%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX239_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 03:14:21 PM UTC 2026
% Result : Theorem 0.21s 0.55s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 83 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 27 |; 10 &)
% ( 6 <=>; 1 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 7 sgn 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
tff(decl_31,type,
cons2: ( $i * $i ) > $i ).
tff(decl_34,type,
nil2: $i ).
tff(decl_41,type,
atom: $i > $i ).
tff(decl_46,type,
y: ( $i * $i ) > $i ).
tff(decl_49,type,
star: $i > $i ).
tff(decl_52,type,
eps: $i ).
tff(decl_58,type,
eps2: $i > $o ).
tff(decl_59,type,
step: ( $i * $i ) > $i ).
tff(decl_60,type,
rec: ( $i * $i ) > $o ).
tff(decl_61,type,
reck2: ( $i * $i ) > $o ).
fof(goal_077,conjecture,
? [X13,X26] :
( rec(X13,X26)
<~> reck2(X13,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_077) ).
fof(axiom_064,axiom,
! [X1,X19,X11] :
( rec(X1,cons2(X19,X11))
<=> rec(step(X1,X19),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_064) ).
fof(axiom_074,axiom,
! [X18,X23,X24] :
( reck2(star(X18),cons2(X23,X24))
<=> ( rec(y(X18,star(X18)),cons2(X23,X24))
& ~ eps2(X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_074) ).
fof(axiom_063,axiom,
! [X1] :
( rec(X1,nil2)
<=> eps2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_063) ).
fof(axiom_054,axiom,
! [X15,X16] :
( eps2(y(X15,X16))
<=> ( eps2(X16)
& eps2(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_054) ).
fof(axiom_062,axiom,
! [X8,X18] : step(star(X18),X8) = y(step(X18,X8),star(X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_062) ).
fof(axiom_055,axiom,
! [X8] : eps2(star(X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_055) ).
fof(axiom_057,axiom,
! [X8,X17] :
( X17 = X8
=> step(atom(X17),X8) = eps ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_057) ).
fof(axiom_052,axiom,
eps2(eps),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_052) ).
fof(c_0_9,negated_conjecture,
~ ? [X13,X26] :
( rec(X13,X26)
<~> reck2(X13,X26) ),
inference(assume_negation,[status(cth)],[goal_077]) ).
fof(c_0_10,negated_conjecture,
~ ? [X13,X26] :
~ ( rec(X13,X26)
<=> reck2(X13,X26) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_11,negated_conjecture,
! [X27,X28] :
( ( rec(X27,X28)
| ~ reck2(X27,X28) )
& ( reck2(X27,X28)
| ~ rec(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X44,X45,X46] :
( ( rec(X44,cons2(X45,X46))
| ~ rec(step(X44,X45),X46) )
& ( rec(step(X44,X45),X46)
| ~ rec(X44,cons2(X45,X46)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_064])])]) ).
fof(c_0_13,plain,
! [X18,X23,X24] :
( reck2(star(X18),cons2(X23,X24))
<=> ( rec(y(X18,star(X18)),cons2(X23,X24))
& ~ eps2(X18) ) ),
inference(fof_simplification,[status(thm)],[axiom_074]) ).
cnf(c_0_14,negated_conjecture,
( ~ rec(X1,X2)
| reck2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ rec(step(X1,X2),X6)
| rec(X1,cons2(X2,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X43] :
( ( rec(X43,nil2)
| ~ eps2(X43) )
& ( eps2(X43)
| ~ rec(X43,nil2) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_063])])]) ).
fof(c_0_17,plain,
! [X47,X48,X49] :
( ( reck2(star(X47),cons2(X48,X49))
| ~ rec(y(X47,star(X47)),cons2(X48,X49))
| eps2(X47) )
& ( ~ reck2(star(X47),cons2(X48,X49))
| rec(y(X47,star(X47)),cons2(X48,X49)) )
& ( ~ reck2(star(X47),cons2(X48,X49))
| ~ eps2(X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ rec(step(X1,X2),X6)
| reck2(X1,cons2(X2,X6)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ eps2(X1)
| rec(X1,nil2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X91,X92] :
( ( eps2(y(X91,X92))
| ~ eps2(X92)
| ~ eps2(X91) )
& ( ~ eps2(y(X91,X92))
| eps2(X92) )
& ( ~ eps2(y(X91,X92))
| eps2(X91) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_054])])])]) ).
fof(c_0_21,plain,
! [X87,X88] : step(star(X88),X87) = y(step(X88,X87),star(X88)),
inference(variable_rename,[status(thm)],[axiom_062]) ).
fof(c_0_22,plain,
! [X86] : eps2(star(X86)),
inference(variable_rename,[status(thm)],[axiom_055]) ).
cnf(c_0_23,plain,
( ~ reck2(star(X1),cons2(X2,X6))
| ~ eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( ~ eps2(step(X1,X2))
| reck2(X1,cons2(X2,nil2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ eps2(X2)
| ~ eps2(X1)
| eps2(y(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
step(star(X1),X2) = y(step(X1,X2),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
eps2(star(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ eps2(X1)
| ~ eps2(step(star(X1),X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ eps2(step(X1,X2))
| eps2(step(star(X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
fof(c_0_30,plain,
! [X72,X73] :
( step(atom(X73),X72) = eps
| X73 != X72 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_057])])]) ).
cnf(c_0_31,negated_conjecture,
( ~ eps2(X1)
| ~ eps2(step(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( X1 != X2
| step(atom(X1),X2) = eps ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ eps2(step(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_27])]) ).
cnf(c_0_34,plain,
step(atom(X1),X1) = eps,
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
eps2(eps),
inference(split_conjunct,[status(thm)],[axiom_052]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX239_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n001.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 10:43:29 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 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
% 0.21/0.55 % Version: 3.5.1
% 0.21/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.55 % Starting sh5l with 300s (1) cores
% 0.21/0.55 % new_bool_3 with pid 2908660 completed with status 0
% 0.21/0.55 % Result found by new_bool_3
% 0.21/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.21/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.55 % SubtermCWHack with pid 2908663 completed with status 0
% 0.21/0.55 % Result found by SubtermCWHack
% 0.21/0.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.21/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.55 % Preprocessing time : 0.003 s
% 0.21/0.55
% 0.21/0.55 % Proof found!
% 0.21/0.55 % SZS status Theorem
% 0.21/0.55 % SZS output start CNFRefutation
% See solution above
% 0.21/0.55 % Parsed axioms : 77
% 0.21/0.55 % Removed by relevancy pruning/SinE : 39
% 0.21/0.55 % Initial clauses : 50
% 0.21/0.55 % Removed in clause preprocessing : 0
% 0.21/0.55 % Initial clauses in saturation : 50
% 0.21/0.55 % Processed clauses : 90
% 0.21/0.55 % ...of these trivial : 0
% 0.21/0.55 % ...subsumed : 9
% 0.21/0.55 % ...remaining for further processing : 81
% 0.21/0.55 % Other redundant clauses eliminated : 2
% 0.21/0.55 % Clauses deleted for lack of memory : 0
% 0.21/0.55 % Backward-subsumed : 9
% 0.21/0.55 % Backward-rewritten : 0
% 0.21/0.55 % Generated clauses : 108
% 0.21/0.55 % ...of the previous two non-redundant : 93
% 0.21/0.55 % ...aggressively subsumed : 0
% 0.21/0.55 % Contextual simplify-reflections : 0
% 0.21/0.55 % Paramodulations : 106
% 0.21/0.55 % Factorizations : 0
% 0.21/0.55 % NegExts : 0
% 0.21/0.55 % Equation resolutions : 2
% 0.21/0.55 % Disequality decompositions : 0
% 0.21/0.55 % Total rewrite steps : 7
% 0.21/0.55 % ...of those cached : 5
% 0.21/0.55 % Propositional unsat checks : 0
% 0.21/0.55 % Propositional check models : 0
% 0.21/0.55 % Propositional check unsatisfiable : 0
% 0.21/0.55 % Propositional clauses : 0
% 0.21/0.55 % Propositional clauses after purity: 0
% 0.21/0.55 % Propositional unsat core size : 0
% 0.21/0.55 % Propositional preprocessing time : 0.000
% 0.21/0.55 % Propositional encoding time : 0.000
% 0.21/0.55 % Propositional solver time : 0.000
% 0.21/0.55 % Success case prop preproc time : 0.000
% 0.21/0.55 % Success case prop encoding time : 0.000
% 0.21/0.55 % Success case prop solver time : 0.000
% 0.21/0.55 % Current number of processed clauses : 70
% 0.21/0.55 % Positive orientable unit clauses : 8
% 0.21/0.55 % Positive unorientable unit clauses: 0
% 0.21/0.55 % Negative unit clauses : 37
% 0.21/0.55 % Non-unit-clauses : 25
% 0.21/0.55 % Current number of unprocessed clauses: 53
% 0.21/0.55 % ...number of literals in the above : 110
% 0.21/0.55 % Current number of archived formulas : 0
% 0.21/0.55 % Current number of archived clauses : 9
% 0.21/0.55 % Clause-clause subsumption calls (NU) : 41
% 0.21/0.55 % Rec. Clause-clause subsumption calls : 39
% 0.21/0.55 % Non-unit clause-clause subsumptions : 2
% 0.21/0.55 % Unit Clause-clause subsumption calls : 72
% 0.21/0.55 % Rewrite failures with RHS unbound : 0
% 0.21/0.55 % BW rewrite match attempts : 1
% 0.21/0.55 % BW rewrite match successes : 0
% 0.21/0.55 % Condensation attempts : 0
% 0.21/0.55 % Condensation successes : 0
% 0.21/0.55 % Termbank termtop insertions : 3848
% 0.21/0.55 % Search garbage collected termcells : 624
% 0.21/0.55
% 0.21/0.55 % -------------------------------------------------
% 0.21/0.55 % User time : 0.011 s
% 0.21/0.55 % System time : 0.006 s
% 0.21/0.55 % Total time : 0.017 s
% 0.21/0.55 % Maximum resident set size: 3660 pages
% 0.21/0.55
% 0.21/0.55 % -------------------------------------------------
% 0.21/0.55 % User time : 0.017 s
% 0.21/0.55 % System time : 0.011 s
% 0.21/0.55 % Total time : 0.028 s
% 0.21/0.55 % Maximum resident set size: 4608 pages
% 0.21/0.55 % E exiting
%------------------------------------------------------------------------------