%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU187+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 05:10:59 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 126 ( 45 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 143 ( 58 ~; 66 |; 11 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 74 ( 1 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
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/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(t60_relat_1,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(c_0_9,plain,
! [X50,X51,X52,X54,X55,X56,X58] :
( ( ~ in(X52,X51)
| in(ordered_pair(X52,esk1_3(X50,X51,X52)),X50)
| X51 != relation_dom(X50)
| ~ relation(X50) )
& ( ~ in(ordered_pair(X54,X55),X50)
| in(X54,X51)
| X51 != relation_dom(X50)
| ~ relation(X50) )
& ( ~ in(esk2_2(X50,X56),X56)
| ~ in(ordered_pair(esk2_2(X50,X56),X58),X50)
| X56 = relation_dom(X50)
| ~ relation(X50) )
& ( in(esk2_2(X50,X56),X56)
| in(ordered_pair(esk2_2(X50,X56),esk3_2(X50,X56)),X50)
| X56 = relation_dom(X50)
| ~ relation(X50) ) ),
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,
! [X70,X71] : ordered_pair(X70,X71) = unordered_pair(unordered_pair(X70,X71),singleton(X70)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,plain,
! [X93,X94] :
( ~ in(X93,X94)
| ~ empty(X94) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_12,plain,
! [X89,X90] :
( ( ~ in(esk12_2(X89,X90),X89)
| ~ in(esk12_2(X89,X90),X90)
| X89 = X90 )
& ( in(esk12_2(X89,X90),X89)
| in(esk12_2(X89,X90),X90)
| X89 = X90 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,esk1_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_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X48,X49] : unordered_pair(X48,X49) = unordered_pair(X49,X48),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(esk12_2(X1,X2),X1)
| in(esk12_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk1_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( X1 = X2
| in(esk12_2(X1,X2),X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
fof(c_0_22,plain,
! [X60,X61,X62,X64,X65,X66,X68] :
( ( ~ in(X62,X61)
| in(ordered_pair(esk4_3(X60,X61,X62),X62),X60)
| X61 != relation_rng(X60)
| ~ relation(X60) )
& ( ~ in(ordered_pair(X65,X64),X60)
| in(X64,X61)
| X61 != relation_rng(X60)
| ~ relation(X60) )
& ( ~ in(esk5_2(X60,X66),X66)
| ~ in(ordered_pair(X68,esk5_2(X60,X66)),X60)
| X66 = relation_rng(X60)
| ~ relation(X60) )
& ( in(esk5_2(X60,X66),X66)
| in(ordered_pair(esk6_2(X60,X66),esk5_2(X60,X66)),X60)
| X66 = relation_rng(X60)
| ~ relation(X60) ) ),
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])])])])])]) ).
cnf(c_0_23,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( empty_set = X1
| in(esk12_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( in(ordered_pair(esk4_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( empty_set = X1
| in(unordered_pair(singleton(esk12_2(empty_set,X1)),unordered_pair(esk12_2(empty_set,X1),esk1_3(X2,X1,esk12_2(empty_set,X1)))),X2)
| X1 != relation_dom(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( in(unordered_pair(unordered_pair(esk4_3(X3,X2,X1),X1),singleton(esk4_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_25,c_0_14]) ).
fof(c_0_28,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[t60_relat_1]) ).
cnf(c_0_29,plain,
( relation_dom(X1) = empty_set
| in(unordered_pair(singleton(esk12_2(empty_set,relation_dom(X1))),unordered_pair(esk12_2(empty_set,relation_dom(X1)),esk1_3(X1,relation_dom(X1),esk12_2(empty_set,relation_dom(X1))))),X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).
cnf(c_0_31,plain,
( in(unordered_pair(unordered_pair(X1,esk4_3(X2,X3,X1)),singleton(esk4_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_27,c_0_19]) ).
fof(c_0_32,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( relation_dom(empty_set) = empty_set
| in(unordered_pair(singleton(esk12_2(empty_set,relation_dom(empty_set))),unordered_pair(esk12_2(empty_set,relation_dom(empty_set)),esk1_3(empty_set,relation_dom(empty_set),esk12_2(empty_set,relation_dom(empty_set))))),empty_set) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( empty_set = X1
| in(unordered_pair(singleton(esk4_3(X2,X1,esk12_2(empty_set,X1))),unordered_pair(esk12_2(empty_set,X1),esk4_3(X2,X1,esk12_2(empty_set,X1)))),X2)
| X1 != relation_rng(X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_24]),c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
relation_dom(empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_33]),c_0_21])]) ).
cnf(c_0_37,plain,
( relation_rng(X1) = empty_set
| in(unordered_pair(singleton(esk4_3(X1,relation_rng(X1),esk12_2(empty_set,relation_rng(X1)))),unordered_pair(esk12_2(empty_set,relation_rng(X1)),esk4_3(X1,relation_rng(X1),esk12_2(empty_set,relation_rng(X1))))),X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
relation_rng(empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_39,plain,
in(unordered_pair(singleton(esk4_3(empty_set,relation_rng(empty_set),esk12_2(empty_set,relation_rng(empty_set)))),unordered_pair(esk12_2(empty_set,relation_rng(empty_set)),esk4_3(empty_set,relation_rng(empty_set),esk12_2(empty_set,relation_rng(empty_set))))),empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_38]) ).
cnf(c_0_40,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_39]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU187+1 : TPTP v9.2.1. Released v3.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 02:47:49 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------