%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:15:54 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 86 ( 33 ~; 34 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X2))
=> in(apply(X2,X1),relation_rng(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X2))
=> in(apply(X2,X1),relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[t12_funct_1]) ).
fof(c_0_3,plain,
! [X46,X47,X48,X50,X51,X52,X54] :
( ( ~ function(X46)
| ~ relation(X46)
| X52 = relation_rng(X46)
| in(esk13_2(X46,X52),X52)
| esk13_2(X46,X52) = apply(X46,esk14_2(X46,X52)) )
& ( ~ function(X46)
| ~ relation(X46)
| X52 = relation_rng(X46)
| in(esk13_2(X46,X52),X52)
| in(esk14_2(X46,X52),relation_dom(X46)) )
& ( ~ function(X46)
| ~ relation(X46)
| X52 = relation_rng(X46)
| esk13_2(X46,X52) != apply(X46,X54)
| ~ in(X54,relation_dom(X46))
| ~ in(esk13_2(X46,X52),X52) )
& ( ~ function(X46)
| ~ relation(X46)
| X47 != relation_rng(X46)
| in(X50,X47)
| X50 != apply(X46,X51)
| ~ in(X51,relation_dom(X46)) )
& ( ~ function(X46)
| ~ relation(X46)
| X47 != relation_rng(X46)
| ~ in(X48,X47)
| X48 = apply(X46,esk12_3(X46,X47,X48)) )
& ( ~ function(X46)
| ~ relation(X46)
| X47 != relation_rng(X46)
| ~ in(X48,X47)
| in(esk12_3(X46,X47,X48),relation_dom(X46)) ) ),
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)],[d5_funct_1])])])])])])]) ).
fof(c_0_4,negated_conjecture,
( ~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0))
& in(esk10_0,relation_dom(esk11_0))
& function(esk11_0)
& relation(esk11_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_rng(X2)
| X3 != apply(X2,X1)
| ~ in(X1,relation_dom(X2))
| in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
~ in(apply(esk11_0,esk10_0),relation_rng(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| in(apply(X1,X2),relation_rng(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_8,negated_conjecture,
in(esk10_0,relation_dom(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n007.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 05:44:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 302157 completed with status 0
% 0.13/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.44 % No SInE strategy applied
% 0.13/0.44 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.13/0.44 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.13/0.44 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/0.44 % SubtermCWHack with pid 302164 completed with status 0
% 0.13/0.44 % Result found by SubtermCWHack
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.44 % No SInE strategy applied
% 0.13/0.44 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.13/0.44 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.44 % Preprocessing time : 0.001 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 31
% 0.13/0.44 % Removed by relevancy pruning/SinE : 0
% 0.13/0.44 % Initial clauses : 51
% 0.13/0.44 % Removed in clause preprocessing : 0
% 0.13/0.44 % Initial clauses in saturation : 51
% 0.13/0.44 % Processed clauses : 165
% 0.13/0.44 % ...of these trivial : 3
% 0.13/0.44 % ...subsumed : 55
% 0.13/0.44 % ...remaining for further processing : 107
% 0.13/0.44 % Other redundant clauses eliminated : 4
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 1
% 0.13/0.44 % Backward-rewritten : 4
% 0.13/0.44 % Generated clauses : 196
% 0.13/0.44 % ...of the previous two non-redundant : 154
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 1
% 0.13/0.44 % Paramodulations : 193
% 0.13/0.44 % Factorizations : 0
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 4
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 48
% 0.13/0.44 % ...of those cached : 32
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 99
% 0.13/0.44 % Positive orientable unit clauses : 24
% 0.13/0.44 % Positive unorientable unit clauses: 0
% 0.13/0.44 % Negative unit clauses : 10
% 0.13/0.44 % Non-unit-clauses : 65
% 0.13/0.44 % Current number of unprocessed clauses: 35
% 0.13/0.44 % ...number of literals in the above : 116
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 5
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 500
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 416
% 0.13/0.44 % Non-unit clause-clause subsumptions : 30
% 0.13/0.44 % Unit Clause-clause subsumption calls : 11
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 11
% 0.13/0.44 % BW rewrite match successes : 3
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 4593
% 0.13/0.44 % Search garbage collected termcells : 525
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.009 s
% 0.13/0.44 % System time : 0.002 s
% 0.13/0.44 % Total time : 0.011 s
% 0.13/0.44 % Maximum resident set size: 3656 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.026 s
% 0.13/0.44 % System time : 0.013 s
% 0.13/0.44 % Total time : 0.039 s
% 0.13/0.44 % Maximum resident set size: 4864 pages
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------