%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:13:06 PM UTC 2026
% Result : Unsatisfiable 4.80s 1.27s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 26 unt; 11 nHn; 41 RR)
% Number of literals : 104 ( 61 equ; 45 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(non_ordered_pair3,axiom,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(equal_ordered_pair,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pair) ).
cnf(non_ordered_pair1,axiom,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
cnf(d_little_set,hypothesis,
little_set(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_little_set) ).
cnf(prove_second_components_equal,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(left_cancellation,axiom,
( non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
cnf(first_components_are_equal,axiom,
( ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
cnf(c_little_set,hypothesis,
little_set(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_little_set) ).
cnf(a_little_set,hypothesis,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
cnf(b_little_set,hypothesis,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_little_set) ).
cnf(c_0_13,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair3]) ).
cnf(c_0_14,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_15,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_16,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_13 ).
cnf(c_0_17,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
equal_ordered_pair ).
cnf(c_0_18,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[non_ordered_pair1]) ).
cnf(c_0_20,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)) = non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_22,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_23,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_19 ).
cnf(c_0_24,hypothesis,
member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_25,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,b)
| non_ordered_pair(c,d) = non_ordered_pair(a,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,hypothesis,
little_set(d),
d_little_set ).
cnf(c_0_27,negated_conjecture,
b != d,
inference(fof_simplification,[status(thm)],[prove_second_components_equal]) ).
cnf(c_0_28,hypothesis,
( member(d,non_ordered_pair(a,b))
| non_ordered_pair(c,d) = non_ordered_pair(a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
b != d,
c_0_27 ).
cnf(c_0_30,hypothesis,
( d = a
| non_ordered_pair(c,d) = non_ordered_pair(a,a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_29]) ).
cnf(c_0_31,plain,
( non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[left_cancellation]) ).
cnf(c_0_32,hypothesis,
( ~ member(X1,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| X1 = non_ordered_pair(c,d)
| X1 = non_ordered_pair(c,c) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_33,hypothesis,
( member(d,non_ordered_pair(a,a))
| d = a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_30]),c_0_26])]) ).
cnf(c_0_34,plain,
( ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[first_components_are_equal]) ).
cnf(c_0_35,plain,
( non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
c_0_31 ).
cnf(c_0_36,hypothesis,
little_set(c),
c_little_set ).
cnf(c_0_37,hypothesis,
( non_ordered_pair(a,b) = non_ordered_pair(c,c)
| non_ordered_pair(c,d) = non_ordered_pair(a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_22])]) ).
cnf(c_0_38,hypothesis,
d = a,
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_39,plain,
( ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1)
| X1 = X2 ),
c_0_34 ).
cnf(c_0_40,hypothesis,
little_set(a),
a_little_set ).
cnf(c_0_41,hypothesis,
( ~ little_set(X1)
| non_ordered_pair(X2,X1) != non_ordered_pair(X2,c)
| X1 = c ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,hypothesis,
( non_ordered_pair(a,b) = non_ordered_pair(c,a)
| non_ordered_pair(a,b) = non_ordered_pair(c,c) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
little_set(b),
b_little_set ).
cnf(c_0_44,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_18]),c_0_18]) ).
cnf(c_0_45,hypothesis,
( ~ little_set(X1)
| non_ordered_pair(X2,X1) != non_ordered_pair(X2,a)
| X1 = a ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_46,hypothesis,
( non_ordered_pair(c,c) != non_ordered_pair(a,c)
| b = c
| non_ordered_pair(a,b) = non_ordered_pair(c,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_48,hypothesis,
( ~ little_set(X1)
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))
| X1 = c ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_36])]) ).
cnf(c_0_49,hypothesis,
( non_ordered_pair(c,c) != non_ordered_pair(a,c)
| non_ordered_pair(c,a) != non_ordered_pair(a,a)
| b = c ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]),c_0_47]) ).
cnf(c_0_50,hypothesis,
c = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_48]),c_0_40])]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:46:05 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.42 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
% 4.80/1.27 % Version: 3.5.1
% 4.80/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.80/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.80/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.80/1.27 % Starting new_bool_3 with 300s (1) cores
% 4.80/1.27 % Starting new_bool_1 with 300s (1) cores
% 4.80/1.27 % Starting sh5l with 300s (1) cores
% 4.80/1.27 % new_bool_3 with pid 585655 completed with status 9
% 4.80/1.27 % new_bool_1 with pid 585656 completed with status 9
% 4.80/1.27 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 585654 completed with status 0
% 4.80/1.27 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 4.80/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.80/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.80/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.80/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.80/1.27 % No SInE strategy applied
% 4.80/1.27 % Search class: FGHSF-FFLM31-MFFFFFNN
% 4.80/1.27 % partial match(1): FGHSM-FFLM31-MFFFFFNN
% 4.80/1.27 % Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 4.80/1.27 % Starting SubtermCWHack with 136s (1) cores
% 4.80/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 4.80/1.27 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 4.80/1.27 % Starting G-E--_208_B07_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 4.80/1.27 % Starting G-E--_200_B07_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 4.80/1.27 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 585663 completed with status 0
% 4.80/1.27 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 4.80/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.80/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.80/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.80/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.80/1.27 % No SInE strategy applied
% 4.80/1.27 % Search class: FGHSF-FFLM31-MFFFFFNN
% 4.80/1.27 % partial match(1): FGHSM-FFLM31-MFFFFFNN
% 4.80/1.27 % Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 4.80/1.27 % Starting SubtermCWHack with 136s (1) cores
% 4.80/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 4.80/1.27 % Preprocessing time : 0.002 s
% 4.80/1.27 % Presaturation interreduction done
% 4.80/1.27
% 4.80/1.27 % Proof found!
% 4.80/1.27 % SZS status Unsatisfiable
% 4.80/1.27 % SZS output start CNFRefutation
% See solution above
% 4.80/1.27 % Parsed axioms : 149
% 4.80/1.27 % Removed by relevancy pruning/SinE : 0
% 4.80/1.27 % Initial clauses : 149
% 4.80/1.27 % Removed in clause preprocessing : 6
% 4.80/1.27 % Initial clauses in saturation : 143
% 4.80/1.27 % Processed clauses : 4385
% 4.80/1.27 % ...of these trivial : 7
% 4.80/1.27 % ...subsumed : 2788
% 4.80/1.27 % ...remaining for further processing : 1590
% 4.80/1.27 % Other redundant clauses eliminated : 50
% 4.80/1.27 % Clauses deleted for lack of memory : 0
% 4.80/1.27 % Backward-subsumed : 46
% 4.80/1.27 % Backward-rewritten : 220
% 4.80/1.27 % Generated clauses : 57063
% 4.80/1.27 % ...of the previous two non-redundant : 55469
% 4.80/1.27 % ...aggressively subsumed : 0
% 4.80/1.27 % Contextual simplify-reflections : 56
% 4.80/1.27 % Paramodulations : 56955
% 4.80/1.27 % Factorizations : 24
% 4.80/1.27 % NegExts : 0
% 4.80/1.27 % Equation resolutions : 84
% 4.80/1.27 % Disequality decompositions : 0
% 4.80/1.27 % Total rewrite steps : 5769
% 4.80/1.27 % ...of those cached : 5428
% 4.80/1.27 % Propositional unsat checks : 0
% 4.80/1.27 % Propositional check models : 0
% 4.80/1.27 % Propositional check unsatisfiable : 0
% 4.80/1.27 % Propositional clauses : 0
% 4.80/1.27 % Propositional clauses after purity: 0
% 4.80/1.27 % Propositional unsat core size : 0
% 4.80/1.27 % Propositional preprocessing time : 0.000
% 4.80/1.27 % Propositional encoding time : 0.000
% 4.80/1.27 % Propositional solver time : 0.000
% 4.80/1.27 % Success case prop preproc time : 0.000
% 4.80/1.27 % Success case prop encoding time : 0.000
% 4.80/1.27 % Success case prop solver time : 0.000
% 4.80/1.27 % Current number of processed clauses : 1167
% 4.80/1.27 % Positive orientable unit clauses : 63
% 4.80/1.27 % Positive unorientable unit clauses: 0
% 4.80/1.27 % Negative unit clauses : 3
% 4.80/1.27 % Non-unit-clauses : 1101
% 4.80/1.27 % Current number of unprocessed clauses: 51147
% 4.80/1.27 % ...number of literals in the above : 143662
% 4.80/1.27 % Current number of archived formulas : 0
% 4.80/1.27 % Current number of archived clauses : 415
% 4.80/1.27 % Clause-clause subsumption calls (NU) : 170143
% 4.80/1.27 % Rec. Clause-clause subsumption calls : 105293
% 4.80/1.27 % Non-unit clause-clause subsumptions : 1323
% 4.80/1.27 % Unit Clause-clause subsumption calls : 3801
% 4.80/1.27 % Rewrite failures with RHS unbound : 0
% 4.80/1.27 % BW rewrite match attempts : 43
% 4.80/1.27 % BW rewrite match successes : 28
% 4.80/1.27 % Condensation attempts : 0
% 4.80/1.27 % Condensation successes : 0
% 4.80/1.27 % Termbank termtop insertions : 689380
% 4.80/1.27 % Search garbage collected termcells : 324
% 4.80/1.27
% 4.80/1.27 % -------------------------------------------------
% 4.80/1.27 % User time : 0.762 s
% 4.80/1.27 % System time : 0.044 s
% 4.80/1.27 % Total time : 0.806 s
% 4.80/1.27 % Maximum resident set size: 3768 pages
% 4.80/1.27
% 4.80/1.27 % -------------------------------------------------
% 4.80/1.27 % User time : 3.892 s
% 4.80/1.27 % System time : 0.241 s
% 4.80/1.27 % Total time : 4.133 s
% 4.80/1.27 % Maximum resident set size: 4608 pages
% 4.80/1.27 % E exiting
%------------------------------------------------------------------------------