TSTP Solution File: HEN006-2 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : HEN006-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 21:33:55 EDT 2024

% Result   : Unsatisfiable 6.49s 1.30s
% Output   : CNFRefutation 6.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   42 (  19 unt;   0 nHn;  37 RR)
%            Number of literals    :   92 (   4 equ;  53 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   91 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(quotient_property,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(closure,axiom,
    quotient(X1,X2,divide(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(quotient_less_equal,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).

cnf(xQz,hypothesis,
    quotient(x,z,xQz),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(xQy,hypothesis,
    quotient(x,y,xQy),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).

cnf(xQyLEz,hypothesis,
    less_equal(xQy,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).

cnf(divisor_existence,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).

cnf(transitivity_of_less_equal,axiom,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).

cnf(less_equal_quotient,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).

cnf(prove_xQzLEy,negated_conjecture,
    ~ less_equal(xQz,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).

cnf(c_0_12,plain,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    inference(fof_simplification,[status(thm)],[quotient_property]) ).

cnf(c_0_13,plain,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    c_0_12 ).

cnf(c_0_14,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_15,plain,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).

cnf(c_0_16,plain,
    ( less_equal(divide(X1,X2),X3)
    | ~ quotient(X4,X5,X3)
    | ~ quotient(X6,X5,X2)
    | ~ quotient(X7,X5,X1)
    | ~ quotient(X7,X6,X4) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    c_0_15 ).

cnf(c_0_18,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X5,X4,X1)
    | ~ quotient(X5,X3,X6)
    | ~ less_equal(X6,X4) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,plain,
    ( less_equal(divide(X1,divide(X2,X3)),zero)
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X2,X5)
    | ~ less_equal(X5,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_20,hypothesis,
    quotient(x,z,xQz),
    xQz ).

cnf(c_0_21,plain,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).

cnf(c_0_22,hypothesis,
    ( less_equal(divide(xQz,divide(X1,z)),zero)
    | ~ quotient(x,X1,X2)
    | ~ less_equal(X2,z) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,hypothesis,
    quotient(x,y,xQy),
    xQy ).

cnf(c_0_24,hypothesis,
    less_equal(xQy,z),
    xQyLEz ).

cnf(c_0_25,plain,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[divisor_existence]) ).

cnf(c_0_26,plain,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    c_0_21 ).

cnf(c_0_27,hypothesis,
    less_equal(divide(xQz,divide(y,z)),zero),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_28,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_29,plain,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    inference(fof_simplification,[status(thm)],[transitivity_of_less_equal]) ).

cnf(c_0_30,plain,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    c_0_25 ).

cnf(c_0_31,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).

cnf(c_0_32,hypothesis,
    divide(xQz,divide(y,z)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_33,plain,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    c_0_29 ).

cnf(c_0_34,plain,
    less_equal(divide(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_30,c_0_14]) ).

cnf(c_0_35,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    c_0_31 ).

cnf(c_0_36,hypothesis,
    quotient(xQz,divide(y,z),zero),
    inference(spm,[status(thm)],[c_0_14,c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    ~ less_equal(xQz,y),
    inference(fof_simplification,[status(thm)],[prove_xQzLEy]) ).

cnf(c_0_38,plain,
    ( less_equal(X1,X2)
    | ~ less_equal(X1,divide(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,hypothesis,
    less_equal(xQz,divide(y,z)),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    ~ less_equal(xQz,y),
    c_0_37 ).

cnf(c_0_41,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : HEN006-2 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 22:48:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order model finding
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.49/1.30  # Version: 3.1.0
% 6.49/1.30  # Preprocessing class: FSMSSMSSSSSNFFN.
% 6.49/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.49/1.30  # Starting new_bool_3 with 300s (1) cores
% 6.49/1.30  # Starting new_bool_1 with 300s (1) cores
% 6.49/1.30  # Starting sh5l with 300s (1) cores
% 6.49/1.30  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4530 completed with status 0
% 6.49/1.30  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.49/1.30  # Preprocessing class: FSMSSMSSSSSNFFN.
% 6.49/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.49/1.30  # No SInE strategy applied
% 6.49/1.30  # Search class: FHUSM-FFSS22-SFFFFFNN
% 6.49/1.30  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.49/1.30  # Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 6.49/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.49/1.30  # Starting new_bool_3 with 136s (1) cores
% 6.49/1.30  # Starting new_bool_1 with 136s (1) cores
% 6.49/1.30  # Starting sh5l with 136s (1) cores
% 6.49/1.30  # G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 4534 completed with status 0
% 6.49/1.30  # Result found by G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 6.49/1.30  # Preprocessing class: FSMSSMSSSSSNFFN.
% 6.49/1.30  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.49/1.30  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.49/1.30  # No SInE strategy applied
% 6.49/1.30  # Search class: FHUSM-FFSS22-SFFFFFNN
% 6.49/1.30  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.49/1.30  # Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 6.49/1.30  # Preprocessing time       : 0.001 s
% 6.49/1.30  # Presaturation interreduction done
% 6.49/1.30  
% 6.49/1.30  # Proof found!
% 6.49/1.30  # SZS status Unsatisfiable
% 6.49/1.30  # SZS output start CNFRefutation
% See solution above
% 6.49/1.30  # Parsed axioms                        : 18
% 6.49/1.30  # Removed by relevancy pruning/SinE    : 0
% 6.49/1.30  # Initial clauses                      : 18
% 6.49/1.30  # Removed in clause preprocessing      : 0
% 6.49/1.30  # Initial clauses in saturation        : 18
% 6.49/1.30  # Processed clauses                    : 8950
% 6.49/1.30  # ...of these trivial                  : 21
% 6.49/1.30  # ...subsumed                          : 7661
% 6.49/1.30  # ...remaining for further processing  : 1268
% 6.49/1.30  # Other redundant clauses eliminated   : 0
% 6.49/1.30  # Clauses deleted for lack of memory   : 0
% 6.49/1.30  # Backward-subsumed                    : 443
% 6.49/1.30  # Backward-rewritten                   : 5
% 6.49/1.30  # Generated clauses                    : 48868
% 6.49/1.30  # ...of the previous two non-redundant : 36576
% 6.49/1.30  # ...aggressively subsumed             : 0
% 6.49/1.30  # Contextual simplify-reflections      : 19
% 6.49/1.30  # Paramodulations                      : 48868
% 6.49/1.30  # Factorizations                       : 0
% 6.49/1.30  # NegExts                              : 0
% 6.49/1.30  # Equation resolutions                 : 0
% 6.49/1.30  # Disequality decompositions           : 0
% 6.49/1.30  # Total rewrite steps                  : 30771
% 6.49/1.30  # ...of those cached                   : 30107
% 6.49/1.30  # Propositional unsat checks           : 0
% 6.49/1.30  #    Propositional check models        : 0
% 6.49/1.30  #    Propositional check unsatisfiable : 0
% 6.49/1.30  #    Propositional clauses             : 0
% 6.49/1.30  #    Propositional clauses after purity: 0
% 6.49/1.30  #    Propositional unsat core size     : 0
% 6.49/1.30  #    Propositional preprocessing time  : 0.000
% 6.49/1.30  #    Propositional encoding time       : 0.000
% 6.49/1.30  #    Propositional solver time         : 0.000
% 6.49/1.30  #    Success case prop preproc time    : 0.000
% 6.49/1.30  #    Success case prop encoding time   : 0.000
% 6.49/1.30  #    Success case prop solver time     : 0.000
% 6.49/1.30  # Current number of processed clauses  : 802
% 6.49/1.30  #    Positive orientable unit clauses  : 68
% 6.49/1.30  #    Positive unorientable unit clauses: 0
% 6.49/1.30  #    Negative unit clauses             : 35
% 6.49/1.30  #    Non-unit-clauses                  : 699
% 6.49/1.30  # Current number of unprocessed clauses: 27301
% 6.49/1.30  # ...number of literals in the above   : 96215
% 6.49/1.30  # Current number of archived formulas  : 0
% 6.49/1.30  # Current number of archived clauses   : 466
% 6.49/1.30  # Clause-clause subsumption calls (NU) : 258440
% 6.49/1.30  # Rec. Clause-clause subsumption calls : 168538
% 6.49/1.30  # Non-unit clause-clause subsumptions  : 6517
% 6.49/1.30  # Unit Clause-clause subsumption calls : 12293
% 6.49/1.30  # Rewrite failures with RHS unbound    : 0
% 6.49/1.30  # BW rewrite match attempts            : 215
% 6.49/1.30  # BW rewrite match successes           : 4
% 6.49/1.30  # Condensation attempts                : 0
% 6.49/1.30  # Condensation successes               : 0
% 6.49/1.30  # Termbank termtop insertions          : 495709
% 6.49/1.30  # Search garbage collected termcells   : 34
% 6.49/1.30  
% 6.49/1.30  # -------------------------------------------------
% 6.49/1.30  # User time                : 0.778 s
% 6.49/1.30  # System time              : 0.020 s
% 6.49/1.30  # Total time               : 0.798 s
% 6.49/1.30  # Maximum resident set size: 1632 pages
% 6.49/1.30  
% 6.49/1.30  # -------------------------------------------------
% 6.49/1.30  # User time                : 3.955 s
% 6.49/1.30  # System time              : 0.048 s
% 6.49/1.30  # Total time               : 4.003 s
% 6.49/1.30  # Maximum resident set size: 1704 pages
% 6.49/1.30  % E---3.1 exiting
%------------------------------------------------------------------------------