%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 03:10:09 PM UTC 2026
% Result : ContradictoryAxioms 3.10s 16.34s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 45 ( 21 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 17 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 7 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_order__root,axiom,
! [X11,X4,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(c_Polynomial_Opoly(X5,X4),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> ( c_Polynomial_Oorder(X5,X11,X4) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact__C0_C,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
fof(fact_constant__def,axiom,
! [X2,X15,X5] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X5,X15,X2)
<=> ! [X3,X16] : hAPP(X2,X3) = hAPP(X2,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(c_0_4,plain,
! [X11,X4,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(c_Polynomial_Opoly(X5,X4),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> ( c_Polynomial_Oorder(X5,X11,X4) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_order__root]) ).
fof(c_0_5,plain,
! [X325,X326,X327] :
( ( ~ class_Rings_Oidom(X327)
| hAPP(c_Polynomial_Opoly(X327,X326),X325) = c_Groups_Ozero__class_Ozero(X327)
| c_Polynomial_Oorder(X327,X325,X326) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ class_Rings_Oidom(X327)
| hAPP(c_Polynomial_Opoly(X327,X326),X325) = c_Groups_Ozero__class_Ozero(X327)
| X326 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X327)) )
& ( ~ class_Rings_Oidom(X327)
| c_Polynomial_Oorder(X327,X325,X326) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X326 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X327))
| hAPP(c_Polynomial_Opoly(X327,X326),X325) != c_Groups_Ozero__class_Ozero(X327) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(fof_simplification,[status(thm)],[fact__C0_C]) ).
cnf(c_0_7,plain,
( ~ class_Rings_Oidom(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_9,plain,
! [X156,X157,X158,X159,X160,X161,X164,X165] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X165,X164,X161)
| hAPP(X161,esk2_1(X161)) != hAPP(X161,esk3_1(X161)) )
& ( hAPP(X156,X159) = hAPP(X156,X160)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X158,X157,X156) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_constant__def])])])])])]) ).
cnf(c_0_10,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_12,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( hAPP(X1,esk2_1(X1)) != hAPP(X1,esk3_1(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11])]) ).
cnf(c_0_16,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14])]) ).
cnf(c_0_17,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.60 % CPULimit : 300
% 0.09/15.60 % WCLimit : 300
% 0.09/15.60 % DateTime : Mon Sep 21 09:43:23 UTC 2026
% 0.09/15.61 % CPUTime :
% 0.09/15.61 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/15.65 Running first-order theorem proving
% 0.09/15.66 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
% 3.10/16.34 % Version: 3.5.1
% 3.10/16.34 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.10/16.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.10/16.34 % Starting new_bool_3 with 300s (1) cores
% 3.10/16.34 % Starting new_bool_1 with 300s (1) cores
% 3.10/16.34 % Starting sh5l with 300s (1) cores
% 3.10/16.34 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3761807 completed with status 0
% 3.10/16.34 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.10/16.34 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.10/16.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.10/16.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.10/16.34 % No SInE strategy applied
% 3.10/16.34 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.10/16.34 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.10/16.34 % Starting SubtermCWHack with 136s (1) cores
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 3.10/16.34 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 3.10/16.34 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 3761814 completed with status 0
% 3.10/16.34 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 3.10/16.34 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.10/16.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.10/16.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.10/16.34 % No SInE strategy applied
% 3.10/16.34 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.10/16.34 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.10/16.34 % Starting SubtermCWHack with 136s (1) cores
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.10/16.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 3.10/16.34 % Preprocessing time : 0.044 s
% 3.10/16.34 % Presaturation interreduction done
% 3.10/16.34
% 3.10/16.34 % Proof found!
% 3.10/16.34 % SZS status ContradictoryAxioms
% 3.10/16.34 % SZS output start CNFRefutation
% See solution above
% 3.10/16.34 % Parsed axioms : 1199
% 3.10/16.34 % Removed by relevancy pruning/SinE : 0
% 3.10/16.34 % Initial clauses : 1592
% 3.10/16.34 % Removed in clause preprocessing : 85
% 3.10/16.34 % Initial clauses in saturation : 1507
% 3.10/16.34 % Processed clauses : 2603
% 3.10/16.34 % ...of these trivial : 25
% 3.10/16.34 % ...subsumed : 439
% 3.10/16.34 % ...remaining for further processing : 2139
% 3.10/16.34 % Other redundant clauses eliminated : 210
% 3.10/16.34 % Clauses deleted for lack of memory : 0
% 3.10/16.34 % Backward-subsumed : 5
% 3.10/16.34 % Backward-rewritten : 16
% 3.10/16.34 % Generated clauses : 2254
% 3.10/16.34 % ...of the previous two non-redundant : 1779
% 3.10/16.34 % ...aggressively subsumed : 0
% 3.10/16.34 % Contextual simplify-reflections : 1
% 3.10/16.34 % Paramodulations : 2061
% 3.10/16.34 % Factorizations : 0
% 3.10/16.34 % NegExts : 0
% 3.10/16.34 % Equation resolutions : 226
% 3.10/16.34 % Disequality decompositions : 0
% 3.10/16.34 % Total rewrite steps : 1340
% 3.10/16.34 % ...of those cached : 907
% 3.10/16.34 % Propositional unsat checks : 0
% 3.10/16.34 % Propositional check models : 0
% 3.10/16.34 % Propositional check unsatisfiable : 0
% 3.10/16.34 % Propositional clauses : 0
% 3.10/16.34 % Propositional clauses after purity: 0
% 3.10/16.34 % Propositional unsat core size : 0
% 3.10/16.34 % Propositional preprocessing time : 0.000
% 3.10/16.34 % Propositional encoding time : 0.000
% 3.10/16.34 % Propositional solver time : 0.000
% 3.10/16.34 % Success case prop preproc time : 0.000
% 3.10/16.34 % Success case prop encoding time : 0.000
% 3.10/16.34 % Success case prop solver time : 0.000
% 3.10/16.34 % Current number of processed clauses : 721
% 3.10/16.34 % Positive orientable unit clauses : 285
% 3.10/16.34 % Positive unorientable unit clauses: 0
% 3.10/16.34 % Negative unit clauses : 38
% 3.10/16.34 % Non-unit-clauses : 398
% 3.10/16.34 % Current number of unprocessed clauses: 1917
% 3.10/16.34 % ...number of literals in the above : 4237
% 3.10/16.34 % Current number of archived formulas : 0
% 3.10/16.34 % Current number of archived clauses : 1262
% 3.10/16.34 % Clause-clause subsumption calls (NU) : 173119
% 3.10/16.34 % Rec. Clause-clause subsumption calls : 100212
% 3.10/16.34 % Non-unit clause-clause subsumptions : 283
% 3.10/16.34 % Unit Clause-clause subsumption calls : 425
% 3.10/16.34 % Rewrite failures with RHS unbound : 11
% 3.10/16.34 % BW rewrite match attempts : 1209
% 3.10/16.34 % BW rewrite match successes : 75
% 3.10/16.34 % Condensation attempts : 0
% 3.10/16.34 % Condensation successes : 0
% 3.10/16.34 % Termbank termtop insertions : 217041
% 3.10/16.34 % Search garbage collected termcells : 19984
% 3.10/16.34
% 3.10/16.34 % -------------------------------------------------
% 3.10/16.34 % User time : 0.522 s
% 3.10/16.34 % System time : 0.033 s
% 3.10/16.34 % Total time : 0.555 s
% 3.10/16.34 % Maximum resident set size: 10780 pages
% 3.10/16.34
% 3.10/16.34 % -------------------------------------------------
% 3.10/16.34 % User time : 1.880 s
% 3.10/16.34 % System time : 0.138 s
% 3.10/16.34 % Total time : 2.018 s
% 3.10/16.34 % Maximum resident set size: 6144 pages
% 3.10/16.34 % E exiting
%------------------------------------------------------------------------------