%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU227+3 : 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 : n005.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 05:11:09 PM UTC 2026
% Result : Theorem 2.27s 2.02s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 207 ( 46 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 285 ( 121 ~; 130 |; 19 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 2 con; 0-4 aty)
% Number of variables : 142 ( 0 sgn 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_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(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d14_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
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(t146_funct_1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_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(c_0_7,plain,
! [X82,X83,X84,X85,X87,X88,X89,X90,X92] :
( ( in(ordered_pair(esk1_4(X82,X83,X84,X85),X85),X82)
| ~ in(X85,X84)
| X84 != relation_image(X82,X83)
| ~ relation(X82) )
& ( in(esk1_4(X82,X83,X84,X85),X83)
| ~ in(X85,X84)
| X84 != relation_image(X82,X83)
| ~ relation(X82) )
& ( ~ in(ordered_pair(X88,X87),X82)
| ~ in(X88,X83)
| in(X87,X84)
| X84 != relation_image(X82,X83)
| ~ relation(X82) )
& ( ~ in(esk2_3(X82,X89,X90),X90)
| ~ in(ordered_pair(X92,esk2_3(X82,X89,X90)),X82)
| ~ in(X92,X89)
| X90 = relation_image(X82,X89)
| ~ relation(X82) )
& ( in(ordered_pair(esk3_3(X82,X89,X90),esk2_3(X82,X89,X90)),X82)
| in(esk2_3(X82,X89,X90),X90)
| X90 = relation_image(X82,X89)
| ~ relation(X82) )
& ( in(esk3_3(X82,X89,X90),X89)
| in(esk2_3(X82,X89,X90),X90)
| X90 = relation_image(X82,X89)
| ~ relation(X82) ) ),
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_relat_1])])])])])]) ).
fof(c_0_8,plain,
! [X122,X123] : ordered_pair(X122,X123) = unordered_pair(unordered_pair(X122,X123),singleton(X122)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X112,X113,X114,X116,X117,X118,X120] :
( ( ~ in(X114,X113)
| in(ordered_pair(X114,esk8_3(X112,X113,X114)),X112)
| X113 != relation_dom(X112)
| ~ relation(X112) )
& ( ~ in(ordered_pair(X116,X117),X112)
| in(X116,X113)
| X113 != relation_dom(X112)
| ~ relation(X112) )
& ( ~ in(esk9_2(X112,X118),X118)
| ~ in(ordered_pair(esk9_2(X112,X118),X120),X112)
| X118 = relation_dom(X112)
| ~ relation(X112) )
& ( in(esk9_2(X112,X118),X118)
| in(ordered_pair(esk9_2(X112,X118),esk10_2(X112,X118)),X112)
| X118 = relation_dom(X112)
| ~ relation(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)],[d4_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X94,X95,X96,X97,X99,X100,X101,X102,X104] :
( ( in(ordered_pair(X97,esk4_4(X94,X95,X96,X97)),X94)
| ~ in(X97,X96)
| X96 != relation_inverse_image(X94,X95)
| ~ relation(X94) )
& ( in(esk4_4(X94,X95,X96,X97),X95)
| ~ in(X97,X96)
| X96 != relation_inverse_image(X94,X95)
| ~ relation(X94) )
& ( ~ in(ordered_pair(X99,X100),X94)
| ~ in(X100,X95)
| in(X99,X96)
| X96 != relation_inverse_image(X94,X95)
| ~ relation(X94) )
& ( ~ in(esk5_3(X94,X101,X102),X102)
| ~ in(ordered_pair(esk5_3(X94,X101,X102),X104),X94)
| ~ in(X104,X101)
| X102 = relation_inverse_image(X94,X101)
| ~ relation(X94) )
& ( in(ordered_pair(esk5_3(X94,X101,X102),esk6_3(X94,X101,X102)),X94)
| in(esk5_3(X94,X101,X102),X102)
| X102 = relation_inverse_image(X94,X101)
| ~ relation(X94) )
& ( in(esk6_3(X94,X101,X102),X101)
| in(esk5_3(X94,X101,X102),X102)
| X102 = relation_inverse_image(X94,X101)
| ~ relation(X94) ) ),
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)],[d14_relat_1])])])])])]) ).
cnf(c_0_11,plain,
( in(X2,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X5 != relation_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X80,X81] : unordered_pair(X80,X81) = unordered_pair(X81,X80),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,esk8_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(X1,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X2,X4)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( in(X2,X5)
| X5 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk8_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
( in(X1,X5)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| X2 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X1)),X3)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk8_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X5)),X3)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_23,plain,
( in(esk8_3(X1,X2,X3),X4)
| X4 != relation_image(X1,X5)
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ in(X3,X5)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
inference(assume_negation,[status(cth)],[t146_funct_1]) ).
cnf(c_0_25,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| X5 != relation_dom(X3)
| ~ relation(X3)
| ~ in(esk8_3(X3,X5,X1),X4)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( in(esk8_3(X1,X2,X3),relation_image(X1,X4))
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ in(X3,X4)
| ~ in(X3,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X106,X107,X108,X109,X110] :
( ( ~ subset(X106,X107)
| ~ in(X108,X106)
| in(X108,X107) )
& ( in(esk7_2(X109,X110),X109)
| subset(X109,X110) )
& ( ~ in(esk7_2(X109,X110),X110)
| subset(X109,X110) ) ),
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_28,negated_conjecture,
( relation(esk23_0)
& subset(esk22_0,relation_dom(esk23_0))
& ~ subset(esk22_0,relation_inverse_image(esk23_0,relation_image(esk23_0,esk22_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_29,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,relation_image(X3,X4))
| X5 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X5)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
subset(esk22_0,relation_dom(esk23_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( in(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| X4 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,relation_dom(esk23_0))
| ~ in(X1,esk22_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| relation_dom(esk23_0) != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,esk22_0)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| relation_dom(esk23_0) != relation_dom(X2)
| ~ relation(X2)
| ~ in(esk7_2(X1,relation_inverse_image(X2,relation_image(X2,X3))),esk22_0)
| ~ in(esk7_2(X1,relation_inverse_image(X2,relation_image(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
( in(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
( subset(esk22_0,relation_inverse_image(X1,relation_image(X1,X2)))
| relation_dom(esk23_0) != relation_dom(X1)
| ~ relation(X1)
| ~ in(esk7_2(esk22_0,relation_inverse_image(X1,relation_image(X1,X2))),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
~ subset(esk22_0,relation_inverse_image(esk23_0,relation_image(esk23_0,esk22_0))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( subset(esk22_0,relation_inverse_image(X1,relation_image(X1,esk22_0)))
| relation_dom(esk23_0) != relation_dom(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU227+3 : 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
% 0.15/0.32 % Computer : n005.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:50:30 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.27/2.02 % Version : CSE_E---1.7
% 2.27/2.02 % Problem : theBenchmark.p
% 2.27/2.02 % SZS status Theorem for theBenchmark.p
% 2.27/2.02 % SZS output start CNFRefutation
% See solution above
% 2.39/2.02 % Total time : 1.372s
%------------------------------------------------------------------------------