%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:13:15 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 38 ( 8 equ; 22 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(two_sets_equal,axiom,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_sets_equal) ).
cnf(apply_for_composition2,axiom,
( ~ function(X1)
| subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition2) ).
cnf(apply_for_composition1,axiom,
( ~ member(X2,domain_of(X1))
| ~ function(X1)
| subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition1) ).
cnf(prove_apply_for_composition3,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
cnf(a_function,hypothesis,
function(a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_function) ).
cnf(member_of_domain,hypothesis,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
cnf(c_0_6,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[two_sets_equal]) ).
cnf(c_0_7,plain,
( ~ function(X1)
| subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3))) ),
inference(fof_simplification,[status(thm)],[apply_for_composition2]) ).
cnf(c_0_8,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
c_0_6 ).
cnf(c_0_9,plain,
( ~ function(X1)
| subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3))) ),
c_0_7 ).
cnf(c_0_10,plain,
( ~ member(X2,domain_of(X1))
| ~ function(X1)
| subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2)) ),
inference(fof_simplification,[status(thm)],[apply_for_composition1]) ).
cnf(c_0_11,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
inference(fof_simplification,[status(thm)],[prove_apply_for_composition3]) ).
cnf(c_0_12,plain,
( ~ subset(apply(X1,apply(X2,X3)),apply(compose(X1,X2),X3))
| ~ function(X2)
| apply(compose(X1,X2),X3) = apply(X1,apply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( ~ member(X2,domain_of(X1))
| ~ function(X1)
| subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2)) ),
c_0_10 ).
cnf(c_0_14,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
c_0_11 ).
cnf(c_0_15,plain,
( ~ member(X3,domain_of(X2))
| ~ function(X2)
| apply(compose(X1,X2),X3) = apply(X1,apply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
function(a_function),
a_function ).
cnf(c_0_17,hypothesis,
member(a,domain_of(a_function)),
member_of_domain ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:49:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % new_bool_3 with pid 2459679 completed with status 0
% 0.14/0.45 % Result found by new_bool_3
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.45 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.14/0.45 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.14/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % SubtermCWHack with pid 2459682 completed with status 0
% 0.14/0.45 % Result found by SubtermCWHack
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.45 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.14/0.45 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.14/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % Preprocessing time : 0.001 s
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 169
% 0.14/0.45 % Removed by relevancy pruning/SinE : 133
% 0.14/0.45 % Initial clauses : 36
% 0.14/0.45 % Removed in clause preprocessing : 0
% 0.14/0.45 % Initial clauses in saturation : 36
% 0.14/0.45 % Processed clauses : 100
% 0.14/0.45 % ...of these trivial : 7
% 0.14/0.45 % ...subsumed : 9
% 0.14/0.45 % ...remaining for further processing : 84
% 0.14/0.45 % Other redundant clauses eliminated : 9
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 0
% 0.14/0.45 % Backward-rewritten : 0
% 0.14/0.45 % Generated clauses : 175
% 0.14/0.45 % ...of the previous two non-redundant : 151
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 6
% 0.14/0.45 % Paramodulations : 164
% 0.14/0.45 % Factorizations : 0
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 11
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 16
% 0.14/0.45 % ...of those cached : 7
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 75
% 0.14/0.45 % Positive orientable unit clauses : 12
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 1
% 0.14/0.45 % Non-unit-clauses : 62
% 0.14/0.45 % Current number of unprocessed clauses: 76
% 0.14/0.45 % ...number of literals in the above : 248
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 0
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 630
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 305
% 0.14/0.45 % Non-unit clause-clause subsumptions : 15
% 0.14/0.45 % Unit Clause-clause subsumption calls : 5
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 21
% 0.14/0.45 % BW rewrite match successes : 0
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 5741
% 0.14/0.45 % Search garbage collected termcells : 716
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.005 s
% 0.14/0.45 % System time : 0.005 s
% 0.14/0.45 % Total time : 0.010 s
% 0.14/0.45 % Maximum resident set size: 3784 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.008 s
% 0.14/0.45 % System time : 0.010 s
% 0.14/0.45 % Total time : 0.019 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------