%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU255+1 : 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 : n005.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 02:24:28 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 110 ( 14 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 123 ( 48 ~; 56 |; 9 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X1)
& in(ordered_pair(X2,X3),X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t16_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,cartesian_product2(X2,X2))
& in(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t25_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(c_0_6,plain,
! [X23,X24,X25] :
( ( ~ relation(X23)
| antisymmetric(X23)
| esk2_1(X23) != esk3_1(X23) )
& ( ~ relation(X23)
| antisymmetric(X23)
| in(ordered_pair(esk3_1(X23),esk2_1(X23)),X23) )
& ( ~ relation(X23)
| antisymmetric(X23)
| in(ordered_pair(esk2_1(X23),esk3_1(X23)),X23) )
& ( ~ relation(X23)
| X24 = X25
| ~ in(ordered_pair(X25,X24),X23)
| ~ in(ordered_pair(X24,X25),X23)
| ~ antisymmetric(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(fof_nnf,[status(thm)],[l3_wellord1])])])])])]) ).
fof(c_0_7,plain,
! [X12,X13] : ordered_pair(X12,X13) = unordered_pair(unordered_pair(X12,X13),singleton(X12)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( ~ relation(X1)
| antisymmetric(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,plain,
( ~ relation(X1)
| antisymmetric(X1)
| in(ordered_pair(esk3_1(X1),esk2_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ relation(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ antisymmetric(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,plain,
! [X33,X34,X35] :
( ( ~ relation(X35)
| in(X33,relation_restriction(X35,X34))
| ~ in(X33,cartesian_product2(X34,X34))
| ~ in(X33,X35) )
& ( ~ relation(X35)
| ~ in(X33,relation_restriction(X35,X34))
| in(X33,cartesian_product2(X34,X34)) )
& ( ~ relation(X35)
| ~ in(X33,relation_restriction(X35,X34))
| in(X33,X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])])]) ).
cnf(c_0_14,plain,
( ~ relation(X1)
| in(unordered_pair(unordered_pair(esk2_1(X1),esk3_1(X1)),singleton(esk2_1(X1))),X1)
| antisymmetric(X1) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X16,X17] :
( relation(relation_restriction(X16,X17))
| ~ relation(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])])]) ).
cnf(c_0_17,plain,
( ~ relation(X1)
| in(unordered_pair(unordered_pair(esk3_1(X1),esk2_1(X1)),singleton(esk3_1(X1))),X1)
| antisymmetric(X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_18,plain,
( ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X1)
| ~ antisymmetric(X1)
| ~ relation(X1)
| X2 = X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_9]),c_0_9]) ).
cnf(c_0_19,plain,
( ~ relation(X2)
| ~ in(X1,relation_restriction(X2,X3))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ relation(X1)
| in(unordered_pair(singleton(esk2_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| antisymmetric(X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ relation(X1)
| in(unordered_pair(singleton(esk3_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| antisymmetric(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_15]),c_0_15]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t25_wellord1]) ).
cnf(c_0_24,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ relation(X3)
| ~ antisymmetric(X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_25,plain,
( ~ relation(X1)
| in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( ~ relation(X1)
| in(unordered_pair(singleton(esk3_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_21]) ).
fof(c_0_27,negated_conjecture,
( ~ antisymmetric(relation_restriction(esk10_0,esk9_0))
& antisymmetric(esk10_0)
& relation(esk10_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_28,plain,
( ~ relation(X1)
| esk2_1(X1) != esk3_1(X1)
| antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,plain,
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X2))
| esk3_1(relation_restriction(X1,X2)) = esk2_1(relation_restriction(X1,X2)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]),c_0_15]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ antisymmetric(relation_restriction(esk10_0,esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]) ).
cnf(c_0_32,negated_conjecture,
antisymmetric(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:03:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2714637 completed with status 0
% 0.09/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.46 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.46 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2714646 completed with status 0
% 0.09/0.46 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.46 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.09/0.46 % Preprocessing time : 0.002 s
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 33
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 47
% 0.09/0.46 % Removed in clause preprocessing : 10
% 0.09/0.46 % Initial clauses in saturation : 37
% 0.09/0.46 % Processed clauses : 325
% 0.09/0.46 % ...of these trivial : 13
% 0.09/0.46 % ...subsumed : 187
% 0.09/0.46 % ...remaining for further processing : 125
% 0.09/0.46 % Other redundant clauses eliminated : 0
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 12
% 0.09/0.46 % Backward-rewritten : 7
% 0.09/0.46 % Generated clauses : 961
% 0.09/0.46 % ...of the previous two non-redundant : 765
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 15
% 0.09/0.46 % Paramodulations : 961
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 0
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 475
% 0.09/0.46 % ...of those cached : 451
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 106
% 0.09/0.46 % Positive orientable unit clauses : 18
% 0.09/0.46 % Positive unorientable unit clauses: 2
% 0.09/0.46 % Negative unit clauses : 8
% 0.09/0.46 % Non-unit-clauses : 78
% 0.09/0.46 % Current number of unprocessed clauses: 462
% 0.09/0.46 % ...number of literals in the above : 2817
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 20
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 4031
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 1367
% 0.09/0.46 % Non-unit clause-clause subsumptions : 167
% 0.09/0.46 % Unit Clause-clause subsumption calls : 59
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 10
% 0.09/0.46 % BW rewrite match successes : 9
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 20698
% 0.09/0.46 % Search garbage collected termcells : 362
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.040 s
% 0.09/0.46 % System time : 0.002 s
% 0.09/0.46 % Total time : 0.042 s
% 0.09/0.46 % Maximum resident set size: 3652 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.179 s
% 0.09/0.46 % System time : 0.020 s
% 0.09/0.46 % Total time : 0.198 s
% 0.09/0.46 % Maximum resident set size: 4864 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------