%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU068+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n003.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 05:10:34 PM UTC 2026
% Result : Theorem 4.05s 3.23s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 258 ( 46 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 366 ( 155 ~; 170 |; 29 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-4 aty)
% Number of variables : 163 ( 5 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t149_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> subset(relation_image(X3,set_intersection2(X1,relation_inverse_image(X3,X2))),set_intersection2(relation_image(X3,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_1) ).
fof(c_0_6,plain,
! [X80,X81,X82,X83,X85,X86,X87,X88,X90] :
( ( in(esk1_4(X80,X81,X82,X83),relation_dom(X80))
| ~ in(X83,X82)
| X82 != relation_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( in(esk1_4(X80,X81,X82,X83),X81)
| ~ in(X83,X82)
| X82 != relation_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( X83 = apply(X80,esk1_4(X80,X81,X82,X83))
| ~ in(X83,X82)
| X82 != relation_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( ~ in(X86,relation_dom(X80))
| ~ in(X86,X81)
| X85 != apply(X80,X86)
| in(X85,X82)
| X82 != relation_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( ~ in(esk2_3(X80,X87,X88),X88)
| ~ in(X90,relation_dom(X80))
| ~ in(X90,X87)
| esk2_3(X80,X87,X88) != apply(X80,X90)
| X88 = relation_image(X80,X87)
| ~ relation(X80)
| ~ function(X80) )
& ( in(esk3_3(X80,X87,X88),relation_dom(X80))
| in(esk2_3(X80,X87,X88),X88)
| X88 = relation_image(X80,X87)
| ~ relation(X80)
| ~ function(X80) )
& ( in(esk3_3(X80,X87,X88),X87)
| in(esk2_3(X80,X87,X88),X88)
| X88 = relation_image(X80,X87)
| ~ relation(X80)
| ~ function(X80) )
& ( esk2_3(X80,X87,X88) = apply(X80,esk3_3(X80,X87,X88))
| in(esk2_3(X80,X87,X88),X88)
| X88 = relation_image(X80,X87)
| ~ relation(X80)
| ~ function(X80) ) ),
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)],[d12_funct_1])])])])])]) ).
fof(c_0_7,plain,
! [X106,X107,X108,X109,X110,X111,X112,X113] :
( ( in(X109,X106)
| ~ in(X109,X108)
| X108 != set_intersection2(X106,X107) )
& ( in(X109,X107)
| ~ in(X109,X108)
| X108 != set_intersection2(X106,X107) )
& ( ~ in(X110,X106)
| ~ in(X110,X107)
| in(X110,X108)
| X108 != set_intersection2(X106,X107) )
& ( ~ in(esk6_3(X111,X112,X113),X113)
| ~ in(esk6_3(X111,X112,X113),X111)
| ~ in(esk6_3(X111,X112,X113),X112)
| X113 = set_intersection2(X111,X112) )
& ( in(esk6_3(X111,X112,X113),X111)
| in(esk6_3(X111,X112,X113),X113)
| X113 = set_intersection2(X111,X112) )
& ( in(esk6_3(X111,X112,X113),X112)
| in(esk6_3(X111,X112,X113),X113)
| X113 = set_intersection2(X111,X112) ) ),
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_xboole_0])])])])])]) ).
fof(c_0_8,plain,
! [X92,X93,X94,X95,X96,X97,X98] :
( ( in(X95,relation_dom(X92))
| ~ in(X95,X94)
| X94 != relation_inverse_image(X92,X93)
| ~ relation(X92)
| ~ function(X92) )
& ( in(apply(X92,X95),X93)
| ~ in(X95,X94)
| X94 != relation_inverse_image(X92,X93)
| ~ relation(X92)
| ~ function(X92) )
& ( ~ in(X96,relation_dom(X92))
| ~ in(apply(X92,X96),X93)
| in(X96,X94)
| X94 != relation_inverse_image(X92,X93)
| ~ relation(X92)
| ~ function(X92) )
& ( ~ in(esk4_3(X92,X97,X98),X98)
| ~ in(esk4_3(X92,X97,X98),relation_dom(X92))
| ~ in(apply(X92,esk4_3(X92,X97,X98)),X97)
| X98 = relation_inverse_image(X92,X97)
| ~ relation(X92)
| ~ function(X92) )
& ( in(esk4_3(X92,X97,X98),relation_dom(X92))
| in(esk4_3(X92,X97,X98),X98)
| X98 = relation_inverse_image(X92,X97)
| ~ relation(X92)
| ~ function(X92) )
& ( in(apply(X92,esk4_3(X92,X97,X98)),X97)
| in(esk4_3(X92,X97,X98),X98)
| X98 = relation_inverse_image(X92,X97)
| ~ relation(X92)
| ~ function(X92) ) ),
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)],[d13_funct_1])])])])])]) ).
cnf(c_0_9,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(X1,relation_image(X2,X3))
| X1 != apply(X2,X4)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,X3) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,relation_image(X2,X3))
| X4 != relation_image(X2,X5)
| ~ relation(X2)
| ~ function(X2)
| ~ in(esk1_4(X2,X5,X4,X1),X3)
| ~ in(X1,X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]),c_0_14]) ).
cnf(c_0_19,plain,
( in(esk1_4(X1,set_intersection2(X2,X3),X4,X5),X3)
| X4 != relation_image(X1,set_intersection2(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( in(apply(X1,esk1_4(X2,relation_inverse_image(X1,X3),X4,X5)),X3)
| X4 != relation_image(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X2)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,relation_image(X2,X3))
| X4 != relation_image(X2,set_intersection2(X5,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X100,X101,X102,X103,X104] :
( ( ~ subset(X100,X101)
| ~ in(X102,X100)
| in(X102,X101) )
& ( in(esk5_2(X103,X104),X103)
| subset(X103,X104) )
& ( ~ in(esk5_2(X103,X104),X104)
| subset(X103,X104) ) ),
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])])])])])]) ).
cnf(c_0_23,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| X3 != relation_image(X4,relation_inverse_image(X4,X2))
| ~ relation(X4)
| ~ function(X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_25,plain,
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_image(X2,set_intersection2(X4,X3))) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X78,X79] : set_intersection2(X78,X79) = set_intersection2(X79,X78),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_28,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_image(X3,relation_inverse_image(X3,X2))) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( subset(relation_image(X1,set_intersection2(X2,X3)),X4)
| in(esk5_2(relation_image(X1,set_intersection2(X2,X3)),X4),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> subset(relation_image(X3,set_intersection2(X1,relation_inverse_image(X3,X2))),set_intersection2(relation_image(X3,X1),X2)) ),
inference(assume_negation,[status(cth)],[t149_funct_1]) ).
cnf(c_0_34,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ in(esk5_2(X1,set_intersection2(X2,X3)),X3)
| ~ in(esk5_2(X1,set_intersection2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( subset(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),X4)
| in(esk5_2(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),X4),X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_image(X2,set_intersection2(X3,X4))) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
fof(c_0_37,negated_conjecture,
( relation(esk20_0)
& function(esk20_0)
& ~ subset(relation_image(esk20_0,set_intersection2(esk18_0,relation_inverse_image(esk20_0,esk19_0))),set_intersection2(relation_image(esk20_0,esk18_0),esk19_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_38,plain,
( subset(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),set_intersection2(X4,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(esk5_2(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),set_intersection2(X4,X3)),X4) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( subset(relation_image(X1,set_intersection2(X2,X3)),X4)
| in(esk5_2(relation_image(X1,set_intersection2(X2,X3)),X4),relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_40,negated_conjecture,
~ subset(relation_image(esk20_0,set_intersection2(esk18_0,relation_inverse_image(esk20_0,esk19_0))),set_intersection2(relation_image(esk20_0,esk18_0),esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
( subset(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),set_intersection2(relation_image(X1,X2),X3))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
~ subset(relation_image(esk20_0,set_intersection2(esk18_0,relation_inverse_image(esk20_0,esk19_0))),set_intersection2(esk19_0,relation_image(esk20_0,esk18_0))),
inference(rw,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_43,plain,
( subset(relation_image(X1,set_intersection2(X2,relation_inverse_image(X1,X3))),set_intersection2(X3,relation_image(X1,X2)))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_44,negated_conjecture,
relation(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
function(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU068+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 5 02:43:11 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 4.05/3.23 % Version : CSE_E---1.7
% 4.05/3.23 % Problem : theBenchmark.p
% 4.05/3.23 % SZS status Theorem for theBenchmark.p
% 4.05/3.23 % SZS output start CNFRefutation
% See solution above
% 4.05/3.24 % Total time : 2.372s
%------------------------------------------------------------------------------