%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:16:03 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.48s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 24 unt; 8 nHn; 29 RR)
% Number of literals : 63 ( 32 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_ordered_pair_determines_components1_1,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
cnf(only_member_in_singleton,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(corollary_to_unordered_pair_axiom2,axiom,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
cnf(prove_ordered_pair_determines_components1_2,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
cnf(prove_ordered_pair_determines_components1_3,negated_conjecture,
w != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
cnf(singleton_is_null_class,axiom,
( singleton(X1) = null_class
| member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(c_0_12,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_13,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_14,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_15,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
prove_ordered_pair_determines_components1_1 ).
cnf(c_0_16,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_18,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_14 ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_21,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).
cnf(c_0_22,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_17 ).
cnf(c_0_23,negated_conjecture,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
inference(fof_simplification,[status(thm)],[corollary_to_unordered_pair_axiom2]) ).
cnf(c_0_25,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
c_0_21 ).
cnf(c_0_26,negated_conjecture,
( unordered_pair(y,y) = unordered_pair(w,w)
| unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
member(w,universal_class),
prove_ordered_pair_determines_components1_2 ).
cnf(c_0_28,negated_conjecture,
w != y,
inference(fof_simplification,[status(thm)],[prove_ordered_pair_determines_components1_3]) ).
cnf(c_0_29,axiom,
( singleton(X1) = null_class
| member(X1,universal_class) ),
singleton_is_null_class ).
cnf(c_0_30,plain,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
c_0_24 ).
cnf(c_0_31,plain,
~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[existence_of_null_class]) ).
cnf(c_0_32,plain,
( ~ member(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_33,negated_conjecture,
( member(w,unordered_pair(y,y))
| unordered_pair(y,y) = unordered_pair(w,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_26]),c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
w != y,
c_0_28 ).
cnf(c_0_35,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(rw,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_36,negated_conjecture,
unordered_pair(X1,w) != null_class,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_37,plain,
~ member(X1,null_class),
c_0_31 ).
cnf(c_0_38,negated_conjecture,
unordered_pair(y,y) = unordered_pair(w,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
member(y,universal_class),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
member(y,unordered_pair(w,w)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_38]),c_0_39])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.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 04:47:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.31/0.48 % Version: 3.5.1
% 0.31/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.31/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.31/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.31/0.48 % Starting sh5l with 300s (1) cores
% 0.31/0.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1582512 completed with status 0
% 0.31/0.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.31/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.31/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.48 % No SInE strategy applied
% 0.31/0.48 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.31/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.31/0.48 % Starting new_bool_3 with 311s (1) cores
% 0.31/0.48 % Starting new_bool_1 with 308s (1) cores
% 0.31/0.48 % Starting sh5l with 304s (1) cores
% 0.31/0.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1582520 completed with status 0
% 0.31/0.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.31/0.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.31/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.48 % No SInE strategy applied
% 0.31/0.48 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.31/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.31/0.48 % Preprocessing time : 0.006 s
% 0.31/0.48 % Presaturation interreduction done
% 0.31/0.48
% 0.31/0.48 % Proof found!
% 0.31/0.48 % SZS status Unsatisfiable
% 0.31/0.48 % SZS output start CNFRefutation
% See solution above
% 0.31/0.48 % Parsed axioms : 168
% 0.31/0.48 % Removed by relevancy pruning/SinE : 0
% 0.31/0.48 % Initial clauses : 168
% 0.31/0.48 % Removed in clause preprocessing : 15
% 0.31/0.48 % Initial clauses in saturation : 153
% 0.31/0.48 % Processed clauses : 244
% 0.31/0.48 % ...of these trivial : 2
% 0.31/0.48 % ...subsumed : 21
% 0.31/0.48 % ...remaining for further processing : 221
% 0.31/0.48 % Other redundant clauses eliminated : 4
% 0.31/0.48 % Clauses deleted for lack of memory : 0
% 0.31/0.48 % Backward-subsumed : 1
% 0.31/0.48 % Backward-rewritten : 4
% 0.31/0.48 % Generated clauses : 233
% 0.31/0.48 % ...of the previous two non-redundant : 165
% 0.31/0.48 % ...aggressively subsumed : 0
% 0.31/0.48 % Contextual simplify-reflections : 0
% 0.31/0.48 % Paramodulations : 229
% 0.31/0.48 % Factorizations : 0
% 0.31/0.48 % NegExts : 0
% 0.31/0.48 % Equation resolutions : 4
% 0.31/0.48 % Disequality decompositions : 0
% 0.31/0.48 % Total rewrite steps : 74
% 0.31/0.48 % ...of those cached : 49
% 0.31/0.48 % Propositional unsat checks : 0
% 0.31/0.48 % Propositional check models : 0
% 0.31/0.48 % Propositional check unsatisfiable : 0
% 0.31/0.48 % Propositional clauses : 0
% 0.31/0.48 % Propositional clauses after purity: 0
% 0.31/0.48 % Propositional unsat core size : 0
% 0.31/0.48 % Propositional preprocessing time : 0.000
% 0.31/0.48 % Propositional encoding time : 0.000
% 0.31/0.48 % Propositional solver time : 0.000
% 0.31/0.48 % Success case prop preproc time : 0.000
% 0.31/0.48 % Success case prop encoding time : 0.000
% 0.31/0.48 % Success case prop solver time : 0.000
% 0.31/0.48 % Current number of processed clauses : 72
% 0.31/0.48 % Positive orientable unit clauses : 21
% 0.31/0.48 % Positive unorientable unit clauses: 1
% 0.31/0.48 % Negative unit clauses : 9
% 0.31/0.48 % Non-unit-clauses : 41
% 0.31/0.48 % Current number of unprocessed clauses: 214
% 0.31/0.48 % ...number of literals in the above : 472
% 0.31/0.48 % Current number of archived formulas : 0
% 0.31/0.48 % Current number of archived clauses : 161
% 0.31/0.48 % Clause-clause subsumption calls (NU) : 2610
% 0.31/0.48 % Rec. Clause-clause subsumption calls : 1412
% 0.31/0.48 % Non-unit clause-clause subsumptions : 10
% 0.31/0.48 % Unit Clause-clause subsumption calls : 31
% 0.31/0.48 % Rewrite failures with RHS unbound : 0
% 0.31/0.48 % BW rewrite match attempts : 46
% 0.31/0.48 % BW rewrite match successes : 44
% 0.31/0.48 % Condensation attempts : 0
% 0.31/0.48 % Condensation successes : 0
% 0.31/0.48 % Termbank termtop insertions : 11206
% 0.31/0.48 % Search garbage collected termcells : 244
% 0.31/0.48
% 0.31/0.48 % -------------------------------------------------
% 0.31/0.48 % User time : 0.034 s
% 0.31/0.48 % System time : 0.006 s
% 0.31/0.48 % Total time : 0.040 s
% 0.31/0.48 % Maximum resident set size: 3760 pages
% 0.31/0.48
% 0.31/0.48 % -------------------------------------------------
% 0.31/0.48 % User time : 0.137 s
% 0.31/0.48 % System time : 0.017 s
% 0.31/0.48 % Total time : 0.154 s
% 0.31/0.48 % Maximum resident set size: 4864 pages
% 0.31/0.48 % E exiting
%------------------------------------------------------------------------------