X1,esk17_0)
| ~ related(esk13_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk12_0))
| ~ element(X1,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_70]),c_0_30]),c_0_58])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_46]),c_0_59]),c_0_47])]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU362+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n028.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 03:03:45 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 3.28/3.02 % Version : CSE_E---1.7
% 3.28/3.02 % Problem : theBenchmark.p
% 3.28/3.02 % SZS status Theorem for theBenchmark.p
% 3.28/3.02 % SZS output start CNFRefutation
% See solution above
% 3.41/3.03 % Total time : 2.371s
%------------------------------------------------------------------------------