%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU055+1 : 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 : n019.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 02:23:44 PM UTC 2026
% Result : Theorem 0.16s 0.69s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 24 unt; 0 def)
% Number of atoms : 116 ( 46 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 44 |; 15 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 2 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t124_funct_1,conjecture,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( apply(X1,X2) = apply(X1,X3)
& in(X3,relation_dom(X1))
& in(X2,relation_dom(X1)) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t20_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t124_funct_1]) ).
fof(c_0_8,negated_conjecture,
! [X45,X46] :
( ~ one_to_one(esk15_0)
& relation_image(esk15_0,set_difference(X45,X46)) = set_difference(relation_image(esk15_0,X45),relation_image(esk15_0,X46))
& function(esk15_0)
& relation(esk15_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_9,plain,
! [X42,X43] :
( relation_image(X43,singleton(X42)) = singleton(apply(X43,X42))
| ~ in(X42,relation_dom(X43))
| ~ function(X43)
| ~ relation(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])])]) ).
fof(c_0_10,plain,
! [X16,X17,X18] :
( ( ~ function(X16)
| ~ relation(X16)
| one_to_one(X16)
| esk2_1(X16) != esk3_1(X16) )
& ( ~ function(X16)
| ~ relation(X16)
| one_to_one(X16)
| apply(X16,esk2_1(X16)) = apply(X16,esk3_1(X16)) )
& ( ~ function(X16)
| ~ relation(X16)
| one_to_one(X16)
| in(esk3_1(X16),relation_dom(X16)) )
& ( ~ function(X16)
| ~ relation(X16)
| one_to_one(X16)
| in(esk2_1(X16),relation_dom(X16)) )
& ( ~ function(X16)
| ~ relation(X16)
| X17 = X18
| apply(X16,X17) != apply(X16,X18)
| ~ in(X18,relation_dom(X16))
| ~ in(X17,relation_dom(X16))
| ~ one_to_one(X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])])]) ).
fof(c_0_11,plain,
! [X53,X54] :
( ( set_difference(X53,X54) = empty_set
| ~ subset(X53,X54) )
& ( subset(X53,X54)
| set_difference(X53,X54) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])]) ).
fof(c_0_12,plain,
! [X41] : subset(X41,X41),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_13,negated_conjecture,
relation_image(esk15_0,set_difference(X1,X2)) = set_difference(relation_image(esk15_0,X1),relation_image(esk15_0,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| relation_image(X1,singleton(X2)) = singleton(apply(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
~ one_to_one(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| in(esk3_1(X1),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_22,plain,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
inference(fof_simplification,[status(thm)],[t20_zfmisc_1]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X1,relation_dom(esk15_0))
| set_difference(singleton(apply(esk15_0,X1)),relation_image(esk15_0,X2)) = relation_image(esk15_0,set_difference(singleton(X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_24,negated_conjecture,
apply(esk15_0,esk3_1(esk15_0)) = apply(esk15_0,esk2_1(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_16])]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
in(esk3_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_16])]),c_0_18]) ).
cnf(c_0_26,plain,
( ~ function(X1)
| ~ relation(X1)
| one_to_one(X1)
| in(esk2_1(X1),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X55] : set_difference(X55,empty_set) = X55,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_29,plain,
! [X49,X50] :
( ( set_difference(singleton(X49),singleton(X50)) = singleton(X49)
| X49 = X50 )
& ( X49 != X50
| set_difference(singleton(X49),singleton(X50)) != singleton(X49) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_30,negated_conjecture,
set_difference(singleton(apply(esk15_0,esk2_1(esk15_0))),relation_image(esk15_0,X1)) = relation_image(esk15_0,set_difference(singleton(esk3_1(esk15_0)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
in(esk2_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_15]),c_0_16])]),c_0_18]) ).
cnf(c_0_32,negated_conjecture,
relation_image(esk15_0,empty_set) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_27]) ).
cnf(c_0_33,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( X1 != X2
| set_difference(singleton(X1),singleton(X2)) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
relation_image(esk15_0,set_difference(singleton(esk3_1(esk15_0)),X1)) = relation_image(esk15_0,set_difference(singleton(esk2_1(esk15_0)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
relation_image(esk15_0,singleton(esk3_1(esk15_0))) = singleton(apply(esk15_0,esk2_1(esk15_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_33]),c_0_33]) ).
cnf(c_0_37,plain,
set_difference(singleton(X1),singleton(X1)) != singleton(X1),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
relation_image(esk15_0,set_difference(singleton(esk2_1(esk15_0)),singleton(esk3_1(esk15_0)))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_27]),c_0_32]) ).
cnf(c_0_39,plain,
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,negated_conjecture,
relation_image(esk15_0,singleton(esk2_1(esk15_0))) = singleton(apply(esk15_0,esk2_1(esk15_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_36]),c_0_33]) ).
cnf(c_0_41,plain,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_42,plain,
( ~ function(X1)
| ~ relation(X1)
| esk2_1(X1) != esk3_1(X1)
| one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,negated_conjecture,
esk3_1(esk15_0) = esk2_1(esk15_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_15]),c_0_16])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU055+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n019.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Mon Sep 21 05:48:22 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.62 Running first-order theorem proving
% 0.14/0.62 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
% 0.16/0.69 % Version: 3.5.1
% 0.16/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.69 % Starting sh5l with 300s (1) cores
% 0.16/0.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1814368 completed with status 0
% 0.16/0.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.69 % No SInE strategy applied
% 0.16/0.69 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.16/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.69 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.16/0.69 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.16/0.69 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with pid 1814376 completed with status 0
% 0.16/0.69 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN
% 0.16/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.69 % No SInE strategy applied
% 0.16/0.69 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.16/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.69 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.69 % Preprocessing time : 0.003 s
% 0.16/0.69
% 0.16/0.69 % Proof found!
% 0.16/0.69 % SZS status Theorem
% 0.16/0.69 % SZS output start CNFRefutation
% See solution above
% 0.16/0.69 % Parsed axioms : 40
% 0.16/0.69 % Removed by relevancy pruning/SinE : 0
% 0.16/0.69 % Initial clauses : 69
% 0.16/0.69 % Removed in clause preprocessing : 2
% 0.16/0.69 % Initial clauses in saturation : 67
% 0.16/0.69 % Processed clauses : 495
% 0.16/0.69 % ...of these trivial : 10
% 0.16/0.69 % ...subsumed : 217
% 0.16/0.69 % ...remaining for further processing : 268
% 0.16/0.69 % Other redundant clauses eliminated : 5
% 0.16/0.69 % Clauses deleted for lack of memory : 0
% 0.16/0.69 % Backward-subsumed : 12
% 0.16/0.69 % Backward-rewritten : 23
% 0.16/0.69 % Generated clauses : 1167
% 0.16/0.69 % ...of the previous two non-redundant : 974
% 0.16/0.69 % ...aggressively subsumed : 0
% 0.16/0.69 % Contextual simplify-reflections : 5
% 0.16/0.69 % Paramodulations : 1152
% 0.16/0.69 % Factorizations : 2
% 0.16/0.69 % NegExts : 0
% 0.16/0.69 % Equation resolutions : 13
% 0.16/0.69 % Disequality decompositions : 0
% 0.16/0.69 % Total rewrite steps : 1447
% 0.16/0.69 % ...of those cached : 1386
% 0.16/0.69 % Propositional unsat checks : 0
% 0.16/0.69 % Propositional check models : 0
% 0.16/0.69 % Propositional check unsatisfiable : 0
% 0.16/0.69 % Propositional clauses : 0
% 0.16/0.69 % Propositional clauses after purity: 0
% 0.16/0.69 % Propositional unsat core size : 0
% 0.16/0.69 % Propositional preprocessing time : 0.000
% 0.16/0.69 % Propositional encoding time : 0.000
% 0.16/0.69 % Propositional solver time : 0.000
% 0.16/0.69 % Success case prop preproc time : 0.000
% 0.16/0.69 % Success case prop encoding time : 0.000
% 0.16/0.69 % Success case prop solver time : 0.000
% 0.16/0.69 % Current number of processed clauses : 231
% 0.16/0.69 % Positive orientable unit clauses : 44
% 0.16/0.69 % Positive unorientable unit clauses: 0
% 0.16/0.69 % Negative unit clauses : 18
% 0.16/0.69 % Non-unit-clauses : 169
% 0.16/0.69 % Current number of unprocessed clauses: 491
% 0.16/0.69 % ...number of literals in the above : 1827
% 0.16/0.69 % Current number of archived formulas : 0
% 0.16/0.69 % Current number of archived clauses : 35
% 0.16/0.69 % Clause-clause subsumption calls (NU) : 7036
% 0.16/0.69 % Rec. Clause-clause subsumption calls : 3930
% 0.16/0.69 % Non-unit clause-clause subsumptions : 157
% 0.16/0.69 % Unit Clause-clause subsumption calls : 603
% 0.16/0.69 % Rewrite failures with RHS unbound : 0
% 0.16/0.69 % BW rewrite match attempts : 21
% 0.16/0.69 % BW rewrite match successes : 10
% 0.16/0.69 % Condensation attempts : 0
% 0.16/0.69 % Condensation successes : 0
% 0.16/0.69 % Termbank termtop insertions : 34365
% 0.16/0.69 % Search garbage collected termcells : 685
% 0.16/0.69
% 0.16/0.69 % -------------------------------------------------
% 0.16/0.69 % User time : 0.049 s
% 0.16/0.69 % System time : 0.010 s
% 0.16/0.69 % Total time : 0.059 s
% 0.16/0.69 % Maximum resident set size: 3660 pages
% 0.16/0.69
% 0.16/0.69 % -------------------------------------------------
% 0.16/0.69 % User time : 0.246 s
% 0.16/0.69 % System time : 0.027 s
% 0.16/0.69 % Total time : 0.273 s
% 0.16/0.69 % Maximum resident set size: 4864 pages
% 0.16/0.69 % E exiting
%------------------------------------------------------------------------------