%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU290+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:24:35 PM UTC 2026
% Result : Theorem 4.94s 6.43s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 156 ( 45 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 184 ( 67 ~; 74 |; 25 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 77 ( 2 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( relation_of2_as_subset(X4,X1,X2)
& quasi_total(X4,X1,X2)
& function(X4) )
=> ( in(X3,X1)
=> ( in(apply(X4,X3),relation_rng(X4))
| X2 = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( X2 = empty_set
=> ( ( quasi_total(X3,X1,X2)
<=> X3 = empty_set )
| X1 = empty_set ) )
& ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( relation_of2_as_subset(X4,X1,X2)
& quasi_total(X4,X1,X2)
& function(X4) )
=> ( in(X3,X1)
=> ( in(apply(X4,X3),relation_rng(X4))
| X2 = empty_set ) ) ),
inference(assume_negation,[status(cth)],[t6_funct_2]) ).
fof(c_0_9,plain,
! [X627,X628,X629] :
( ( relation_of2_as_subset(X629,X627,X628)
| ~ relation_of2(X629,X627,X628) )
& ( relation_of2(X629,X627,X628)
| ~ relation_of2_as_subset(X629,X627,X628) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_10,negated_conjecture,
( ~ in(apply(esk255_0,esk254_0),relation_rng(esk255_0))
& esk253_0 != empty_set
& in(esk254_0,esk252_0)
& relation_of2_as_subset(esk255_0,esk252_0,esk253_0)
& quasi_total(esk255_0,esk252_0,esk253_0)
& function(esk255_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_11,plain,
! [X160,X161,X162] :
( ( relation_of2(X162,X160,X161)
| ~ subset(X162,cartesian_product2(X160,X161)) )
& ( subset(X162,cartesian_product2(X160,X161))
| ~ relation_of2(X162,X160,X161) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])])]) ).
cnf(c_0_12,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
relation_of2_as_subset(esk255_0,esk252_0,esk253_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X614,X615,X616] :
( relation_dom_as_subset(X614,X615,X616) = relation_dom(X616)
| ~ relation_of2(X616,X614,X615) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])])]) ).
fof(c_0_15,plain,
! [X1084,X1085] :
( ( element(X1084,powerset(X1085))
| ~ subset(X1084,X1085) )
& ( subset(X1084,X1085)
| ~ element(X1084,powerset(X1085)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_16,plain,
( ~ relation_of2(X1,X2,X3)
| subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
relation_of2(esk255_0,esk252_0,esk253_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X354,X355,X356,X358,X359,X360,X362] :
( ( ~ function(X354)
| ~ relation(X354)
| X360 = relation_rng(X354)
| in(esk69_2(X354,X360),X360)
| esk69_2(X354,X360) = apply(X354,esk70_2(X354,X360)) )
& ( ~ function(X354)
| ~ relation(X354)
| X360 = relation_rng(X354)
| in(esk69_2(X354,X360),X360)
| in(esk70_2(X354,X360),relation_dom(X354)) )
& ( ~ function(X354)
| ~ relation(X354)
| X360 = relation_rng(X354)
| esk69_2(X354,X360) != apply(X354,X362)
| ~ in(X362,relation_dom(X354))
| ~ in(esk69_2(X354,X360),X360) )
& ( ~ function(X354)
| ~ relation(X354)
| X355 != relation_rng(X354)
| in(X358,X355)
| X358 != apply(X354,X359)
| ~ in(X359,relation_dom(X354)) )
& ( ~ function(X354)
| ~ relation(X354)
| X355 != relation_rng(X354)
| ~ in(X356,X355)
| X356 = apply(X354,esk68_3(X354,X355,X356)) )
& ( ~ function(X354)
| ~ relation(X354)
| X355 != relation_rng(X354)
| ~ in(X356,X355)
| in(esk68_3(X354,X355,X356),relation_dom(X354)) ) ),
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_funct_1])])])])])])]) ).
fof(c_0_19,plain,
! [X134,X135,X136] :
( ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 != empty_set
| X134 = empty_set
| quasi_total(X136,X134,X135)
| X136 != empty_set )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 != empty_set
| X134 = empty_set
| X136 = empty_set
| ~ quasi_total(X136,X134,X135) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X134 != empty_set
| quasi_total(X136,X134,X135)
| X134 != relation_dom_as_subset(X134,X135,X136) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X134 != empty_set
| X134 = relation_dom_as_subset(X134,X135,X136)
| ~ quasi_total(X136,X134,X135) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 = empty_set
| quasi_total(X136,X134,X135)
| X134 != relation_dom_as_subset(X134,X135,X136) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 = empty_set
| X134 = relation_dom_as_subset(X134,X135,X136)
| ~ quasi_total(X136,X134,X135) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])])]) ).
cnf(c_0_20,plain,
( ~ relation_of2(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = relation_dom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X26,X27,X28] :
( relation(X28)
| ~ element(X28,powerset(cartesian_product2(X26,X27))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
cnf(c_0_22,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
subset(esk255_0,cartesian_product2(esk252_0,esk253_0)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_rng(X2)
| X3 != apply(X2,X1)
| ~ in(X1,relation_dom(X2))
| in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| X3 = empty_set
| X2 = relation_dom_as_subset(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
quasi_total(esk255_0,esk252_0,esk253_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
relation_dom_as_subset(esk252_0,esk253_0,esk255_0) = relation_dom(esk255_0),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
esk253_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
element(esk255_0,powerset(cartesian_product2(esk252_0,esk253_0))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),relation_rng(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
relation_dom(esk255_0) = esk252_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_13])]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
relation(esk255_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
function(esk255_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( ~ in(X1,esk252_0)
| in(apply(esk255_0,X1),relation_rng(esk255_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_36,negated_conjecture,
in(esk254_0,esk252_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,negated_conjecture,
~ in(apply(esk255_0,esk254_0),relation_rng(esk255_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU290+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.58 % Computer : n003.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Mon Sep 21 06:09:36 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.62 Running first-order theorem proving
% 0.14/5.62 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 4.94/6.43 % Version: 3.5.1
% 4.94/6.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.94/6.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/6.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.94/6.43 % Starting new_bool_3 with 300s (1) cores
% 4.94/6.43 % Starting new_bool_1 with 300s (1) cores
% 4.94/6.43 % Starting sh5l with 300s (1) cores
% 4.94/6.43 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3578599 completed with status 0
% 4.94/6.43 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.94/6.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.94/6.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/6.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.94/6.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.94/6.43 % No SInE strategy applied
% 4.94/6.43 % Search class: FGHSM-SMLM32-MFFFFFNN
% 4.94/6.43 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/6.43 % Starting SubtermCWHack with 136s (1) cores
% 4.94/6.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.94/6.43 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 113s (1) cores
% 4.94/6.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 113s (1) cores
% 4.94/6.43 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 113s (1) cores
% 4.94/6.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S2g with pid 3578609 completed with status 0
% 4.94/6.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2g
% 4.94/6.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.94/6.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/6.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.94/6.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.94/6.43 % No SInE strategy applied
% 4.94/6.43 % Search class: FGHSM-SMLM32-MFFFFFNN
% 4.94/6.43 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/6.43 % Starting SubtermCWHack with 136s (1) cores
% 4.94/6.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.94/6.43 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 113s (1) cores
% 4.94/6.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 113s (1) cores
% 4.94/6.43 % Preprocessing time : 0.017 s
% 4.94/6.43 % Presaturation interreduction done
% 4.94/6.43
% 4.94/6.43 % Proof found!
% 4.94/6.43 % SZS status Theorem
% 4.94/6.43 % SZS output start CNFRefutation
% See solution above
% 4.94/6.43 % Parsed axioms : 383
% 4.94/6.43 % Removed by relevancy pruning/SinE : 0
% 4.94/6.43 % Initial clauses : 1449
% 4.94/6.43 % Removed in clause preprocessing : 33
% 4.94/6.43 % Initial clauses in saturation : 1416
% 4.94/6.43 % Processed clauses : 5998
% 4.94/6.43 % ...of these trivial : 132
% 4.94/6.43 % ...subsumed : 1771
% 4.94/6.43 % ...remaining for further processing : 4095
% 4.94/6.43 % Other redundant clauses eliminated : 467
% 4.94/6.43 % Clauses deleted for lack of memory : 0
% 4.94/6.43 % Backward-subsumed : 21
% 4.94/6.43 % Backward-rewritten : 226
% 4.94/6.43 % Generated clauses : 25844
% 4.94/6.43 % ...of the previous two non-redundant : 24793
% 4.94/6.43 % ...aggressively subsumed : 0
% 4.94/6.43 % Contextual simplify-reflections : 188
% 4.94/6.43 % Paramodulations : 25480
% 4.94/6.43 % Factorizations : 2
% 4.94/6.43 % NegExts : 0
% 4.94/6.43 % Equation resolutions : 472
% 4.94/6.43 % Disequality decompositions : 0
% 4.94/6.43 % Total rewrite steps : 5331
% 4.94/6.43 % ...of those cached : 4540
% 4.94/6.43 % Propositional unsat checks : 0
% 4.94/6.43 % Propositional check models : 0
% 4.94/6.43 % Propositional check unsatisfiable : 0
% 4.94/6.43 % Propositional clauses : 0
% 4.94/6.43 % Propositional clauses after purity: 0
% 4.94/6.43 % Propositional unsat core size : 0
% 4.94/6.43 % Propositional preprocessing time : 0.000
% 4.94/6.43 % Propositional encoding time : 0.000
% 4.94/6.43 % Propositional solver time : 0.000
% 4.94/6.43 % Success case prop preproc time : 0.000
% 4.94/6.43 % Success case prop encoding time : 0.000
% 4.94/6.43 % Success case prop solver time : 0.000
% 4.94/6.43 % Current number of processed clauses : 2206
% 4.94/6.43 % Positive orientable unit clauses : 542
% 4.94/6.43 % Positive unorientable unit clauses: 3
% 4.94/6.43 % Negative unit clauses : 308
% 4.94/6.43 % Non-unit-clauses : 1353
% 4.94/6.43 % Current number of unprocessed clauses: 21395
% 4.94/6.43 % ...number of literals in the above : 48173
% 4.94/6.43 % Current number of archived formulas : 0
% 4.94/6.43 % Current number of archived clauses : 1562
% 4.94/6.43 % Clause-clause subsumption calls (NU) : 1550792
% 4.94/6.43 % Rec. Clause-clause subsumption calls : 369508
% 4.94/6.43 % Non-unit clause-clause subsumptions : 1011
% 4.94/6.43 % Unit Clause-clause subsumption calls : 66894
% 4.94/6.43 % Rewrite failures with RHS unbound : 0
% 4.94/6.43 % BW rewrite match attempts : 316
% 4.94/6.43 % BW rewrite match successes : 118
% 4.94/6.43 % Condensation attempts : 0
% 4.94/6.43 % Condensation successes : 0
% 4.94/6.43 % Termbank termtop insertions : 449634
% 4.94/6.43 % Search garbage collected termcells : 19692
% 4.94/6.43
% 4.94/6.43 % -------------------------------------------------
% 4.94/6.43 % User time : 0.729 s
% 4.94/6.43 % System time : 0.032 s
% 4.94/6.43 % Total time : 0.761 s
% 4.94/6.43 % Maximum resident set size: 7692 pages
% 4.94/6.43
% 4.94/6.43 % -------------------------------------------------
% 4.94/6.43 % User time : 3.385 s
% 4.94/6.43 % System time : 0.128 s
% 4.94/6.43 % Total time : 3.513 s
% 4.94/6.43 % Maximum resident set size: 5376 pages
% 4.94/6.43 % E exiting
%------------------------------------------------------------------------------