%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW278+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 03:10:13 PM UTC 2026
% Result : Theorem 5.98s 1.72s
% Output : CNFRefutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 28 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 20 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X15,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(conj_0,conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_poly__mult,axiom,
! [X4,X11,X12,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X12),X11)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Polynomial_Opoly(X5,X12),X4)),hAPP(c_Polynomial_Opoly(X5,X11),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_h,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_s,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
fof(c_0_7,plain,
! [X853,X854] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X854),X853),c_Groups_Ozero__class_Ozero(X854)) = c_Groups_Ozero__class_Ozero(X854)
| ~ class_Rings_Ocomm__semiring__1(X854) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])]) ).
fof(c_0_8,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_9,plain,
! [X855,X856,X857,X858] :
( hAPP(c_Polynomial_Opoly(X858,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X858)),X857),X856)),X855) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X858),hAPP(c_Polynomial_Opoly(X858,X857),X855)),hAPP(c_Polynomial_Opoly(X858,X856),X855))
| ~ class_Rings_Ocomm__semiring__0(X858) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])])]) ).
cnf(c_0_10,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_12,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_h]) ).
cnf(c_0_15,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_17,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),v_s____)),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(split_conjunct,[status(thm)],[fact_s]) ).
cnf(c_0_20,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW278+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:44:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 5.98/1.72 % Version: 3.5.1
% 5.98/1.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.98/1.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.98/1.72 % Starting new_bool_3 with 300s (1) cores
% 5.98/1.72 % Starting new_bool_1 with 300s (1) cores
% 5.98/1.72 % Starting sh5l with 300s (1) cores
% 5.98/1.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 477119 completed with status 0
% 5.98/1.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.98/1.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.98/1.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.98/1.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.98/1.72 % No SInE strategy applied
% 5.98/1.72 % Search class: FGHSM-SSLM32-DFFFFFNN
% 5.98/1.72 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 5.98/1.72 % Starting SubtermCWHack with 136s (1) cores
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 5.98/1.72 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 5.98/1.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 477158 completed with status 0
% 5.98/1.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.98/1.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.98/1.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.98/1.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.98/1.72 % No SInE strategy applied
% 5.98/1.72 % Search class: FGHSM-SSLM32-DFFFFFNN
% 5.98/1.72 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 5.98/1.72 % Starting SubtermCWHack with 136s (1) cores
% 5.98/1.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.98/1.72 % Preprocessing time : 0.029 s
% 5.98/1.72 % Presaturation interreduction done
% 5.98/1.72
% 5.98/1.72 % Proof found!
% 5.98/1.72 % SZS status Theorem
% 5.98/1.72 % SZS output start CNFRefutation
% See solution above
% 5.98/1.72 % Parsed axioms : 1200
% 5.98/1.72 % Removed by relevancy pruning/SinE : 0
% 5.98/1.72 % Initial clauses : 1582
% 5.98/1.72 % Removed in clause preprocessing : 78
% 5.98/1.72 % Initial clauses in saturation : 1504
% 5.98/1.72 % Processed clauses : 5634
% 5.98/1.72 % ...of these trivial : 246
% 5.98/1.72 % ...subsumed : 2228
% 5.98/1.72 % ...remaining for further processing : 3160
% 5.98/1.72 % Other redundant clauses eliminated : 605
% 5.98/1.72 % Clauses deleted for lack of memory : 0
% 5.98/1.72 % Backward-subsumed : 12
% 5.98/1.72 % Backward-rewritten : 21
% 5.98/1.72 % Generated clauses : 37507
% 5.98/1.72 % ...of the previous two non-redundant : 32031
% 5.98/1.72 % ...aggressively subsumed : 0
% 5.98/1.72 % Contextual simplify-reflections : 3
% 5.98/1.72 % Paramodulations : 36886
% 5.98/1.72 % Factorizations : 8
% 5.98/1.72 % NegExts : 0
% 5.98/1.72 % Equation resolutions : 641
% 5.98/1.72 % Disequality decompositions : 0
% 5.98/1.72 % Total rewrite steps : 26587
% 5.98/1.72 % ...of those cached : 24413
% 5.98/1.72 % Propositional unsat checks : 0
% 5.98/1.72 % Propositional check models : 0
% 5.98/1.72 % Propositional check unsatisfiable : 0
% 5.98/1.72 % Propositional clauses : 0
% 5.98/1.72 % Propositional clauses after purity: 0
% 5.98/1.72 % Propositional unsat core size : 0
% 5.98/1.72 % Propositional preprocessing time : 0.000
% 5.98/1.72 % Propositional encoding time : 0.000
% 5.98/1.72 % Propositional solver time : 0.000
% 5.98/1.72 % Success case prop preproc time : 0.000
% 5.98/1.72 % Success case prop encoding time : 0.000
% 5.98/1.72 % Success case prop solver time : 0.000
% 5.98/1.72 % Current number of processed clauses : 1776
% 5.98/1.72 % Positive orientable unit clauses : 349
% 5.98/1.72 % Positive unorientable unit clauses: 10
% 5.98/1.72 % Negative unit clauses : 74
% 5.98/1.72 % Non-unit-clauses : 1343
% 5.98/1.72 % Current number of unprocessed clauses: 29083
% 5.98/1.72 % ...number of literals in the above : 86333
% 5.98/1.72 % Current number of archived formulas : 0
% 5.98/1.72 % Current number of archived clauses : 1244
% 5.98/1.72 % Clause-clause subsumption calls (NU) : 431806
% 5.98/1.72 % Rec. Clause-clause subsumption calls : 266715
% 5.98/1.72 % Non-unit clause-clause subsumptions : 1326
% 5.98/1.72 % Unit Clause-clause subsumption calls : 3982
% 5.98/1.72 % Rewrite failures with RHS unbound : 0
% 5.98/1.72 % BW rewrite match attempts : 1834
% 5.98/1.72 % BW rewrite match successes : 217
% 5.98/1.72 % Condensation attempts : 0
% 5.98/1.72 % Condensation successes : 0
% 5.98/1.72 % Termbank termtop insertions : 948914
% 5.98/1.72 % Search garbage collected termcells : 20360
% 5.98/1.72
% 5.98/1.72 % -------------------------------------------------
% 5.98/1.72 % User time : 1.118 s
% 5.98/1.72 % System time : 0.060 s
% 5.98/1.72 % Total time : 1.178 s
% 5.98/1.72 % Maximum resident set size: 9840 pages
% 5.98/1.72
% 5.98/1.72 % -------------------------------------------------
% 5.98/1.72 % User time : 4.189 s
% 5.98/1.72 % System time : 0.214 s
% 5.98/1.72 % Total time : 4.402 s
% 5.98/1.72 % Maximum resident set size: 5888 pages
% 5.98/1.72 % E exiting
%------------------------------------------------------------------------------