%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:16 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 142 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 175 ( 69 ~; 71 |; 18 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 3 sgn 33 !; 1 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t8_funct_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( X2 = apply(X3,X1)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(d4_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_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(c_0_5,plain,
! [X14,X15,X16,X18,X19,X20,X22] :
( ( ~ relation(X14)
| X20 = relation_dom(X14)
| in(ordered_pair(esk2_2(X14,X20),esk3_2(X14,X20)),X14)
| in(esk2_2(X14,X20),X20) )
& ( ~ relation(X14)
| X20 = relation_dom(X14)
| ~ in(ordered_pair(esk2_2(X14,X20),X22),X14)
| ~ in(esk2_2(X14,X20),X20) )
& ( ~ relation(X14)
| X15 != relation_dom(X14)
| in(X18,X15)
| ~ in(ordered_pair(X18,X19),X14) )
& ( ~ relation(X14)
| X15 != relation_dom(X14)
| in(ordered_pair(X16,esk1_3(X14,X15,X16)),X14)
| ~ in(X16,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_6,plain,
! [X24,X25] : ordered_pair(X24,X25) = unordered_pair(unordered_pair(X24,X25),singleton(X24)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( X2 = apply(X3,X1)
& in(X1,relation_dom(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t8_funct_1]) ).
fof(c_0_8,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_9,plain,
( ~ relation(X3)
| X4 != relation_dom(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ( in(ordered_pair(esk13_0,esk14_0),esk15_0)
| esk14_0 = apply(esk15_0,esk13_0) )
& ( in(ordered_pair(esk13_0,esk14_0),esk15_0)
| in(esk13_0,relation_dom(esk15_0)) )
& ( esk14_0 != apply(esk15_0,esk13_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| ~ in(ordered_pair(esk13_0,esk14_0),esk15_0) )
& function(esk15_0)
& relation(esk15_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_12,plain,
! [X11,X12,X13] :
( ( ~ function(X11)
| ~ relation(X11)
| in(X12,relation_dom(X11))
| X13 = apply(X11,X12)
| X13 != empty_set )
& ( ~ function(X11)
| ~ relation(X11)
| in(X12,relation_dom(X11))
| X13 = empty_set
| X13 != apply(X11,X12) )
& ( ~ function(X11)
| ~ relation(X11)
| ~ in(X12,relation_dom(X11))
| X13 = apply(X11,X12)
| ~ in(ordered_pair(X12,X13),X11) )
& ( ~ function(X11)
| ~ relation(X11)
| ~ in(X12,relation_dom(X11))
| in(ordered_pair(X12,X13),X11)
| X13 != apply(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X4 != relation_dom(X3)
| in(X1,X4) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( in(ordered_pair(esk13_0,esk14_0),esk15_0)
| in(esk13_0,relation_dom(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(ordered_pair(X1,X2),X3)
| X2 = apply(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( esk14_0 != apply(esk15_0,esk13_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| ~ in(ordered_pair(esk13_0,esk14_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0)
| in(esk13_0,relation_dom(esk15_0)) ),
inference(rw,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3)
| X2 = apply(X3,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( in(ordered_pair(esk13_0,esk14_0),esk15_0)
| esk14_0 = apply(esk15_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| in(ordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_23,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| esk14_0 != apply(esk15_0,esk13_0) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_25,negated_conjecture,
in(esk13_0,relation_dom(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_26,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| ~ function(X2)
| ~ relation(X2)
| X1 = apply(X2,X3) ),
inference(csr,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0)
| esk14_0 = apply(esk15_0,esk13_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_28,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,plain,
( ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| X1 != apply(X2,X3)
| in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0)
| apply(esk15_0,esk13_0) != esk14_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_32,negated_conjecture,
apply(esk15_0,esk13_0) = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_28])]) ).
cnf(c_0_33,plain,
( ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_19]),c_0_28]),c_0_25])]),c_0_30]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:59:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2158622 completed with status 0
% 0.14/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.14/0.43 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.43 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 0.14/0.43 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.14/0.43 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.14/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2158627 completed with status 0
% 0.14/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.14/0.43 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43 % Presaturation interreduction done
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 35
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 56
% 0.14/0.43 % Removed in clause preprocessing : 1
% 0.14/0.43 % Initial clauses in saturation : 55
% 0.14/0.43 % Processed clauses : 144
% 0.14/0.43 % ...of these trivial : 4
% 0.14/0.43 % ...subsumed : 12
% 0.14/0.43 % ...remaining for further processing : 127
% 0.14/0.43 % Other redundant clauses eliminated : 5
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 3
% 0.14/0.43 % Backward-rewritten : 10
% 0.14/0.43 % Generated clauses : 87
% 0.14/0.43 % ...of the previous two non-redundant : 77
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 1
% 0.14/0.43 % Paramodulations : 82
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 5
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 41
% 0.14/0.43 % ...of those cached : 27
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 59
% 0.14/0.43 % Positive orientable unit clauses : 20
% 0.14/0.43 % Positive unorientable unit clauses: 1
% 0.14/0.43 % Negative unit clauses : 10
% 0.14/0.43 % Non-unit-clauses : 28
% 0.14/0.43 % Current number of unprocessed clauses: 37
% 0.14/0.43 % ...number of literals in the above : 114
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 64
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 329
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 296
% 0.14/0.43 % Non-unit clause-clause subsumptions : 5
% 0.14/0.43 % Unit Clause-clause subsumption calls : 107
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 13
% 0.14/0.43 % BW rewrite match successes : 13
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 4237
% 0.14/0.43 % Search garbage collected termcells : 582
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.010 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.013 s
% 0.14/0.43 % Maximum resident set size: 3352 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.031 s
% 0.14/0.43 % System time : 0.013 s
% 0.14/0.43 % Total time : 0.044 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------