%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG385-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:56:01 AM UTC 2026
% Result : Unsatisfiable 9.44s 1.99s
% Output : CNFRefutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 36 ( 21 unt; 0 nHn; 20 RR)
% Number of literals : 54 ( 24 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 54 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_smult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
cnf(cls_add__poly__code_I2_J_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_synthetic__div__unique_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X5 = c_Polynomial_Opoly(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
cnf(cls_cs0_0,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cs0_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_CHAINED_0_01,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_0_12,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(fof_simplification,[status(thm)],[cls_smult__eq__0__iff_2]) ).
cnf(c_0_13,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_add__poly__code_I2_J_0]) ).
cnf(c_0_14,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__c_0]) ).
cnf(c_0_15,plain,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X5 = c_Polynomial_Opoly(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_synthetic__div__unique_0]) ).
cnf(c_0_16,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_12 ).
cnf(c_0_17,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_cs0_0 ).
cnf(c_0_18,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_19,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
c_0_13 ).
cnf(c_0_20,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_21,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
c_0_14 ).
cnf(c_0_22,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_23,negated_conjecture,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_24,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_poly__pCons_0]) ).
cnf(c_0_25,plain,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X5 = c_Polynomial_Opoly(X2,X3,X1) ),
c_0_15 ).
cnf(c_0_26,plain,
c_Polynomial_Osmult(X1,v_cs____,tc_Complex_Ocomplex) = v_cs____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_27,plain,
c_HOL_Oplus__class_Oplus(X1,v_cs____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
cnf(c_0_28,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_29,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_CHAINED_0_01 ).
cnf(c_0_30,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
c_0_23 ).
cnf(c_0_32,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
c_0_24 ).
cnf(c_0_33,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_cs____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])])]) ).
cnf(c_0_34,plain,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_30]),c_0_34]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG385-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n009.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 13:18:28 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.52 Running first-order theorem proving
% 0.20/0.52 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
% 9.44/1.99 % Version: 3.5.1
% 9.44/1.99 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.44/1.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.99 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.44/1.99 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.99 % Starting new_bool_1 with 300s (1) cores
% 9.44/1.99 % Starting sh5l with 300s (1) cores
% 9.44/1.99 % sh5l with pid 1846362 completed with status 0
% 9.44/1.99 % Result found by sh5l
% 9.44/1.99 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.44/1.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.99 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.44/1.99 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.99 % Starting new_bool_1 with 300s (1) cores
% 9.44/1.99 % Starting sh5l with 300s (1) cores
% 9.44/1.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 9.44/1.99 % SinE strategy is gf500_gu_R04_F100_L20000
% 9.44/1.99 % Search class: FGHSM-FSLM32-MFFFFFNN
% 9.44/1.99 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 9.44/1.99 % Starting SubtermCWHack with 28s (1) cores
% 9.44/1.99 % SubtermCWHack with pid 1846364 completed with status 0
% 9.44/1.99 % Result found by SubtermCWHack
% 9.44/1.99 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.44/1.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.99 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.44/1.99 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.99 % Starting new_bool_1 with 300s (1) cores
% 9.44/1.99 % Starting sh5l with 300s (1) cores
% 9.44/1.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 9.44/1.99 % SinE strategy is gf500_gu_R04_F100_L20000
% 9.44/1.99 % Search class: FGHSM-FSLM32-MFFFFFNN
% 9.44/1.99 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 9.44/1.99 % Starting SubtermCWHack with 28s (1) cores
% 9.44/1.99 % Preprocessing time : 0.015 s
% 9.44/1.99
% 9.44/1.99 % Proof found!
% 9.44/1.99 % SZS status Unsatisfiable
% 9.44/1.99 % SZS output start CNFRefutation
% See solution above
% 9.44/1.99 % Parsed axioms : 1034
% 9.44/1.99 % Removed by relevancy pruning/SinE : 187
% 9.44/1.99 % Initial clauses : 847
% 9.44/1.99 % Removed in clause preprocessing : 0
% 9.44/1.99 % Initial clauses in saturation : 847
% 9.44/1.99 % Processed clauses : 6732
% 9.44/1.99 % ...of these trivial : 312
% 9.44/1.99 % ...subsumed : 4736
% 9.44/1.99 % ...remaining for further processing : 1684
% 9.44/1.99 % Other redundant clauses eliminated : 189
% 9.44/1.99 % Clauses deleted for lack of memory : 0
% 9.44/1.99 % Backward-subsumed : 12
% 9.44/1.99 % Backward-rewritten : 28
% 9.44/1.99 % Generated clauses : 45807
% 9.44/1.99 % ...of the previous two non-redundant : 39047
% 9.44/1.99 % ...aggressively subsumed : 0
% 9.44/1.99 % Contextual simplify-reflections : 1
% 9.44/1.99 % Paramodulations : 45595
% 9.44/1.99 % Factorizations : 8
% 9.44/1.99 % NegExts : 0
% 9.44/1.99 % Equation resolutions : 204
% 9.44/1.99 % Disequality decompositions : 0
% 9.44/1.99 % Total rewrite steps : 34836
% 9.44/1.99 % ...of those cached : 33269
% 9.44/1.99 % Propositional unsat checks : 0
% 9.44/1.99 % Propositional check models : 0
% 9.44/1.99 % Propositional check unsatisfiable : 0
% 9.44/1.99 % Propositional clauses : 0
% 9.44/1.99 % Propositional clauses after purity: 0
% 9.44/1.99 % Propositional unsat core size : 0
% 9.44/1.99 % Propositional preprocessing time : 0.000
% 9.44/1.99 % Propositional encoding time : 0.000
% 9.44/1.99 % Propositional solver time : 0.000
% 9.44/1.99 % Success case prop preproc time : 0.000
% 9.44/1.99 % Success case prop encoding time : 0.000
% 9.44/1.99 % Success case prop solver time : 0.000
% 9.44/1.99 % Current number of processed clauses : 1644
% 9.44/1.99 % Positive orientable unit clauses : 404
% 9.44/1.99 % Positive unorientable unit clauses: 5
% 9.44/1.99 % Negative unit clauses : 219
% 9.44/1.99 % Non-unit-clauses : 1016
% 9.44/1.99 % Current number of unprocessed clauses: 33139
% 9.44/1.99 % ...number of literals in the above : 91396
% 9.44/1.99 % Current number of archived formulas : 0
% 9.44/1.99 % Current number of archived clauses : 40
% 9.44/1.99 % Clause-clause subsumption calls (NU) : 105419
% 9.44/1.99 % Rec. Clause-clause subsumption calls : 67984
% 9.44/1.99 % Non-unit clause-clause subsumptions : 2003
% 9.44/1.99 % Unit Clause-clause subsumption calls : 7213
% 9.44/1.99 % Rewrite failures with RHS unbound : 0
% 9.44/1.99 % BW rewrite match attempts : 401
% 9.44/1.99 % BW rewrite match successes : 50
% 9.44/1.99 % Condensation attempts : 0
% 9.44/1.99 % Condensation successes : 0
% 9.44/1.99 % Termbank termtop insertions : 697099
% 9.44/1.99 % Search garbage collected termcells : 2259
% 9.44/1.99
% 9.44/1.99 % -------------------------------------------------
% 9.44/1.99 % User time : 1.142 s
% 9.44/1.99 % System time : 0.053 s
% 9.44/1.99 % Total time : 1.195 s
% 9.44/1.99 % Maximum resident set size: 5120 pages
% 9.44/1.99
% 9.44/1.99 % -------------------------------------------------
% 9.44/1.99 % User time : 1.188 s
% 9.44/1.99 % System time : 0.064 s
% 9.44/1.99 % Total time : 1.252 s
% 9.44/1.99 % Maximum resident set size: 5376 pages
% 9.44/1.99 % E exiting
%------------------------------------------------------------------------------