%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG387-1 : 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 : n001.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 12:02:04 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 6 unt; 2 nHn; 12 RR)
% Number of literals : 22 ( 0 equ; 11 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_v_0,axiom,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_v_0) ).
cnf(cls_v0_0,axiom,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_v0_0) ).
cnf(cls_ath_0,axiom,
( c_lessequals(X2,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ath_0) ).
cnf(c_0_4,negated_conjecture,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_5,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_v_0]) ).
cnf(c_0_6,plain,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_v0_0]) ).
cnf(c_0_7,negated_conjecture,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
c_0_4 ).
cnf(c_0_8,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
c_0_5 ).
cnf(c_0_9,plain,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
c_0_6 ).
cnf(c_0_10,negated_conjecture,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
( c_lessequals(X2,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_ath_0 ).
cnf(c_0_12,negated_conjecture,
~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG387-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 13:24:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.21/0.52 % Version: 3.5.1
% 0.21/0.52 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.52 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.52 % Starting sh5l with 300s (1) cores
% 0.21/0.52 % new_bool_3 with pid 3218685 completed with status 0
% 0.21/0.52 % Result found by new_bool_3
% 0.21/0.52 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.52 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52 % Search class: FGUSM-FFLM32-MFFFFFNN
% 0.21/0.52 % partial match(1): FGHSM-FFLM32-MFFFFFNN
% 0.21/0.52 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.52 % Starting SubtermCWHack with 61s (1) cores
% 0.21/0.52 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 361s (1) cores
% 0.21/0.52 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with pid 3218690 completed with status 0
% 0.21/0.52 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN
% 0.21/0.52 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.21/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.21/0.52 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52 % Search class: FGUSM-FFLM32-MFFFFFNN
% 0.21/0.52 % partial match(1): FGHSM-FFLM32-MFFFFFNN
% 0.21/0.52 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.52 % Starting SubtermCWHack with 61s (1) cores
% 0.21/0.52 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 361s (1) cores
% 0.21/0.52 % Preprocessing time : 0.019 s
% 0.21/0.52
% 0.21/0.52 % Proof found!
% 0.21/0.52 % SZS status Unsatisfiable
% 0.21/0.52 % SZS output start CNFRefutation
% See solution above
% 0.21/0.52 % Parsed axioms : 884
% 0.21/0.52 % Removed by relevancy pruning/SinE : 772
% 0.21/0.52 % Initial clauses : 112
% 0.21/0.52 % Removed in clause preprocessing : 0
% 0.21/0.52 % Initial clauses in saturation : 112
% 0.21/0.52 % Processed clauses : 151
% 0.21/0.52 % ...of these trivial : 0
% 0.21/0.52 % ...subsumed : 18
% 0.21/0.52 % ...remaining for further processing : 133
% 0.21/0.52 % Other redundant clauses eliminated : 0
% 0.21/0.52 % Clauses deleted for lack of memory : 0
% 0.21/0.52 % Backward-subsumed : 1
% 0.21/0.52 % Backward-rewritten : 1
% 0.21/0.52 % Generated clauses : 877
% 0.21/0.52 % ...of the previous two non-redundant : 805
% 0.21/0.52 % ...aggressively subsumed : 0
% 0.21/0.52 % Contextual simplify-reflections : 0
% 0.21/0.52 % Paramodulations : 873
% 0.21/0.52 % Factorizations : 2
% 0.21/0.52 % NegExts : 0
% 0.21/0.52 % Equation resolutions : 2
% 0.21/0.52 % Disequality decompositions : 0
% 0.21/0.52 % Total rewrite steps : 355
% 0.21/0.52 % ...of those cached : 321
% 0.21/0.52 % Propositional unsat checks : 0
% 0.21/0.52 % Propositional check models : 0
% 0.21/0.52 % Propositional check unsatisfiable : 0
% 0.21/0.52 % Propositional clauses : 0
% 0.21/0.52 % Propositional clauses after purity: 0
% 0.21/0.52 % Propositional unsat core size : 0
% 0.21/0.52 % Propositional preprocessing time : 0.000
% 0.21/0.52 % Propositional encoding time : 0.000
% 0.21/0.52 % Propositional solver time : 0.000
% 0.21/0.52 % Success case prop preproc time : 0.000
% 0.21/0.52 % Success case prop encoding time : 0.000
% 0.21/0.52 % Success case prop solver time : 0.000
% 0.21/0.52 % Current number of processed clauses : 131
% 0.21/0.52 % Positive orientable unit clauses : 19
% 0.21/0.52 % Positive unorientable unit clauses: 2
% 0.21/0.52 % Negative unit clauses : 10
% 0.21/0.52 % Non-unit-clauses : 100
% 0.21/0.52 % Current number of unprocessed clauses: 759
% 0.21/0.52 % ...number of literals in the above : 1924
% 0.21/0.52 % Current number of archived formulas : 0
% 0.21/0.52 % Current number of archived clauses : 2
% 0.21/0.52 % Clause-clause subsumption calls (NU) : 958
% 0.21/0.52 % Rec. Clause-clause subsumption calls : 899
% 0.21/0.52 % Non-unit clause-clause subsumptions : 10
% 0.21/0.52 % Unit Clause-clause subsumption calls : 22
% 0.21/0.52 % Rewrite failures with RHS unbound : 0
% 0.21/0.52 % BW rewrite match attempts : 12
% 0.21/0.52 % BW rewrite match successes : 7
% 0.21/0.52 % Condensation attempts : 0
% 0.21/0.52 % Condensation successes : 0
% 0.21/0.52 % Termbank termtop insertions : 27003
% 0.21/0.52 % Search garbage collected termcells : 2653
% 0.21/0.52
% 0.21/0.52 % -------------------------------------------------
% 0.21/0.52 % User time : 0.048 s
% 0.21/0.52 % System time : 0.006 s
% 0.21/0.52 % Total time : 0.054 s
% 0.21/0.52 % Maximum resident set size: 4492 pages
% 0.21/0.52
% 0.21/0.52 % -------------------------------------------------
% 0.21/0.52 % User time : 0.116 s
% 0.21/0.52 % System time : 0.012 s
% 0.21/0.52 % Total time : 0.128 s
% 0.21/0.52 % Maximum resident set size: 5376 pages
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------