%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW206+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 : n017.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 03:11:44 PM UTC 2026
% Result : Theorem 43.07s 6.80s
% Output : CNFRefutation 43.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 21 unt; 0 def)
% Number of atoms : 34 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 6 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-5 aty)
% Number of variables : 40 ( 7 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_BseqI2_H,axiom,
! [X45,X8,X46,X9] :
( class_RealVector_Oreal__normed__vector(X9)
=> ( ! [X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X5))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X9,hAPP(X8,X5))),X45)) )
=> c_SEQ_OBseq(X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqI2_H) ).
fof(help_c__COMBB__1,axiom,
! [X114,X115,X80,X38,X9,X34] : hAPP(c_COMBB(X34,X9,X38,X80,X115),X114) = hAPP(X80,hAPP(X115,X114)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_real__norm__def,axiom,
! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_th,axiom,
! [X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(fact_complex__Im__i,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__i) ).
fof(c_0_7,negated_conjecture,
~ c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_8,negated_conjecture,
~ c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_9,negated_conjecture,
~ c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X660,X661,X662,X663] :
( ( ~ class_RealVector_Oreal__normed__vector(X663)
| c_SEQ_OBseq(X663,X661)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X663,hAPP(X661,esk18_4(X660,X661,X662,X663)))),X660)) )
& ( ~ class_RealVector_Oreal__normed__vector(X663)
| c_SEQ_OBseq(X663,X661)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X662),esk18_4(X660,X661,X662,X663))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BseqI2_H])])])])]) ).
fof(c_0_11,plain,
! [X2846,X2847,X2848,X2849,X2850,X2851] : hAPP(c_COMBB(X2851,X2850,X2849,X2848,X2847),X2846) = hAPP(X2848,hAPP(X2847,X2846)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(c_0_12,plain,
! [X204] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X204) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X204),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_13,plain,
! [X132] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X132)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[fact_th]) ).
cnf(c_0_14,negated_conjecture,
~ c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk18_4(X3,X2,X4,X1)))),X3))
| c_SEQ_OBseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_17,plain,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Im__i]) ).
cnf(c_0_21,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk18_4(X1,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))),X2,tc_RealDef_Oreal))))))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_17]),c_0_17]),c_0_18])]) ).
cnf(c_0_22,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_21,c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW206+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:36:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 43.07/6.80 % Version: 3.5.1
% 43.07/6.80 % Preprocessing class: FMLMSMSMSSSNFFN.
% 43.07/6.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 43.07/6.80 % Starting new_bool_3 with 300s (1) cores
% 43.07/6.80 % Starting new_bool_1 with 300s (1) cores
% 43.07/6.80 % Starting sh5l with 300s (1) cores
% 43.07/6.80 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2011433 completed with status 0
% 43.07/6.80 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 43.07/6.80 % Preprocessing class: FMLMSMSMSSSNFFN.
% 43.07/6.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 43.07/6.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 43.07/6.80 % No SInE strategy applied
% 43.07/6.80 % Search class: FGHSM-SSLM32-DFFFFFNN
% 43.07/6.80 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 43.07/6.80 % Starting SubtermCWHack with 136s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 43.07/6.80 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 43.07/6.80 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 2011444 completed with status 0
% 43.07/6.80 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 43.07/6.80 % Preprocessing class: FMLMSMSMSSSNFFN.
% 43.07/6.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 43.07/6.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 43.07/6.80 % No SInE strategy applied
% 43.07/6.80 % Search class: FGHSM-SSLM32-DFFFFFNN
% 43.07/6.80 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 43.07/6.80 % Starting SubtermCWHack with 136s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 43.07/6.80 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 43.07/6.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 43.07/6.80 % Preprocessing time : 0.029 s
% 43.07/6.80 % Presaturation interreduction done
% 43.07/6.80
% 43.07/6.80 % Proof found!
% 43.07/6.80 % SZS status Theorem
% 43.07/6.80 % SZS output start CNFRefutation
% See solution above
% 43.07/6.80 % Parsed axioms : 1272
% 43.07/6.80 % Removed by relevancy pruning/SinE : 0
% 43.07/6.80 % Initial clauses : 1666
% 43.07/6.80 % Removed in clause preprocessing : 47
% 43.07/6.80 % Initial clauses in saturation : 1619
% 43.07/6.80 % Processed clauses : 23205
% 43.07/6.80 % ...of these trivial : 454
% 43.07/6.80 % ...subsumed : 13558
% 43.07/6.80 % ...remaining for further processing : 9193
% 43.07/6.80 % Other redundant clauses eliminated : 1960
% 43.07/6.80 % Clauses deleted for lack of memory : 0
% 43.07/6.80 % Backward-subsumed : 141
% 43.07/6.80 % Backward-rewritten : 225
% 43.07/6.80 % Generated clauses : 193836
% 43.07/6.80 % ...of the previous two non-redundant : 181579
% 43.07/6.80 % ...aggressively subsumed : 0
% 43.07/6.80 % Contextual simplify-reflections : 7
% 43.07/6.80 % Paramodulations : 191785
% 43.07/6.80 % Factorizations : 18
% 43.07/6.80 % NegExts : 0
% 43.07/6.80 % Equation resolutions : 2045
% 43.07/6.80 % Disequality decompositions : 0
% 43.07/6.80 % Total rewrite steps : 62928
% 43.07/6.80 % ...of those cached : 55044
% 43.07/6.80 % Propositional unsat checks : 1
% 43.07/6.80 % Propositional check models : 0
% 43.07/6.80 % Propositional check unsatisfiable : 0
% 43.07/6.80 % Propositional clauses : 0
% 43.07/6.80 % Propositional clauses after purity: 0
% 43.07/6.80 % Propositional unsat core size : 0
% 43.07/6.80 % Propositional preprocessing time : 0.000
% 43.07/6.80 % Propositional encoding time : 0.067
% 43.07/6.80 % Propositional solver time : 0.050
% 43.07/6.80 % Success case prop preproc time : 0.000
% 43.07/6.80 % Success case prop encoding time : 0.000
% 43.07/6.80 % Success case prop solver time : 0.000
% 43.07/6.80 % Current number of processed clauses : 7351
% 43.07/6.80 % Positive orientable unit clauses : 1240
% 43.07/6.80 % Positive unorientable unit clauses: 22
% 43.07/6.80 % Negative unit clauses : 1618
% 43.07/6.80 % Non-unit-clauses : 4471
% 43.07/6.80 % Current number of unprocessed clauses: 160870
% 43.07/6.80 % ...number of literals in the above : 314096
% 43.07/6.80 % Current number of archived formulas : 0
% 43.07/6.80 % Current number of archived clauses : 1724
% 43.07/6.80 % Clause-clause subsumption calls (NU) : 996979
% 43.07/6.80 % Rec. Clause-clause subsumption calls : 834576
% 43.07/6.80 % Non-unit clause-clause subsumptions : 4647
% 43.07/6.80 % Unit Clause-clause subsumption calls : 408040
% 43.07/6.80 % Rewrite failures with RHS unbound : 0
% 43.07/6.80 % BW rewrite match attempts : 35136
% 43.07/6.80 % BW rewrite match successes : 591
% 43.07/6.80 % Condensation attempts : 0
% 43.07/6.80 % Condensation successes : 0
% 43.07/6.80 % Termbank termtop insertions : 3892228
% 43.07/6.80 % Search garbage collected termcells : 19094
% 43.07/6.80
% 43.07/6.80 % -------------------------------------------------
% 43.07/6.80 % User time : 5.975 s
% 43.07/6.80 % System time : 0.203 s
% 43.07/6.80 % Total time : 6.178 s
% 43.07/6.80 % Maximum resident set size: 10528 pages
% 43.07/6.80
% 43.07/6.80 % -------------------------------------------------
% 43.07/6.80 % User time : 29.422 s
% 43.07/6.80 % System time : 1.038 s
% 43.07/6.80 % Total time : 30.460 s
% 43.07/6.80 % Maximum resident set size: 6400 pages
% 43.07/6.80 % E exiting
%------------------------------------------------------------------------------