%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:13:05 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 30 unt; 5 nHn; 21 RR)
% Number of literals : 59 ( 35 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(unordered_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(singleton_member_of_ordered_pair,axiom,
member(singleton(X1),ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
cnf(prove_ordered_pair_determines_components1_1,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
cnf(prove_ordered_pair_determines_components1_2,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(only_member_in_singleton,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(prove_ordered_pair_determines_components1_3,negated_conjecture,
w != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
cnf(unordered_pairs_and_singletons,axiom,
unordered_pair(X1,X2) = union(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_15,axiom,
member(singleton(X1),ordered_pair(X1,X2)),
singleton_member_of_ordered_pair ).
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,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
prove_ordered_pair_determines_components1_1 ).
cnf(c_0_18,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_14 ).
cnf(c_0_19,negated_conjecture,
member(w,universal_class),
prove_ordered_pair_determines_components1_2 ).
cnf(c_0_20,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_21,plain,
member(unordered_pair(X1,X1),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_16]) ).
cnf(c_0_22,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_17,c_0_16]),c_0_16]) ).
cnf(c_0_23,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).
cnf(c_0_24,negated_conjecture,
member(w,unordered_pair(X1,w)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_26,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_20 ).
cnf(c_0_27,negated_conjecture,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
c_0_23 ).
cnf(c_0_29,negated_conjecture,
member(w,unordered_pair(w,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,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_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
w != y,
inference(fof_simplification,[status(thm)],[prove_ordered_pair_determines_components1_3]) ).
cnf(c_0_32,axiom,
unordered_pair(X1,X2) = union(singleton(X1),singleton(X2)),
unordered_pairs_and_singletons ).
cnf(c_0_33,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_34,plain,
( ~ member(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( member(w,unordered_pair(y,y))
| unordered_pair(y,y) = unordered_pair(w,w) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
w != y,
c_0_31 ).
cnf(c_0_37,plain,
unordered_pair(X1,X2) = complement(intersection(complement(unordered_pair(X1,X1)),complement(unordered_pair(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_13]),c_0_13]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
unordered_pair(y,y) = unordered_pair(w,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
unordered_pair(y,X1) = unordered_pair(w,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
unordered_pair(w,X1) = unordered_pair(X1,y),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,unordered_pair(w,w))
| X1 = y ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_36]),
[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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:45:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2452692 completed with status 0
% 0.14/0.46 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.46 % No SInE strategy applied
% 0.14/0.46 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46 % Starting new_bool_3 with 311s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 308s (1) cores
% 0.14/0.46 % Starting sh5l with 304s (1) cores
% 0.14/0.46 % new_bool_1 with pid 2452702 completed with status 0
% 0.14/0.46 % Result found by new_bool_1
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.46 % No SInE strategy applied
% 0.14/0.46 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46 % Starting new_bool_3 with 311s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 308s (1) cores
% 0.14/0.46 % Preprocessing time : 0.002 s
% 0.14/0.46 % Presaturation interreduction done
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 168
% 0.14/0.46 % Removed by relevancy pruning/SinE : 0
% 0.14/0.46 % Initial clauses : 168
% 0.14/0.46 % Removed in clause preprocessing : 15
% 0.14/0.46 % Initial clauses in saturation : 153
% 0.14/0.46 % Processed clauses : 515
% 0.14/0.46 % ...of these trivial : 9
% 0.14/0.46 % ...subsumed : 207
% 0.14/0.46 % ...remaining for further processing : 299
% 0.14/0.46 % Other redundant clauses eliminated : 10
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 1
% 0.14/0.46 % Backward-rewritten : 21
% 0.14/0.46 % Generated clauses : 850
% 0.14/0.46 % ...of the previous two non-redundant : 630
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 839
% 0.14/0.46 % Factorizations : 1
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 10
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 369
% 0.14/0.46 % ...of those cached : 260
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 133
% 0.14/0.46 % Positive orientable unit clauses : 40
% 0.14/0.46 % Positive unorientable unit clauses: 2
% 0.14/0.46 % Negative unit clauses : 23
% 0.14/0.46 % Non-unit-clauses : 68
% 0.14/0.46 % Current number of unprocessed clauses: 368
% 0.14/0.46 % ...number of literals in the above : 759
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 178
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 3583
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 2098
% 0.14/0.46 % Non-unit clause-clause subsumptions : 63
% 0.14/0.46 % Unit Clause-clause subsumption calls : 138
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 63
% 0.14/0.46 % BW rewrite match successes : 59
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 17884
% 0.14/0.46 % Search garbage collected termcells : 244
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.024 s
% 0.14/0.46 % System time : 0.005 s
% 0.14/0.46 % Total time : 0.029 s
% 0.14/0.46 % Maximum resident set size: 4016 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.106 s
% 0.14/0.46 % System time : 0.022 s
% 0.14/0.46 % Total time : 0.128 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------