%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET038-3 : 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 : 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 02:13:14 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.66s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 52 ( 12 unt; 0 nHn; 49 RR)
% Number of literals : 126 ( 16 equ; 78 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maps3,axiom,
( ~ maps(X1,X2,X3)
| subset(range_of(X1),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps3) ).
cnf(subset1,axiom,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(a_mapping,hypothesis,
maps(a_function,a_domain,a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_mapping) ).
cnf(range_of4,axiom,
( X1 != second(X3)
| ~ member(X3,X2)
| ~ ordered_pair_predicate(X3)
| ~ little_set(X1)
| member(X1,range_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',range_of4) ).
cnf(second_component_is_small,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_component_is_small) ).
cnf(ordered_pair_predicate4,axiom,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
cnf(property_of_second,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_second) ).
cnf(apply_for_functions2,axiom,
( apply(X1,X2) != X3
| ~ member(X2,domain_of(X1))
| ~ function(X1)
| member(ordered_pair(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_functions2) ).
cnf(maps1,axiom,
( ~ maps(X1,X2,X3)
| function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps1) ).
cnf(maps2,axiom,
( ~ maps(X1,X2,X3)
| domain_of(X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps2) ).
cnf(a2,axiom,
( ~ member(X1,X2)
| little_set(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(prove_mapping_in_range,negated_conjecture,
~ member(apply(a_function,a),a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mapping_in_range) ).
cnf(member_of_domain,hypothesis,
member(a,a_domain),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
cnf(function_values_are_small,axiom,
( ~ function(X1)
| little_set(apply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_values_are_small) ).
cnf(c_0_14,plain,
( ~ maps(X1,X2,X3)
| subset(range_of(X1),X3) ),
inference(fof_simplification,[status(thm)],[maps3]) ).
cnf(c_0_15,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subset1]) ).
cnf(c_0_16,plain,
( ~ maps(X1,X2,X3)
| subset(range_of(X1),X3) ),
c_0_14 ).
cnf(c_0_17,hypothesis,
maps(a_function,a_domain,a_range),
a_mapping ).
cnf(c_0_18,plain,
( X1 != second(X3)
| ~ member(X3,X2)
| ~ ordered_pair_predicate(X3)
| ~ little_set(X1)
| member(X1,range_of(X2)) ),
inference(fof_simplification,[status(thm)],[range_of4]) ).
cnf(c_0_19,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(fof_simplification,[status(thm)],[second_component_is_small]) ).
cnf(c_0_20,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
c_0_15 ).
cnf(c_0_21,hypothesis,
subset(range_of(a_function),a_range),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( X1 != second(X3)
| ~ member(X3,X2)
| ~ ordered_pair_predicate(X3)
| ~ little_set(X1)
| member(X1,range_of(X2)) ),
c_0_18 ).
cnf(c_0_23,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
c_0_19 ).
cnf(c_0_24,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate4]) ).
cnf(c_0_25,hypothesis,
( ~ member(X1,range_of(a_function))
| member(X1,a_range) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| ~ ordered_pair_predicate(X1)
| member(second(X1),range_of(X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[property_of_second]) ).
cnf(c_0_28,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
c_0_24 ).
cnf(c_0_29,plain,
( apply(X1,X2) != X3
| ~ member(X2,domain_of(X1))
| ~ function(X1)
| member(ordered_pair(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[apply_for_functions2]) ).
cnf(c_0_30,plain,
( ~ maps(X1,X2,X3)
| function(X1) ),
inference(fof_simplification,[status(thm)],[maps1]) ).
cnf(c_0_31,plain,
( ~ maps(X1,X2,X3)
| domain_of(X1) = X2 ),
inference(fof_simplification,[status(thm)],[maps2]) ).
cnf(c_0_32,hypothesis,
( ~ member(X1,a_function)
| ~ ordered_pair_predicate(X1)
| member(second(X1),a_range) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
c_0_27 ).
cnf(c_0_34,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair_predicate(ordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( apply(X1,X2) != X3
| ~ member(X2,domain_of(X1))
| ~ function(X1)
| member(ordered_pair(X2,X3),X1) ),
c_0_29 ).
cnf(c_0_36,plain,
( ~ maps(X1,X2,X3)
| function(X1) ),
c_0_30 ).
cnf(c_0_37,plain,
( ~ maps(X1,X2,X3)
| domain_of(X1) = X2 ),
c_0_31 ).
cnf(c_0_38,plain,
( ~ member(X1,X2)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[a2]) ).
cnf(c_0_39,negated_conjecture,
~ member(apply(a_function,a),a_range),
inference(fof_simplification,[status(thm)],[prove_mapping_in_range]) ).
cnf(c_0_40,hypothesis,
( ~ member(ordered_pair(X2,X1),a_function)
| ~ little_set(X2)
| ~ little_set(X1)
| member(X1,a_range) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( ~ member(X1,domain_of(X2))
| ~ function(X2)
| member(ordered_pair(X1,apply(X2,X1)),X2) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_42,hypothesis,
function(a_function),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_43,hypothesis,
domain_of(a_function) = a_domain,
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_44,plain,
( ~ member(X1,X2)
| little_set(X1) ),
c_0_38 ).
cnf(c_0_45,negated_conjecture,
~ member(apply(a_function,a),a_range),
c_0_39 ).
cnf(c_0_46,hypothesis,
( ~ member(X1,a_domain)
| ~ little_set(apply(a_function,X1))
| member(apply(a_function,X1),a_range) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_47,hypothesis,
member(a,a_domain),
member_of_domain ).
cnf(c_0_48,plain,
( ~ function(X1)
| little_set(apply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[function_values_are_small]) ).
cnf(c_0_49,negated_conjecture,
~ little_set(apply(a_function,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_50,plain,
( ~ function(X1)
| little_set(apply(X1,X2)) ),
c_0_48 ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.58 % Computer : n007.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Mon Sep 21 04:44:21 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.62 Running first-order theorem proving
% 0.09/0.62 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
% 0.14/0.66 % Version: 3.5.1
% 0.14/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.66 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.66 % Starting sh5l with 300s (1) cores
% 0.14/0.66 % new_bool_3 with pid 200499 completed with status 0
% 0.14/0.66 % Result found by new_bool_3
% 0.14/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.66 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.14/0.66 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.14/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.66 % SubtermCWHack with pid 200506 completed with status 0
% 0.14/0.66 % Result found by SubtermCWHack
% 0.14/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.66 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.14/0.66 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.14/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.66 % Preprocessing time : 0.002 s
% 0.14/0.66
% 0.14/0.66 % Proof found!
% 0.14/0.66 % SZS status Unsatisfiable
% 0.14/0.66 % SZS output start CNFRefutation
% See solution above
% 0.14/0.66 % Parsed axioms : 166
% 0.14/0.66 % Removed by relevancy pruning/SinE : 133
% 0.14/0.66 % Initial clauses : 33
% 0.14/0.66 % Removed in clause preprocessing : 0
% 0.14/0.66 % Initial clauses in saturation : 33
% 0.14/0.66 % Processed clauses : 112
% 0.14/0.66 % ...of these trivial : 7
% 0.14/0.66 % ...subsumed : 9
% 0.14/0.66 % ...remaining for further processing : 96
% 0.14/0.66 % Other redundant clauses eliminated : 9
% 0.14/0.66 % Clauses deleted for lack of memory : 0
% 0.14/0.66 % Backward-subsumed : 0
% 0.14/0.66 % Backward-rewritten : 0
% 0.14/0.66 % Generated clauses : 166
% 0.14/0.66 % ...of the previous two non-redundant : 141
% 0.14/0.66 % ...aggressively subsumed : 0
% 0.14/0.66 % Contextual simplify-reflections : 5
% 0.14/0.66 % Paramodulations : 155
% 0.14/0.66 % Factorizations : 0
% 0.14/0.66 % NegExts : 0
% 0.14/0.66 % Equation resolutions : 11
% 0.14/0.66 % Disequality decompositions : 0
% 0.14/0.66 % Total rewrite steps : 29
% 0.14/0.66 % ...of those cached : 14
% 0.14/0.66 % Propositional unsat checks : 0
% 0.14/0.66 % Propositional check models : 0
% 0.14/0.66 % Propositional check unsatisfiable : 0
% 0.14/0.66 % Propositional clauses : 0
% 0.14/0.66 % Propositional clauses after purity: 0
% 0.14/0.66 % Propositional unsat core size : 0
% 0.14/0.66 % Propositional preprocessing time : 0.000
% 0.14/0.66 % Propositional encoding time : 0.000
% 0.14/0.66 % Propositional solver time : 0.000
% 0.14/0.66 % Success case prop preproc time : 0.000
% 0.14/0.66 % Success case prop encoding time : 0.000
% 0.14/0.66 % Success case prop solver time : 0.000
% 0.14/0.66 % Current number of processed clauses : 87
% 0.14/0.66 % Positive orientable unit clauses : 18
% 0.14/0.66 % Positive unorientable unit clauses: 0
% 0.14/0.66 % Negative unit clauses : 2
% 0.14/0.66 % Non-unit-clauses : 67
% 0.14/0.66 % Current number of unprocessed clauses: 62
% 0.14/0.66 % ...number of literals in the above : 170
% 0.14/0.66 % Current number of archived formulas : 0
% 0.14/0.66 % Current number of archived clauses : 0
% 0.14/0.66 % Clause-clause subsumption calls (NU) : 1032
% 0.14/0.66 % Rec. Clause-clause subsumption calls : 483
% 0.14/0.66 % Non-unit clause-clause subsumptions : 14
% 0.14/0.66 % Unit Clause-clause subsumption calls : 15
% 0.14/0.66 % Rewrite failures with RHS unbound : 0
% 0.14/0.66 % BW rewrite match attempts : 25
% 0.14/0.66 % BW rewrite match successes : 0
% 0.14/0.66 % Condensation attempts : 0
% 0.14/0.66 % Condensation successes : 0
% 0.14/0.66 % Termbank termtop insertions : 5186
% 0.14/0.66 % Search garbage collected termcells : 711
% 0.14/0.66
% 0.14/0.66 % -------------------------------------------------
% 0.14/0.66 % User time : 0.010 s
% 0.14/0.66 % System time : 0.004 s
% 0.14/0.66 % Total time : 0.014 s
% 0.14/0.66 % Maximum resident set size: 3780 pages
% 0.14/0.66
% 0.14/0.66 % -------------------------------------------------
% 0.14/0.66 % User time : 0.016 s
% 0.14/0.66 % System time : 0.007 s
% 0.14/0.66 % Total time : 0.023 s
% 0.14/0.66 % Maximum resident set size: 4608 pages
% 0.14/0.66 % E exiting
%------------------------------------------------------------------------------