%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU225+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 : 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 02:28:37 PM UTC 2026
% Result : Theorem 2.46s 0.94s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 62 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 19 ~; 14 |; 11 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 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 : 36 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t72_funct_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t94_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(t23_funct_1,lemma,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( function(identity_relation(X1))
& relation(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t71_relat_1,lemma,
! [X1] :
( relation_rng(identity_relation(X1)) = X1
& relation_dom(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(t35_funct_1,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
fof(c_0_8,negated_conjecture,
( apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0)
& in(esk81_0,esk80_0)
& function(esk82_0)
& relation(esk82_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,lemma,
! [X634,X635] :
( relation_dom_restriction(X635,X634) = relation_composition(identity_relation(X634),X635)
| ~ relation(X635) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t94_relat_1])])]) ).
cnf(c_0_10,negated_conjecture,
apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,lemma,
( ~ relation(X1)
| relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,lemma,
! [X461,X462,X463] :
( apply(relation_composition(X462,X463),X461) = apply(X463,apply(X462,X461))
| ~ in(X461,relation_dom(X462))
| ~ function(X463)
| ~ relation(X463)
| ~ function(X462)
| ~ relation(X462) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])])]) ).
fof(c_0_14,plain,
! [X271] : relation(identity_relation(X271)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_15,plain,
! [X297] :
( function(identity_relation(X297))
& relation(identity_relation(X297)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_16,lemma,
! [X600] :
( relation_rng(identity_relation(X600)) = X600
& relation_dom(identity_relation(X600)) = X600 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
cnf(c_0_17,negated_conjecture,
apply(relation_composition(identity_relation(esk80_0),esk82_0),esk81_0) != apply(esk82_0,esk81_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_18,lemma,
( ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
function(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
in(esk81_0,esk80_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_24,lemma,
! [X492,X493] :
( apply(identity_relation(X492),X493) = X493
| ~ in(X493,X492) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])])]) ).
cnf(c_0_25,lemma,
apply(esk82_0,apply(identity_relation(esk80_0),esk81_0)) != apply(esk82_0,esk81_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,lemma,
( ~ in(X1,X2)
| apply(identity_relation(X2),X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 06:03:16 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.44 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
% 2.46/0.94 % Version: 3.5.1
% 2.46/0.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.46/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.46/0.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.46/0.94 % Starting new_bool_3 with 300s (1) cores
% 2.46/0.94 % Starting new_bool_1 with 300s (1) cores
% 2.46/0.94 % Starting sh5l with 300s (1) cores
% 2.46/0.94 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2588979 completed with status 0
% 2.46/0.94 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.46/0.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.46/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.46/0.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.46/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.46/0.94 % No SInE strategy applied
% 2.46/0.94 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.46/0.94 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.46/0.94 % Starting SubtermCWHack with 136s (1) cores
% 2.46/0.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.46/0.94 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 2.46/0.94 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 2.46/0.94 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 2.46/0.94 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with pid 2588987 completed with status 0
% 2.46/0.94 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y
% 2.46/0.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.46/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.46/0.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.46/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.46/0.94 % No SInE strategy applied
% 2.46/0.94 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.46/0.94 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.46/0.94 % Starting SubtermCWHack with 136s (1) cores
% 2.46/0.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.46/0.94 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 2.46/0.94 % Preprocessing time : 0.011 s
% 2.46/0.94 % Presaturation interreduction done
% 2.46/0.94
% 2.46/0.94 % Proof found!
% 2.46/0.94 % SZS status Theorem
% 2.46/0.94 % SZS output start CNFRefutation
% See solution above
% 2.46/0.94 % Parsed axioms : 240
% 2.46/0.94 % Removed by relevancy pruning/SinE : 0
% 2.46/0.94 % Initial clauses : 461
% 2.46/0.94 % Removed in clause preprocessing : 26
% 2.46/0.94 % Initial clauses in saturation : 435
% 2.46/0.94 % Processed clauses : 2702
% 2.46/0.94 % ...of these trivial : 56
% 2.46/0.94 % ...subsumed : 1163
% 2.46/0.94 % ...remaining for further processing : 1483
% 2.46/0.94 % Other redundant clauses eliminated : 134
% 2.46/0.94 % Clauses deleted for lack of memory : 0
% 2.46/0.94 % Backward-subsumed : 13
% 2.46/0.94 % Backward-rewritten : 24
% 2.46/0.94 % Generated clauses : 17374
% 2.46/0.94 % ...of the previous two non-redundant : 15473
% 2.46/0.94 % ...aggressively subsumed : 0
% 2.46/0.94 % Contextual simplify-reflections : 41
% 2.46/0.94 % Paramodulations : 17230
% 2.46/0.94 % Factorizations : 14
% 2.46/0.94 % NegExts : 0
% 2.46/0.94 % Equation resolutions : 141
% 2.46/0.94 % Disequality decompositions : 0
% 2.46/0.94 % Total rewrite steps : 3668
% 2.46/0.94 % ...of those cached : 3265
% 2.46/0.94 % Propositional unsat checks : 0
% 2.46/0.94 % Propositional check models : 0
% 2.46/0.94 % Propositional check unsatisfiable : 0
% 2.46/0.94 % Propositional clauses : 0
% 2.46/0.94 % Propositional clauses after purity: 0
% 2.46/0.94 % Propositional unsat core size : 0
% 2.46/0.94 % Propositional preprocessing time : 0.000
% 2.46/0.94 % Propositional encoding time : 0.000
% 2.46/0.94 % Propositional solver time : 0.000
% 2.46/0.94 % Success case prop preproc time : 0.000
% 2.46/0.94 % Success case prop encoding time : 0.000
% 2.46/0.94 % Success case prop solver time : 0.000
% 2.46/0.94 % Current number of processed clauses : 988
% 2.46/0.94 % Positive orientable unit clauses : 194
% 2.46/0.94 % Positive unorientable unit clauses: 5
% 2.46/0.94 % Negative unit clauses : 57
% 2.46/0.94 % Non-unit-clauses : 732
% 2.46/0.94 % Current number of unprocessed clauses: 13496
% 2.46/0.94 % ...number of literals in the above : 41795
% 2.46/0.94 % Current number of archived formulas : 0
% 2.46/0.94 % Current number of archived clauses : 422
% 2.46/0.94 % Clause-clause subsumption calls (NU) : 129816
% 2.46/0.94 % Rec. Clause-clause subsumption calls : 68721
% 2.46/0.94 % Non-unit clause-clause subsumptions : 898
% 2.46/0.94 % Unit Clause-clause subsumption calls : 15256
% 2.46/0.94 % Rewrite failures with RHS unbound : 22
% 2.46/0.94 % BW rewrite match attempts : 193
% 2.46/0.94 % BW rewrite match successes : 69
% 2.46/0.94 % Condensation attempts : 0
% 2.46/0.94 % Condensation successes : 0
% 2.46/0.94 % Termbank termtop insertions : 260926
% 2.46/0.94 % Search garbage collected termcells : 7861
% 2.46/0.94
% 2.46/0.94 % -------------------------------------------------
% 2.46/0.94 % User time : 0.408 s
% 2.46/0.94 % System time : 0.025 s
% 2.46/0.94 % Total time : 0.433 s
% 2.46/0.94 % Maximum resident set size: 5160 pages
% 2.46/0.94
% 2.46/0.94 % -------------------------------------------------
% 2.46/0.94 % User time : 1.312 s
% 2.46/0.95 % System time : 0.092 s
% 2.46/0.95 % Total time : 1.404 s
% 2.46/0.95 % Maximum resident set size: 5120 pages
% 2.46/0.95 % E exiting
%------------------------------------------------------------------------------