%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG400-1 : 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 : n020.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 11:56:02 AM UTC 2026
% Result : Unsatisfiable 7.58s 1.47s
% Output : CNFRefutation 7.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 10 unt; 2 nHn; 12 RR)
% Number of literals : 32 ( 9 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_class__semiring_Osemiring__rules_I7_J_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_Osemiring__rules_I7_J_0) ).
cnf(cls_poly__smult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
cnf(cls_complex__divide__def_0,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
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_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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(c_0_7,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_Osemiring__rules_I7_J_0]) ).
cnf(c_0_8,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_poly__smult_0]) ).
cnf(c_0_9,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_complex__divide__def_0 ).
cnf(c_0_10,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_7 ).
cnf(c_0_11,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_12,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_13,negated_conjecture,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_conjecture_1 ).
cnf(c_0_14,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1) ),
c_0_8 ).
cnf(c_0_15,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_16,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_17,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_12 ).
cnf(c_0_18,negated_conjecture,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[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,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_16]),c_0_18]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG400-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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 13:20:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 7.58/1.47 % Version: 3.5.1
% 7.58/1.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.58/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.58/1.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.58/1.47 % Starting new_bool_3 with 300s (1) cores
% 7.58/1.47 % Starting new_bool_1 with 300s (1) cores
% 7.58/1.47 % Starting sh5l with 300s (1) cores
% 7.58/1.47 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3019647 completed with status 0
% 7.58/1.47 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.58/1.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.58/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.58/1.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.58/1.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.58/1.47 % No SInE strategy applied
% 7.58/1.47 % Search class: FGHSS-FSLM32-DFFFFFNN
% 7.58/1.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.58/1.47 % Starting SubtermCWHack with 136s (1) cores
% 7.58/1.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.58/1.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 7.58/1.47 % Starting new_bool_3 with 136s (1) cores
% 7.58/1.47 % Starting new_bool_1 with 136s (1) cores
% 7.58/1.47 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3019654 completed with status 0
% 7.58/1.47 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.58/1.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.58/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.58/1.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.58/1.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.58/1.47 % No SInE strategy applied
% 7.58/1.47 % Search class: FGHSS-FSLM32-DFFFFFNN
% 7.58/1.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.58/1.47 % Starting SubtermCWHack with 136s (1) cores
% 7.58/1.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.58/1.47 % Preprocessing time : 0.009 s
% 7.58/1.47 % Presaturation interreduction done
% 7.58/1.47
% 7.58/1.47 % Proof found!
% 7.58/1.47 % SZS status Unsatisfiable
% 7.58/1.47 % SZS output start CNFRefutation
% See solution above
% 7.58/1.47 % Parsed axioms : 604
% 7.58/1.47 % Removed by relevancy pruning/SinE : 0
% 7.58/1.47 % Initial clauses : 604
% 7.58/1.47 % Removed in clause preprocessing : 0
% 7.58/1.47 % Initial clauses in saturation : 604
% 7.58/1.47 % Processed clauses : 7804
% 7.58/1.47 % ...of these trivial : 254
% 7.58/1.47 % ...subsumed : 5654
% 7.58/1.47 % ...remaining for further processing : 1896
% 7.58/1.47 % Other redundant clauses eliminated : 450
% 7.58/1.47 % Clauses deleted for lack of memory : 0
% 7.58/1.47 % Backward-subsumed : 63
% 7.58/1.47 % Backward-rewritten : 94
% 7.58/1.47 % Generated clauses : 40117
% 7.58/1.47 % ...of the previous two non-redundant : 34451
% 7.58/1.47 % ...aggressively subsumed : 0
% 7.58/1.47 % Contextual simplify-reflections : 20
% 7.58/1.47 % Paramodulations : 39637
% 7.58/1.47 % Factorizations : 22
% 7.58/1.47 % NegExts : 0
% 7.58/1.47 % Equation resolutions : 458
% 7.58/1.47 % Disequality decompositions : 0
% 7.58/1.47 % Total rewrite steps : 44314
% 7.58/1.47 % ...of those cached : 43609
% 7.58/1.47 % Propositional unsat checks : 0
% 7.58/1.47 % Propositional check models : 0
% 7.58/1.47 % Propositional check unsatisfiable : 0
% 7.58/1.47 % Propositional clauses : 0
% 7.58/1.47 % Propositional clauses after purity: 0
% 7.58/1.47 % Propositional unsat core size : 0
% 7.58/1.47 % Propositional preprocessing time : 0.000
% 7.58/1.47 % Propositional encoding time : 0.000
% 7.58/1.47 % Propositional solver time : 0.000
% 7.58/1.47 % Success case prop preproc time : 0.000
% 7.58/1.47 % Success case prop encoding time : 0.000
% 7.58/1.47 % Success case prop solver time : 0.000
% 7.58/1.47 % Current number of processed clauses : 1295
% 7.58/1.47 % Positive orientable unit clauses : 211
% 7.58/1.47 % Positive unorientable unit clauses: 4
% 7.58/1.47 % Negative unit clauses : 73
% 7.58/1.47 % Non-unit-clauses : 1007
% 7.58/1.47 % Current number of unprocessed clauses: 27417
% 7.58/1.47 % ...number of literals in the above : 119820
% 7.58/1.47 % Current number of archived formulas : 0
% 7.58/1.47 % Current number of archived clauses : 601
% 7.58/1.47 % Clause-clause subsumption calls (NU) : 239513
% 7.58/1.47 % Rec. Clause-clause subsumption calls : 105978
% 7.58/1.47 % Non-unit clause-clause subsumptions : 3312
% 7.58/1.47 % Unit Clause-clause subsumption calls : 5829
% 7.58/1.47 % Rewrite failures with RHS unbound : 0
% 7.58/1.47 % BW rewrite match attempts : 1488
% 7.58/1.47 % BW rewrite match successes : 127
% 7.58/1.47 % Condensation attempts : 0
% 7.58/1.47 % Condensation successes : 0
% 7.58/1.47 % Termbank termtop insertions : 781963
% 7.58/1.47 % Search garbage collected termcells : 1505
% 7.58/1.47
% 7.58/1.47 % -------------------------------------------------
% 7.58/1.47 % User time : 0.955 s
% 7.58/1.47 % System time : 0.039 s
% 7.58/1.47 % Total time : 0.994 s
% 7.58/1.47 % Maximum resident set size: 4856 pages
% 7.58/1.47
% 7.58/1.47 % -------------------------------------------------
% 7.58/1.47 % User time : 4.695 s
% 7.58/1.47 % System time : 0.186 s
% 7.58/1.47 % Total time : 4.881 s
% 7.58/1.47 % Maximum resident set size: 5120 pages
% 7.58/1.47 % E exiting
%------------------------------------------------------------------------------