%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU210+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 : n026.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 05:11:04 PM UTC 2026
% Result : Theorem 3.91s 3.21s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 25 unt; 0 def)
% Number of atoms : 201 ( 32 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 223 ( 96 ~; 92 |; 23 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 140 ( 14 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t166_relat_1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t174_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_15,plain,
! [X123] :
( ~ empty(X123)
| X123 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_16,plain,
! [X100] :
( element(esk10_1(X100),powerset(X100))
& empty(esk10_1(X100)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_17,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
empty(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X73,X74,X75,X77,X78,X79,X81] :
( ( ~ in(X75,X74)
| in(ordered_pair(esk2_3(X73,X74,X75),X75),X73)
| X74 != relation_rng(X73)
| ~ relation(X73) )
& ( ~ in(ordered_pair(X78,X77),X73)
| in(X77,X74)
| X74 != relation_rng(X73)
| ~ relation(X73) )
& ( ~ in(esk3_2(X73,X79),X79)
| ~ in(ordered_pair(X81,esk3_2(X73,X79)),X73)
| X79 = relation_rng(X73)
| ~ relation(X73) )
& ( in(esk3_2(X73,X79),X79)
| in(ordered_pair(esk4_2(X73,X79),esk3_2(X73,X79)),X73)
| X79 = relation_rng(X73)
| ~ relation(X73) ) ),
inference(distribute,[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)],[d5_relat_1])])])])])]) ).
fof(c_0_20,plain,
! [X83,X84] : ordered_pair(X83,X84) = unordered_pair(unordered_pair(X83,X84),singleton(X83)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_21,plain,
! [X120,X121,X122] :
( ~ in(X120,X121)
| ~ element(X121,powerset(X122))
| ~ empty(X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_22,plain,
element(esk10_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
esk10_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( in(ordered_pair(esk2_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X65,X66] : unordered_pair(X65,X66) = unordered_pair(X66,X65),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(esk2_3(X3,X2,X1),X1),singleton(esk2_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X113,X114] :
( ~ element(X113,X114)
| empty(X114)
| in(X113,X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_32,plain,
! [X85] : element(esk5_1(X85),X85),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_33,plain,
! [X104,X105,X106,X108] :
( ( in(esk12_3(X104,X105,X106),relation_rng(X106))
| ~ in(X104,relation_inverse_image(X106,X105))
| ~ relation(X106) )
& ( in(ordered_pair(X104,esk12_3(X104,X105,X106)),X106)
| ~ in(X104,relation_inverse_image(X106,X105))
| ~ relation(X106) )
& ( in(esk12_3(X104,X105,X106),X105)
| ~ in(X104,relation_inverse_image(X106,X105))
| ~ relation(X106) )
& ( ~ in(X108,relation_rng(X106))
| ~ in(ordered_pair(X104,X108),X106)
| ~ in(X108,X105)
| in(X104,relation_inverse_image(X106,X105))
| ~ relation(X106) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t166_relat_1])])])])]) ).
cnf(c_0_34,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X2,relation_rng(X2),X1)),singleton(esk2_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_37,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).
cnf(c_0_38,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( in(X3,relation_inverse_image(X2,X4))
| ~ in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_42,plain,
( ~ empty(X1)
| ~ in(X2,relation_rng(empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_43,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( in(X3,relation_inverse_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_45,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_41]) ).
fof(c_0_46,plain,
! [X124,X125] :
( ~ in(X124,X125)
| ~ empty(X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_47,plain,
! [X64] :
( ~ empty(X64)
| relation(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
cnf(c_0_48,plain,
( empty(relation_rng(empty_set))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
fof(c_0_50,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
inference(assume_negation,[status(cth)],[t174_relat_1]) ).
cnf(c_0_51,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),X2)
| ~ in(X4,X3) ),
inference(csr,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
empty(relation_rng(empty_set)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_55,plain,
! [X67,X68,X69,X70,X71] :
( ( ~ subset(X67,X68)
| ~ in(X69,X67)
| in(X69,X68) )
& ( in(esk1_2(X70,X71),X70)
| subset(X70,X71) )
& ( ~ in(esk1_2(X70,X71),X71)
| subset(X70,X71) ) ),
inference(distribute,[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)],[d3_tarski])])])])])]) ).
fof(c_0_56,negated_conjecture,
( relation(esk14_0)
& esk13_0 != empty_set
& subset(esk13_0,relation_rng(esk14_0))
& relation_inverse_image(esk14_0,esk13_0) = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_57,plain,
( in(esk3_2(X1,X2),X2)
| in(ordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_58,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X1)),X2)
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_30]) ).
cnf(c_0_59,plain,
( ~ empty(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_36]),c_0_53]) ).
cnf(c_0_60,plain,
relation_rng(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_17,c_0_54]) ).
cnf(c_0_61,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,negated_conjecture,
subset(esk13_0,relation_rng(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( X2 = relation_rng(X1)
| in(esk3_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),singleton(esk4_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_57,c_0_25]) ).
cnf(c_0_64,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_65,negated_conjecture,
relation_inverse_image(esk14_0,esk13_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,plain,
~ in(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_49])]) ).
cnf(c_0_68,negated_conjecture,
( in(X1,relation_rng(esk14_0))
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( X1 = relation_rng(X2)
| in(unordered_pair(singleton(esk4_2(X2,X1)),unordered_pair(esk3_2(X2,X1),esk4_2(X2,X1))),X2)
| in(esk3_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_30]),c_0_30]) ).
cnf(c_0_70,negated_conjecture,
~ in(X1,esk13_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]),c_0_67]),c_0_68]) ).
cnf(c_0_71,plain,
( X1 = empty_set
| in(esk3_2(empty_set,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_69]),c_0_60]),c_0_37])]) ).
cnf(c_0_72,negated_conjecture,
esk13_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU210+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:48:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.91/3.21 % Version : CSE_E---1.7
% 3.91/3.21 % Problem : theBenchmark.p
% 3.91/3.21 % SZS status Theorem for theBenchmark.p
% 3.91/3.21 % SZS output start CNFRefutation
% See solution above
% 3.91/3.22 % Total time : 2.371s
%------------------------------------------------------------------------------