TSTP Solution File: RNG005-1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n001.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:15:17 EDT 2023

% Result   : Unsatisfiable 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   63 (  33 unt;   0 nHn;  43 RR)
%            Number of literals    :  125 (  18 equ;  64 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  142 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',addition_is_well_defined) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',additive_identity2) ).

cnf(associativity_of_addition2,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',associativity_of_addition2) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',left_inverse) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',closure_of_addition) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',additive_identity1) ).

cnf(distributivity3,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ product(X6,X2,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',distributivity3) ).

cnf(a_times_b,hypothesis,
    product(a,b,d),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',a_times_b) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',commutativity_of_addition) ).

cnf(distributivity4,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',distributivity4) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',multiplication_is_well_defined) ).

cnf(a_inverse_times_b,hypothesis,
    product(additive_inverse(a),b,c),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',a_inverse_times_b) ).

cnf(associativity_of_addition1,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',associativity_of_addition1) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',closure_of_multiplication) ).

cnf(right_inverse,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',right_inverse) ).

cnf(prove_sum_is_additive_id,negated_conjecture,
    ~ sum(c,d,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.OdtHn0b73m/E---3.1_32613.p',prove_sum_is_additive_id) ).

cnf(c_0_16,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined ).

cnf(c_0_17,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_18,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    associativity_of_addition2 ).

cnf(c_0_19,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    left_inverse ).

cnf(c_0_20,plain,
    ( X1 = X2
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition ).

cnf(c_0_22,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_inverse(X2),X1)
    | ~ sum(X4,additive_identity,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    add(X1,additive_identity) = X1,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_25,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ product(X6,X2,X7) ),
    distributivity3 ).

cnf(c_0_26,hypothesis,
    product(a,b,d),
    a_times_b ).

cnf(c_0_27,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X3,additive_inverse(X2),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

cnf(c_0_29,hypothesis,
    ( sum(X1,X2,d)
    | ~ product(X3,b,X2)
    | ~ product(X4,b,X1)
    | ~ sum(X4,X3,a) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition ).

cnf(c_0_31,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    distributivity4 ).

cnf(c_0_32,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_33,hypothesis,
    product(additive_inverse(a),b,c),
    a_inverse_times_b ).

cnf(c_0_34,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    associativity_of_addition1 ).

cnf(c_0_35,plain,
    ( X1 = add(X2,X3)
    | ~ sum(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_36,plain,
    sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
    inference(spm,[status(thm)],[c_0_27,c_0_19]) ).

cnf(c_0_37,plain,
    add(additive_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_21]) ).

cnf(c_0_38,hypothesis,
    ( sum(X1,d,d)
    | ~ product(X2,b,X1)
    | ~ sum(X2,a,a) ),
    inference(spm,[status(thm)],[c_0_29,c_0_26]) ).

cnf(c_0_39,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_40,plain,
    ( X1 = additive_identity
    | ~ sum(additive_inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_19]) ).

cnf(c_0_41,plain,
    sum(X1,X2,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_30,c_0_21]) ).

cnf(c_0_42,hypothesis,
    ( product(X1,b,X2)
    | ~ product(X3,b,X4)
    | ~ sum(X4,d,X2)
    | ~ sum(X3,a,X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_26]) ).

cnf(c_0_43,hypothesis,
    ( X1 = c
    | ~ product(additive_inverse(a),b,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_44,plain,
    ( sum(X1,X2,additive_identity)
    | ~ sum(X1,X3,additive_inverse(X4))
    | ~ sum(X3,X4,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_19]) ).

cnf(c_0_45,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    right_inverse ).

cnf(c_0_46,plain,
    additive_inverse(additive_inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).

cnf(c_0_47,hypothesis,
    ( sum(multiply(X1,b),d,d)
    | ~ sum(X1,a,a) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_48,plain,
    sum(add(X1,additive_inverse(X2)),X2,X1),
    inference(spm,[status(thm)],[c_0_27,c_0_21]) ).

cnf(c_0_49,plain,
    add(X1,additive_inverse(X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_50,hypothesis,
    ( product(X1,b,X2)
    | ~ sum(multiply(X3,b),d,X2)
    | ~ sum(X3,a,X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_39]) ).

cnf(c_0_51,hypothesis,
    multiply(additive_inverse(a),b) = c,
    inference(spm,[status(thm)],[c_0_43,c_0_39]) ).

cnf(c_0_52,plain,
    ( sum(X1,additive_identity,additive_identity)
    | ~ sum(X1,X2,X2) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).

cnf(c_0_53,hypothesis,
    sum(multiply(additive_identity,b),d,d),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

cnf(c_0_54,hypothesis,
    ( product(additive_identity,b,X1)
    | ~ sum(c,d,X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_51]) ).

cnf(c_0_55,plain,
    add(X1,X2) = add(X2,X1),
    inference(spm,[status(thm)],[c_0_35,c_0_41]) ).

cnf(c_0_56,hypothesis,
    sum(multiply(additive_identity,b),additive_identity,additive_identity),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_57,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_39]) ).

cnf(c_0_58,hypothesis,
    product(additive_identity,b,add(d,c)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_21]),c_0_55]) ).

cnf(c_0_59,hypothesis,
    multiply(additive_identity,b) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_23]) ).

cnf(c_0_60,hypothesis,
    add(d,c) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    ~ sum(c,d,additive_identity),
    prove_sum_is_additive_id ).

cnf(c_0_62,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_61]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 2400
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Oct  2 20:13:22 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order model finding
% 0.19/0.47  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/tmp/tmp.OdtHn0b73m/E---3.1_32613.p
% 0.19/0.57  # Version: 3.1pre001
% 0.19/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.57  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.57  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.57  # Starting sh5l with 300s (1) cores
% 0.19/0.57  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 32692 completed with status 0
% 0.19/0.57  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.57  # No SInE strategy applied
% 0.19/0.57  # Search class: FHUSM-FFMF21-SFFFFFNN
% 0.19/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/0.57  # Starting new_bool_3 with 136s (1) cores
% 0.19/0.57  # Starting new_bool_1 with 136s (1) cores
% 0.19/0.57  # Starting sh5l with 136s (1) cores
% 0.19/0.57  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 32696 completed with status 0
% 0.19/0.57  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 0.19/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.57  # No SInE strategy applied
% 0.19/0.57  # Search class: FHUSM-FFMF21-SFFFFFNN
% 0.19/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 0.19/0.57  # Preprocessing time       : 0.001 s
% 0.19/0.57  # Presaturation interreduction done
% 0.19/0.57  
% 0.19/0.57  # Proof found!
% 0.19/0.57  # SZS status Unsatisfiable
% 0.19/0.57  # SZS output start CNFRefutation
% See solution above
% 0.19/0.57  # Parsed axioms                        : 20
% 0.19/0.57  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.57  # Initial clauses                      : 20
% 0.19/0.57  # Removed in clause preprocessing      : 0
% 0.19/0.57  # Initial clauses in saturation        : 20
% 0.19/0.57  # Processed clauses                    : 1212
% 0.19/0.57  # ...of these trivial                  : 103
% 0.19/0.57  # ...subsumed                          : 575
% 0.19/0.57  # ...remaining for further processing  : 534
% 0.19/0.57  # Other redundant clauses eliminated   : 0
% 0.19/0.57  # Clauses deleted for lack of memory   : 0
% 0.19/0.57  # Backward-subsumed                    : 1
% 0.19/0.57  # Backward-rewritten                   : 35
% 0.19/0.57  # Generated clauses                    : 4575
% 0.19/0.57  # ...of the previous two non-redundant : 3062
% 0.19/0.57  # ...aggressively subsumed             : 0
% 0.19/0.57  # Contextual simplify-reflections      : 0
% 0.19/0.57  # Paramodulations                      : 4575
% 0.19/0.57  # Factorizations                       : 0
% 0.19/0.57  # NegExts                              : 0
% 0.19/0.57  # Equation resolutions                 : 0
% 0.19/0.57  # Total rewrite steps                  : 3395
% 0.19/0.57  # Propositional unsat checks           : 0
% 0.19/0.57  #    Propositional check models        : 0
% 0.19/0.57  #    Propositional check unsatisfiable : 0
% 0.19/0.57  #    Propositional clauses             : 0
% 0.19/0.57  #    Propositional clauses after purity: 0
% 0.19/0.57  #    Propositional unsat core size     : 0
% 0.19/0.57  #    Propositional preprocessing time  : 0.000
% 0.19/0.57  #    Propositional encoding time       : 0.000
% 0.19/0.57  #    Propositional solver time         : 0.000
% 0.19/0.57  #    Success case prop preproc time    : 0.000
% 0.19/0.57  #    Success case prop encoding time   : 0.000
% 0.19/0.57  #    Success case prop solver time     : 0.000
% 0.19/0.57  # Current number of processed clauses  : 478
% 0.19/0.57  #    Positive orientable unit clauses  : 68
% 0.19/0.57  #    Positive unorientable unit clauses: 1
% 0.19/0.57  #    Negative unit clauses             : 1
% 0.19/0.57  #    Non-unit-clauses                  : 408
% 0.19/0.57  # Current number of unprocessed clauses: 1499
% 0.19/0.57  # ...number of literals in the above   : 2837
% 0.19/0.57  # Current number of archived formulas  : 0
% 0.19/0.57  # Current number of archived clauses   : 56
% 0.19/0.57  # Clause-clause subsumption calls (NU) : 30969
% 0.19/0.57  # Rec. Clause-clause subsumption calls : 24999
% 0.19/0.57  # Non-unit clause-clause subsumptions  : 559
% 0.19/0.57  # Unit Clause-clause subsumption calls : 16
% 0.19/0.57  # Rewrite failures with RHS unbound    : 0
% 0.19/0.57  # BW rewrite match attempts            : 107
% 0.19/0.57  # BW rewrite match successes           : 25
% 0.19/0.57  # Condensation attempts                : 0
% 0.19/0.57  # Condensation successes               : 0
% 0.19/0.57  # Termbank termtop insertions          : 47854
% 0.19/0.57  
% 0.19/0.57  # -------------------------------------------------
% 0.19/0.57  # User time                : 0.078 s
% 0.19/0.57  # System time              : 0.007 s
% 0.19/0.57  # Total time               : 0.085 s
% 0.19/0.57  # Maximum resident set size: 1632 pages
% 0.19/0.57  
% 0.19/0.57  # -------------------------------------------------
% 0.19/0.57  # User time                : 0.362 s
% 0.19/0.57  # System time              : 0.011 s
% 0.19/0.57  # Total time               : 0.372 s
% 0.19/0.57  # Maximum resident set size: 1688 pages
% 0.19/0.57  % E---3.1 exiting
%------------------------------------------------------------------------------