%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU204+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:28:30 PM UTC 2026
% Result : Theorem 1.66s 0.68s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 108 ( 22 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 130 ( 52 ~; 56 |; 12 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-4 aty)
% Number of variables : 78 ( 1 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X2)
& in(ordered_pair(X5,X4),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(t144_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_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(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_6,plain,
! [X29,X30,X31,X33,X34,X35,X37] :
( ( ~ relation(X29)
| X35 = relation_rng(X29)
| in(ordered_pair(esk7_2(X29,X35),esk6_2(X29,X35)),X29)
| in(esk6_2(X29,X35),X35) )
& ( ~ relation(X29)
| X35 = relation_rng(X29)
| ~ in(ordered_pair(X37,esk6_2(X29,X35)),X29)
| ~ in(esk6_2(X29,X35),X35) )
& ( ~ relation(X29)
| X30 != relation_rng(X29)
| in(X33,X30)
| ~ in(ordered_pair(X34,X33),X29) )
& ( ~ relation(X29)
| X30 != relation_rng(X29)
| in(ordered_pair(esk5_3(X29,X30,X31),X31),X29)
| ~ in(X31,X30) ) ),
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)],[d5_relat_1])])])])])])]) ).
fof(c_0_7,plain,
! [X39,X40] : ordered_pair(X39,X40) = unordered_pair(unordered_pair(X39,X40),singleton(X39)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),X18) )
& ( ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(ordered_pair(esk3_3(X11,X18,X19),esk2_3(X11,X18,X19)),X11) )
& ( ~ relation(X11)
| X19 = relation_image(X11,X18)
| ~ in(X21,X18)
| ~ in(ordered_pair(X21,esk2_3(X11,X18,X19)),X11)
| ~ in(esk2_3(X11,X18,X19),X19) )
& ( ~ relation(X11)
| X13 != relation_image(X11,X12)
| in(X16,X13)
| ~ in(X17,X12)
| ~ in(ordered_pair(X17,X16),X11) )
& ( ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),X12) )
& ( ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(ordered_pair(esk1_4(X11,X12,X13,X14),X14),X11) ) ),
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)],[d13_relat_1])])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
inference(assume_negation,[status(cth)],[t144_relat_1]) ).
cnf(c_0_10,plain,
( ~ relation(X3)
| X4 != relation_rng(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( ~ relation(X1)
| X3 != relation_image(X1,X2)
| ~ in(X4,X3)
| in(ordered_pair(esk1_4(X1,X2,X3,X4),X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
( ~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0))
& relation(esk16_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_15,plain,
! [X23,X24,X25,X26,X27] :
( ( subset(X26,X27)
| ~ in(esk4_2(X26,X27),X27) )
& ( subset(X26,X27)
| in(esk4_2(X26,X27),X26) )
& ( in(X25,X24)
| ~ in(X25,X23)
| ~ subset(X23,X24) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_16,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X4 != relation_rng(X3)
| in(X2,X4) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ in(X4,X3)
| ~ relation(X1)
| X3 != relation_image(X1,X2)
| in(unordered_pair(unordered_pair(esk1_4(X1,X2,X3,X4),X4),singleton(esk1_4(X1,X2,X3,X4))),X1) ),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_22,plain,
( ~ in(X3,relation_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(singleton(esk1_4(X1,X2,relation_image(X1,X2),X3)),unordered_pair(X3,esk1_4(X1,X2,relation_image(X1,X2),X3))),X1) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_17]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
in(esk4_2(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),relation_image(esk16_0,esk15_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
in(unordered_pair(singleton(esk1_4(esk16_0,esk15_0,relation_image(esk16_0,esk15_0),esk4_2(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)))),unordered_pair(esk4_2(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),esk1_4(esk16_0,esk15_0,relation_image(esk16_0,esk15_0),esk4_2(relation_image(esk16_0,esk15_0),relation_rng(esk16_0))))),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk4_2(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),relation_rng(esk16_0)),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:57:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 1.66/0.68 % Version: 3.5.1
% 1.66/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.66/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.66/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.66/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.66/0.68 % Starting sh5l with 300s (1) cores
% 1.66/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1123389 completed with status 0
% 1.66/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.66/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.66/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.66/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.66/0.68 % No SInE strategy applied
% 1.66/0.68 % Search class: FGHSM-FFMM31-MFFFFFNN
% 1.66/0.68 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1.66/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.66/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.66/0.68 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 1.66/0.68 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 1.66/0.68 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 1.66/0.68 % G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with pid 1123395 completed with status 0
% 1.66/0.68 % Result found by G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I
% 1.66/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.66/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.66/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.66/0.68 % No SInE strategy applied
% 1.66/0.68 % Search class: FGHSM-FFMM31-MFFFFFNN
% 1.66/0.68 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1.66/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.66/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.66/0.68 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 1.66/0.68 % Preprocessing time : 0.002 s
% 1.66/0.68 % Presaturation interreduction done
% 1.66/0.68
% 1.66/0.68 % Proof found!
% 1.66/0.68 % SZS status Theorem
% 1.66/0.68 % SZS output start CNFRefutation
% See solution above
% 1.66/0.68 % Parsed axioms : 40
% 1.66/0.68 % Removed by relevancy pruning/SinE : 0
% 1.66/0.68 % Initial clauses : 58
% 1.66/0.68 % Removed in clause preprocessing : 9
% 1.66/0.68 % Initial clauses in saturation : 49
% 1.66/0.68 % Processed clauses : 1700
% 1.66/0.68 % ...of these trivial : 14
% 1.66/0.68 % ...subsumed : 707
% 1.66/0.68 % ...remaining for further processing : 979
% 1.66/0.68 % Other redundant clauses eliminated : 5
% 1.66/0.68 % Clauses deleted for lack of memory : 0
% 1.66/0.68 % Backward-subsumed : 22
% 1.66/0.68 % Backward-rewritten : 8
% 1.66/0.68 % Generated clauses : 11846
% 1.66/0.68 % ...of the previous two non-redundant : 10669
% 1.66/0.68 % ...aggressively subsumed : 0
% 1.66/0.68 % Contextual simplify-reflections : 0
% 1.66/0.68 % Paramodulations : 11841
% 1.66/0.68 % Factorizations : 0
% 1.66/0.68 % NegExts : 0
% 1.66/0.68 % Equation resolutions : 5
% 1.66/0.68 % Disequality decompositions : 0
% 1.66/0.68 % Total rewrite steps : 4474
% 1.66/0.68 % ...of those cached : 4393
% 1.66/0.68 % Propositional unsat checks : 0
% 1.66/0.68 % Propositional check models : 0
% 1.66/0.68 % Propositional check unsatisfiable : 0
% 1.66/0.68 % Propositional clauses : 0
% 1.66/0.68 % Propositional clauses after purity: 0
% 1.66/0.68 % Propositional unsat core size : 0
% 1.66/0.68 % Propositional preprocessing time : 0.000
% 1.66/0.68 % Propositional encoding time : 0.000
% 1.66/0.68 % Propositional solver time : 0.000
% 1.66/0.68 % Success case prop preproc time : 0.000
% 1.66/0.68 % Success case prop encoding time : 0.000
% 1.66/0.68 % Success case prop solver time : 0.000
% 1.66/0.68 % Current number of processed clauses : 897
% 1.66/0.68 % Positive orientable unit clauses : 85
% 1.66/0.68 % Positive unorientable unit clauses: 1
% 1.66/0.68 % Negative unit clauses : 76
% 1.66/0.68 % Non-unit-clauses : 735
% 1.66/0.68 % Current number of unprocessed clauses: 9023
% 1.66/0.68 % ...number of literals in the above : 27196
% 1.66/0.68 % Current number of archived formulas : 0
% 1.66/0.68 % Current number of archived clauses : 78
% 1.66/0.68 % Clause-clause subsumption calls (NU) : 134703
% 1.66/0.68 % Rec. Clause-clause subsumption calls : 77790
% 1.66/0.68 % Non-unit clause-clause subsumptions : 563
% 1.66/0.68 % Unit Clause-clause subsumption calls : 9722
% 1.66/0.68 % Rewrite failures with RHS unbound : 0
% 1.66/0.68 % BW rewrite match attempts : 56
% 1.66/0.68 % BW rewrite match successes : 10
% 1.66/0.68 % Condensation attempts : 0
% 1.66/0.68 % Condensation successes : 0
% 1.66/0.68 % Termbank termtop insertions : 229986
% 1.66/0.68 % Search garbage collected termcells : 703
% 1.66/0.68
% 1.66/0.68 % -------------------------------------------------
% 1.66/0.68 % User time : 0.234 s
% 1.66/0.68 % System time : 0.012 s
% 1.66/0.68 % Total time : 0.246 s
% 1.66/0.68 % Maximum resident set size: 3660 pages
% 1.66/0.68
% 1.66/0.68 % -------------------------------------------------
% 1.66/0.68 % User time : 1.100 s
% 1.66/0.68 % System time : 0.054 s
% 1.66/0.68 % Total time : 1.155 s
% 1.66/0.68 % Maximum resident set size: 4608 pages
% 1.66/0.68 % E exiting
%------------------------------------------------------------------------------