%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU180+2 : 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 : n018.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 02:28:25 PM UTC 2026
% Result : Theorem 1.20s 0.80s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 72 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 27 ~; 24 |; 8 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(t30_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X2,relation_field(X3))
& in(X1,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_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(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X2,relation_rng(X3))
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(c_0_6,lemma,
! [X94,X95] : subset(X94,set_union2(X94,X95)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_7,plain,
! [X65,X66] : set_union2(X65,X66) = set_union2(X66,X65),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_8,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X28] :
( relation_field(X28) = set_union2(relation_dom(X28),relation_rng(X28))
| ~ relation(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X2,relation_field(X3))
& in(X1,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
fof(c_0_12,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ in(esk5_2(X22,X23),X23) )
& ( subset(X22,X23)
| in(esk5_2(X22,X23),X22) )
& ( in(X21,X20)
| ~ in(X21,X19)
| ~ subset(X19,X20) ) ),
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_13,lemma,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( ~ relation(X1)
| relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,lemma,
! [X109,X110,X111] :
( ( ~ relation(X111)
| ~ in(ordered_pair(X109,X110),X111)
| in(X110,relation_rng(X111)) )
& ( ~ relation(X111)
| ~ in(ordered_pair(X109,X110),X111)
| in(X109,relation_dom(X111)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])])]) ).
fof(c_0_16,negated_conjecture,
( ( ~ in(esk2_0,relation_field(esk3_0))
| ~ in(esk1_0,relation_field(esk3_0)) )
& in(ordered_pair(esk1_0,esk2_0),esk3_0)
& relation(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_17,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,lemma,
( ~ relation(X1)
| subset(relation_rng(X1),relation_field(X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,lemma,
( ~ relation(X2)
| ~ in(ordered_pair(X3,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
in(ordered_pair(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk2_0,relation_field(esk3_0))
| ~ in(esk1_0,relation_field(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,lemma,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
in(esk2_0,relation_rng(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,lemma,
( ~ relation(X1)
| subset(relation_dom(X1),relation_field(X1)) ),
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_26,lemma,
( ~ relation(X2)
| ~ in(ordered_pair(X1,X3),X2)
| in(X1,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk1_0,relation_field(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_21]),c_0_24])]) ).
cnf(c_0_28,lemma,
( ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_21])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 05:57:59 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 Running first-order theorem proving
% 0.17/0.47 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
% 1.20/0.80 % Version: 3.5.1
% 1.20/0.80 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.20/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.80 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.20/0.80 % Starting new_bool_3 with 300s (1) cores
% 1.20/0.80 % Starting new_bool_1 with 300s (1) cores
% 1.20/0.80 % Starting sh5l with 300s (1) cores
% 1.20/0.80 % new_bool_1 with pid 1119811 completed with status 0
% 1.20/0.80 % Result found by new_bool_1
% 1.20/0.80 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.20/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.80 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.20/0.80 % Starting new_bool_3 with 300s (1) cores
% 1.20/0.80 % Starting new_bool_1 with 300s (1) cores
% 1.20/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.20/0.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.20/0.80 % Search class: FGHSM-FFLM32-SFFFFFNN
% 1.20/0.80 % partial match(1): FGHSM-FFMM32-SFFFFFNN
% 1.20/0.80 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.20/0.80 % Starting SubtermCWHack with 28s (1) cores
% 1.20/0.80 % SubtermCWHack with pid 1119819 completed with status 0
% 1.20/0.80 % Result found by SubtermCWHack
% 1.20/0.80 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.20/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.80 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.20/0.80 % Starting new_bool_3 with 300s (1) cores
% 1.20/0.80 % Starting new_bool_1 with 300s (1) cores
% 1.20/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.20/0.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.20/0.80 % Search class: FGHSM-FFLM32-SFFFFFNN
% 1.20/0.80 % partial match(1): FGHSM-FFMM32-SFFFFFNN
% 1.20/0.80 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.20/0.80 % Starting SubtermCWHack with 28s (1) cores
% 1.20/0.80 % Preprocessing time : 0.004 s
% 1.20/0.80
% 1.20/0.80 % Proof found!
% 1.20/0.80 % SZS status Theorem
% 1.20/0.80 % SZS output start CNFRefutation
% See solution above
% 1.20/0.80 % Parsed axioms : 150
% 1.20/0.80 % Removed by relevancy pruning/SinE : 62
% 1.20/0.80 % Initial clauses : 159
% 1.20/0.80 % Removed in clause preprocessing : 0
% 1.20/0.80 % Initial clauses in saturation : 159
% 1.20/0.80 % Processed clauses : 2079
% 1.20/0.80 % ...of these trivial : 27
% 1.20/0.80 % ...subsumed : 1471
% 1.20/0.80 % ...remaining for further processing : 581
% 1.20/0.80 % Other redundant clauses eliminated : 54
% 1.20/0.80 % Clauses deleted for lack of memory : 0
% 1.20/0.80 % Backward-subsumed : 32
% 1.20/0.80 % Backward-rewritten : 18
% 1.20/0.80 % Generated clauses : 5993
% 1.20/0.80 % ...of the previous two non-redundant : 5029
% 1.20/0.80 % ...aggressively subsumed : 0
% 1.20/0.80 % Contextual simplify-reflections : 0
% 1.20/0.80 % Paramodulations : 5921
% 1.74/0.80 % Factorizations : 14
% 1.74/0.80 % NegExts : 0
% 1.74/0.80 % Equation resolutions : 59
% 1.74/0.80 % Disequality decompositions : 0
% 1.74/0.80 % Total rewrite steps : 1511
% 1.74/0.80 % ...of those cached : 1286
% 1.74/0.80 % Propositional unsat checks : 0
% 1.74/0.80 % Propositional check models : 0
% 1.74/0.80 % Propositional check unsatisfiable : 0
% 1.74/0.80 % Propositional clauses : 0
% 1.74/0.80 % Propositional clauses after purity: 0
% 1.74/0.80 % Propositional unsat core size : 0
% 1.74/0.80 % Propositional preprocessing time : 0.000
% 1.74/0.80 % Propositional encoding time : 0.000
% 1.74/0.80 % Propositional solver time : 0.000
% 1.74/0.80 % Success case prop preproc time : 0.000
% 1.74/0.80 % Success case prop encoding time : 0.000
% 1.74/0.80 % Success case prop solver time : 0.000
% 1.74/0.80 % Current number of processed clauses : 500
% 1.74/0.80 % Positive orientable unit clauses : 85
% 1.74/0.80 % Positive unorientable unit clauses: 4
% 1.74/0.80 % Negative unit clauses : 133
% 1.74/0.80 % Non-unit-clauses : 278
% 1.74/0.80 % Current number of unprocessed clauses: 3037
% 1.74/0.80 % ...number of literals in the above : 7389
% 1.74/0.80 % Current number of archived formulas : 0
% 1.74/0.80 % Current number of archived clauses : 53
% 1.74/0.80 % Clause-clause subsumption calls (NU) : 7688
% 1.74/0.80 % Rec. Clause-clause subsumption calls : 5660
% 1.74/0.80 % Non-unit clause-clause subsumptions : 448
% 1.74/0.80 % Unit Clause-clause subsumption calls : 6471
% 1.74/0.80 % Rewrite failures with RHS unbound : 0
% 1.74/0.80 % BW rewrite match attempts : 79
% 1.74/0.80 % BW rewrite match successes : 22
% 1.74/0.80 % Condensation attempts : 0
% 1.74/0.80 % Condensation successes : 0
% 1.74/0.80 % Termbank termtop insertions : 56631
% 1.74/0.80 % Search garbage collected termcells : 2824
% 1.74/0.80
% 1.74/0.80 % -------------------------------------------------
% 1.74/0.80 % User time : 0.160 s
% 1.74/0.80 % System time : 0.014 s
% 1.74/0.80 % Total time : 0.174 s
% 1.74/0.80 % Maximum resident set size: 4032 pages
% 1.74/0.80
% 1.74/0.80 % -------------------------------------------------
% 1.74/0.80 % User time : 0.169 s
% 1.74/0.80 % System time : 0.018 s
% 1.74/0.80 % Total time : 0.187 s
% 1.74/0.80 % Maximum resident set size: 4864 pages
% 1.74/0.80 % E exiting
%------------------------------------------------------------------------------