%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU226+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 : n002.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 02:24:21 PM UTC 2026
% Result : Theorem 8.52s 1.69s
% Output : CNFRefutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 160 ( 30 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 226 ( 91 ~; 102 |; 23 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d13_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d12_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( X4 = apply(X1,X5)
& in(X5,X2)
& in(X5,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_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(t145_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(c_0_4,plain,
! [X23,X24,X25,X26,X27,X28,X29] :
( ( ~ function(X23)
| ~ relation(X23)
| X29 = relation_inverse_image(X23,X28)
| in(esk4_3(X23,X28,X29),X29)
| in(apply(X23,esk4_3(X23,X28,X29)),X28) )
& ( ~ function(X23)
| ~ relation(X23)
| X29 = relation_inverse_image(X23,X28)
| in(esk4_3(X23,X28,X29),X29)
| in(esk4_3(X23,X28,X29),relation_dom(X23)) )
& ( ~ function(X23)
| ~ relation(X23)
| X29 = relation_inverse_image(X23,X28)
| ~ in(apply(X23,esk4_3(X23,X28,X29)),X28)
| ~ in(esk4_3(X23,X28,X29),relation_dom(X23))
| ~ in(esk4_3(X23,X28,X29),X29) )
& ( ~ function(X23)
| ~ relation(X23)
| X25 != relation_inverse_image(X23,X24)
| in(X27,X25)
| ~ in(apply(X23,X27),X24)
| ~ in(X27,relation_dom(X23)) )
& ( ~ function(X23)
| ~ relation(X23)
| X25 != relation_inverse_image(X23,X24)
| ~ in(X26,X25)
| in(apply(X23,X26),X24) )
& ( ~ function(X23)
| ~ relation(X23)
| X25 != relation_inverse_image(X23,X24)
| ~ in(X26,X25)
| in(X26,relation_dom(X23)) ) ),
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_funct_1])])])])])])]) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19)) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),X18) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| esk2_3(X11,X18,X19) != apply(X11,X21)
| ~ in(X21,X18)
| ~ in(X21,relation_dom(X11))
| ~ in(esk2_3(X11,X18,X19),X19) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| in(X16,X13)
| X16 != apply(X11,X17)
| ~ in(X17,X12)
| ~ in(X17,relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| X14 = apply(X11,esk1_4(X11,X12,X13,X14)) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),X12) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),relation_dom(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)],[d12_funct_1])])])])])])]) ).
cnf(c_0_6,plain,
( ~ function(X1)
| ~ relation(X1)
| X4 != relation_inverse_image(X1,X3)
| ~ in(X2,X4)
| in(apply(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_image(X2,X3)
| ~ in(X1,X4)
| X1 = apply(X2,esk1_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ in(X1,X5)
| ~ in(esk1_4(X4,X6,X5,X1),X3)
| ~ function(X4)
| ~ relation(X4)
| X5 != relation_image(X4,X6)
| X3 != relation_inverse_image(X4,X2)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
( ~ function(X1)
| ~ relation(X1)
| X3 != relation_image(X1,X2)
| ~ in(X4,X3)
| in(esk1_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( ~ in(X1,X5)
| ~ function(X4)
| ~ relation(X4)
| X5 != relation_image(X4,X3)
| X3 != relation_inverse_image(X4,X2)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
( ~ in(X1,X3)
| ~ function(X4)
| ~ relation(X4)
| X3 != relation_image(X4,relation_inverse_image(X4,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
fof(c_0_12,plain,
! [X31,X32,X33,X34,X35] :
( ( subset(X34,X35)
| ~ in(esk5_2(X34,X35),X35) )
& ( subset(X34,X35)
| in(esk5_2(X34,X35),X34) )
& ( in(X33,X32)
| ~ in(X33,X31)
| ~ subset(X31,X32) ) ),
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])])])])])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
inference(assume_negation,[status(cth)],[t145_funct_1]) ).
cnf(c_0_14,plain,
( ~ in(X1,relation_image(X3,relation_inverse_image(X3,X2)))
| ~ function(X3)
| ~ relation(X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
( ~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0)
& function(esk18_0)
& relation(esk18_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_17,plain,
( ~ function(X1)
| ~ relation(X1)
| in(esk5_2(relation_image(X1,relation_inverse_image(X1,X2)),X3),X2)
| subset(relation_image(X1,relation_inverse_image(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ in(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( in(esk5_2(relation_image(esk18_0,relation_inverse_image(esk18_0,X1)),X2),X1)
| subset(relation_image(esk18_0,relation_inverse_image(esk18_0,X1)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
subset(relation_image(esk18_0,relation_inverse_image(esk18_0,X1)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU226+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 06:03:02 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 8.52/1.69 % Version: 3.5.1
% 8.52/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.52/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.52/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.52/1.69 % Starting new_bool_3 with 300s (1) cores
% 8.52/1.69 % Starting new_bool_1 with 300s (1) cores
% 8.52/1.69 % Starting sh5l with 300s (1) cores
% 8.52/1.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2588169 completed with status 0
% 8.52/1.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.52/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.52/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.52/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.52/1.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.52/1.69 % No SInE strategy applied
% 8.52/1.69 % Search class: FGHSM-FFMM32-SFFFFFNN
% 8.52/1.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.52/1.69 % Starting SubtermCWHack with 136s (1) cores
% 8.52/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.52/1.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 8.52/1.69 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.52/1.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 8.52/1.69 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with pid 2588180 completed with status 0
% 8.52/1.69 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN
% 8.52/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.52/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.52/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.52/1.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.52/1.69 % No SInE strategy applied
% 8.52/1.69 % Search class: FGHSM-FFMM32-SFFFFFNN
% 8.52/1.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.52/1.69 % Starting SubtermCWHack with 136s (1) cores
% 8.52/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.52/1.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 8.52/1.69 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.52/1.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 8.52/1.69 % Preprocessing time : 0.004 s
% 8.52/1.69
% 8.52/1.69 % Proof found!
% 8.52/1.69 % SZS status Theorem
% 8.52/1.69 % SZS output start CNFRefutation
% See solution above
% 8.52/1.69 % Parsed axioms : 34
% 8.52/1.69 % Removed by relevancy pruning/SinE : 0
% 8.52/1.69 % Initial clauses : 67
% 8.52/1.69 % Removed in clause preprocessing : 2
% 8.52/1.69 % Initial clauses in saturation : 65
% 8.52/1.69 % Processed clauses : 1410
% 8.52/1.69 % ...of these trivial : 7
% 8.52/1.69 % ...subsumed : 773
% 8.52/1.69 % ...remaining for further processing : 630
% 8.52/1.69 % Other redundant clauses eliminated : 3
% 8.52/1.69 % Clauses deleted for lack of memory : 0
% 8.52/1.69 % Backward-subsumed : 68
% 8.52/1.69 % Backward-rewritten : 18
% 8.52/1.69 % Generated clauses : 20513
% 8.52/1.69 % ...of the previous two non-redundant : 20116
% 8.52/1.69 % ...aggressively subsumed : 0
% 8.52/1.69 % Contextual simplify-reflections : 47
% 8.52/1.69 % Paramodulations : 20398
% 8.52/1.69 % Factorizations : 38
% 8.52/1.69 % NegExts : 0
% 8.52/1.69 % Equation resolutions : 77
% 8.52/1.69 % Disequality decompositions : 0
% 8.52/1.69 % Total rewrite steps : 4760
% 8.52/1.69 % ...of those cached : 4726
% 8.52/1.69 % Propositional unsat checks : 0
% 8.52/1.69 % Propositional check models : 0
% 8.52/1.69 % Propositional check unsatisfiable : 0
% 8.52/1.69 % Propositional clauses : 0
% 8.52/1.69 % Propositional clauses after purity: 0
% 8.52/1.69 % Propositional unsat core size : 0
% 8.52/1.69 % Propositional preprocessing time : 0.000
% 8.52/1.69 % Propositional encoding time : 0.000
% 8.52/1.69 % Propositional solver time : 0.000
% 8.52/1.69 % Success case prop preproc time : 0.000
% 8.52/1.69 % Success case prop encoding time : 0.000
% 8.52/1.69 % Success case prop solver time : 0.000
% 8.52/1.69 % Current number of processed clauses : 544
% 8.52/1.69 % Positive orientable unit clauses : 28
% 8.52/1.69 % Positive unorientable unit clauses: 0
% 8.52/1.69 % Negative unit clauses : 11
% 8.52/1.69 % Non-unit-clauses : 505
% 8.52/1.69 % Current number of unprocessed clauses: 18566
% 8.52/1.69 % ...number of literals in the above : 119003
% 8.52/1.69 % Current number of archived formulas : 0
% 8.52/1.69 % Current number of archived clauses : 86
% 8.52/1.69 % Clause-clause subsumption calls (NU) : 57895
% 8.52/1.69 % Rec. Clause-clause subsumption calls : 11217
% 8.52/1.69 % Non-unit clause-clause subsumptions : 619
% 8.52/1.69 % Unit Clause-clause subsumption calls : 733
% 8.52/1.69 % Rewrite failures with RHS unbound : 0
% 8.52/1.69 % BW rewrite match attempts : 13
% 8.52/1.69 % BW rewrite match successes : 9
% 8.52/1.69 % Condensation attempts : 0
% 8.52/1.69 % Condensation successes : 0
% 8.52/1.69 % Termbank termtop insertions : 475444
% 8.52/1.69 % Search garbage collected termcells : 842
% 8.52/1.69
% 8.52/1.69 % -------------------------------------------------
% 8.52/1.69 % User time : 1.063 s
% 8.52/1.69 % System time : 0.044 s
% 8.52/1.69 % Total time : 1.107 s
% 8.52/1.69 % Maximum resident set size: 3660 pages
% 8.52/1.69
% 8.52/1.69 % -------------------------------------------------
% 8.52/1.69 % User time : 5.195 s
% 8.52/1.69 % System time : 0.223 s
% 8.52/1.69 % Total time : 5.417 s
% 8.52/1.69 % Maximum resident set size: 4864 pages
% 8.52/1.69 % E exiting
%------------------------------------------------------------------------------