TSTP Solution File: GRP039-1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 17:36:12 EDT 2023

% Result   : Unsatisfiable 0.17s 0.47s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   67 (  31 unt;   4 nHn;  50 RR)
%            Number of literals    :  132 (  12 equ;  65 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   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   :  107 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',associativity1) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',left_identity) ).

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',associativity2) ).

cnf(a_times_c_is_d,negated_conjecture,
    product(a,c,d),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',a_times_c_is_d) ).

cnf(right_inverse,axiom,
    product(X1,inverse(X1),identity),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',right_inverse) ).

cnf(total_function2,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',total_function2) ).

cnf(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',right_identity) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',left_inverse) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',total_function1) ).

cnf(closure_of_product,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',closure_of_product) ).

cnf(b_times_a_inverse_is_c,negated_conjecture,
    product(b,inverse(a),c),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',b_times_a_inverse_is_c) ).

cnf(b_is_in_subgroup,negated_conjecture,
    subgroup_member(b),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',b_is_in_subgroup) ).

cnf(prove_d_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(d),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',prove_d_is_in_subgroup) ).

cnf(closure_of_inverse,axiom,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',closure_of_inverse) ).

cnf(property_of_O2,axiom,
    ( product(X1,element_in_O2(X1,X2),X2)
    | subgroup_member(X2)
    | subgroup_member(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',property_of_O2) ).

cnf(an_element_in_O2,axiom,
    ( subgroup_member(element_in_O2(X1,X2))
    | subgroup_member(X2)
    | subgroup_member(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p',an_element_in_O2) ).

cnf(c_0_16,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    associativity1 ).

cnf(c_0_17,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_18,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_19,negated_conjecture,
    product(a,c,d),
    a_times_c_is_d ).

cnf(c_0_20,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,identity)
    | ~ product(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
    product(X1,inverse(X1),identity),
    right_inverse ).

cnf(c_0_22,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_23,axiom,
    product(X1,identity,X1),
    right_identity ).

cnf(c_0_24,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_25,negated_conjecture,
    ( product(X1,c,X2)
    | ~ product(X3,d,X2)
    | ~ product(X3,a,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_26,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_27,plain,
    ( product(X1,X2,X3)
    | ~ product(inverse(X1),X3,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | ~ product(X2,identity,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,plain,
    ( product(inverse(X1),X2,X3)
    | ~ product(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( product(X1,c,identity)
    | ~ product(inverse(d),a,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_31,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_26]) ).

cnf(c_0_32,plain,
    product(X1,identity,inverse(inverse(X1))),
    inference(spm,[status(thm)],[c_0_27,c_0_21]) ).

cnf(c_0_33,plain,
    multiply(X1,identity) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_26]) ).

cnf(c_0_34,plain,
    ( X1 = inverse(X2)
    | ~ product(X2,X1,identity) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    product(multiply(inverse(d),a),c,identity),
    inference(spm,[status(thm)],[c_0_30,c_0_26]) ).

cnf(c_0_36,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    inverse(multiply(inverse(d),a)) = c,
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    multiply(inverse(d),a) = inverse(c),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    product(inverse(d),a,inverse(c)),
    inference(spm,[status(thm)],[c_0_26,c_0_38]) ).

cnf(c_0_40,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,X2,X3) ),
    closure_of_product ).

cnf(c_0_41,negated_conjecture,
    product(b,inverse(a),c),
    b_times_a_inverse_is_c ).

cnf(c_0_42,negated_conjecture,
    subgroup_member(b),
    b_is_in_subgroup ).

cnf(c_0_43,negated_conjecture,
    ~ subgroup_member(d),
    prove_d_is_in_subgroup ).

cnf(c_0_44,negated_conjecture,
    ( product(X1,X2,d)
    | ~ product(X3,c,X2)
    | ~ product(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_16,c_0_19]) ).

cnf(c_0_45,negated_conjecture,
    ( X1 = inverse(c)
    | ~ product(inverse(d),a,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_39]) ).

cnf(c_0_46,negated_conjecture,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).

cnf(c_0_47,axiom,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    closure_of_inverse ).

cnf(c_0_48,negated_conjecture,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    ( product(X1,multiply(X2,c),d)
    | ~ product(X1,X2,a) ),
    inference(spm,[status(thm)],[c_0_44,c_0_26]) ).

cnf(c_0_50,negated_conjecture,
    ( X1 = inverse(c)
    | ~ product(d,X1,a) ),
    inference(spm,[status(thm)],[c_0_45,c_0_29]) ).

cnf(c_0_51,axiom,
    ( product(X1,element_in_O2(X1,X2),X2)
    | subgroup_member(X2)
    | subgroup_member(X1) ),
    property_of_O2 ).

cnf(c_0_52,negated_conjecture,
    ~ subgroup_member(a),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    ( ~ subgroup_member(multiply(X1,c))
    | ~ subgroup_member(X2)
    | ~ product(X2,X1,a) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_43]) ).

cnf(c_0_54,plain,
    ( subgroup_member(multiply(X1,X2))
    | ~ subgroup_member(X2)
    | ~ subgroup_member(X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_26]) ).

cnf(c_0_55,axiom,
    ( subgroup_member(element_in_O2(X1,X2))
    | subgroup_member(X2)
    | subgroup_member(X1) ),
    an_element_in_O2 ).

cnf(c_0_56,negated_conjecture,
    element_in_O2(d,a) = inverse(c),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_43]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,X2,a) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_58,plain,
    ( subgroup_member(X1)
    | ~ subgroup_member(inverse(X1)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_36]) ).

cnf(c_0_59,negated_conjecture,
    subgroup_member(inverse(c)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52]),c_0_43]) ).

cnf(c_0_60,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,inverse(X2),X1)
    | ~ product(X4,identity,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_24]) ).

cnf(c_0_61,negated_conjecture,
    ( ~ subgroup_member(inverse(X1))
    | ~ subgroup_member(c)
    | ~ subgroup_member(X2)
    | ~ product(X1,a,X2) ),
    inference(spm,[status(thm)],[c_0_57,c_0_29]) ).

cnf(c_0_62,negated_conjecture,
    subgroup_member(c),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_63,negated_conjecture,
    ( product(c,a,X1)
    | ~ product(b,identity,X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_41]) ).

cnf(c_0_64,negated_conjecture,
    ( ~ subgroup_member(inverse(X1))
    | ~ subgroup_member(X2)
    | ~ product(X1,a,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).

cnf(c_0_65,negated_conjecture,
    product(c,a,b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_26]),c_0_33]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_59]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n013.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 2400
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Oct  3 02:18:29 EDT 2023
% 0.11/0.33  % CPUTime    : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.RqeN4whmwE/E---3.1_21602.p
% 0.17/0.47  # Version: 3.1pre001
% 0.17/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.47  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.47  # Starting sh5l with 300s (1) cores
% 0.17/0.47  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 21680 completed with status 0
% 0.17/0.47  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.47  # No SInE strategy applied
% 0.17/0.47  # Search class: FGUSM-FFSS21-SFFFFFNN
% 0.17/0.47  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.47  # Starting C07_19_nc_SAT001_MinMin_p005000_rr with 811s (1) cores
% 0.17/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.47  # Starting new_bool_3 with 136s (1) cores
% 0.17/0.47  # Starting new_bool_1 with 136s (1) cores
% 0.17/0.47  # Starting sh5l with 136s (1) cores
% 0.17/0.47  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 21685 completed with status 0
% 0.17/0.47  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.47  # No SInE strategy applied
% 0.17/0.47  # Search class: FGUSM-FFSS21-SFFFFFNN
% 0.17/0.47  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.47  # Starting C07_19_nc_SAT001_MinMin_p005000_rr with 811s (1) cores
% 0.17/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.47  # Preprocessing time       : 0.001 s
% 0.17/0.47  # Presaturation interreduction done
% 0.17/0.47  
% 0.17/0.47  # Proof found!
% 0.17/0.47  # SZS status Unsatisfiable
% 0.17/0.47  # SZS output start CNFRefutation
% See solution above
% 0.17/0.47  # Parsed axioms                        : 16
% 0.17/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.47  # Initial clauses                      : 16
% 0.17/0.47  # Removed in clause preprocessing      : 0
% 0.17/0.47  # Initial clauses in saturation        : 16
% 0.17/0.47  # Processed clauses                    : 424
% 0.17/0.47  # ...of these trivial                  : 3
% 0.17/0.47  # ...subsumed                          : 177
% 0.17/0.47  # ...remaining for further processing  : 244
% 0.17/0.47  # Other redundant clauses eliminated   : 0
% 0.17/0.47  # Clauses deleted for lack of memory   : 0
% 0.17/0.47  # Backward-subsumed                    : 42
% 0.17/0.47  # Backward-rewritten                   : 31
% 0.17/0.47  # Generated clauses                    : 1288
% 0.17/0.47  # ...of the previous two non-redundant : 1141
% 0.17/0.47  # ...aggressively subsumed             : 0
% 0.17/0.47  # Contextual simplify-reflections      : 3
% 0.17/0.47  # Paramodulations                      : 1288
% 0.17/0.47  # Factorizations                       : 0
% 0.17/0.47  # NegExts                              : 0
% 0.17/0.47  # Equation resolutions                 : 0
% 0.17/0.47  # Total rewrite steps                  : 326
% 0.17/0.47  # Propositional unsat checks           : 0
% 0.17/0.47  #    Propositional check models        : 0
% 0.17/0.47  #    Propositional check unsatisfiable : 0
% 0.17/0.47  #    Propositional clauses             : 0
% 0.17/0.47  #    Propositional clauses after purity: 0
% 0.17/0.47  #    Propositional unsat core size     : 0
% 0.17/0.47  #    Propositional preprocessing time  : 0.000
% 0.17/0.47  #    Propositional encoding time       : 0.000
% 0.17/0.47  #    Propositional solver time         : 0.000
% 0.17/0.47  #    Success case prop preproc time    : 0.000
% 0.17/0.47  #    Success case prop encoding time   : 0.000
% 0.17/0.47  #    Success case prop solver time     : 0.000
% 0.17/0.47  # Current number of processed clauses  : 155
% 0.17/0.47  #    Positive orientable unit clauses  : 26
% 0.17/0.47  #    Positive unorientable unit clauses: 0
% 0.17/0.47  #    Negative unit clauses             : 11
% 0.17/0.47  #    Non-unit-clauses                  : 118
% 0.17/0.47  # Current number of unprocessed clauses: 635
% 0.17/0.47  # ...number of literals in the above   : 2063
% 0.17/0.47  # Current number of archived formulas  : 0
% 0.17/0.47  # Current number of archived clauses   : 89
% 0.17/0.47  # Clause-clause subsumption calls (NU) : 5279
% 0.17/0.47  # Rec. Clause-clause subsumption calls : 4616
% 0.17/0.47  # Non-unit clause-clause subsumptions  : 130
% 0.17/0.47  # Unit Clause-clause subsumption calls : 894
% 0.17/0.47  # Rewrite failures with RHS unbound    : 0
% 0.17/0.47  # BW rewrite match attempts            : 50
% 0.17/0.47  # BW rewrite match successes           : 7
% 0.17/0.47  # Condensation attempts                : 0
% 0.17/0.47  # Condensation successes               : 0
% 0.17/0.47  # Termbank termtop insertions          : 13267
% 0.17/0.47  
% 0.17/0.47  # -------------------------------------------------
% 0.17/0.47  # User time                : 0.024 s
% 0.17/0.47  # System time              : 0.003 s
% 0.17/0.47  # Total time               : 0.027 s
% 0.17/0.47  # Maximum resident set size: 1640 pages
% 0.17/0.47  
% 0.17/0.47  # -------------------------------------------------
% 0.17/0.47  # User time                : 0.125 s
% 0.17/0.47  # System time              : 0.008 s
% 0.17/0.47  # Total time               : 0.133 s
% 0.17/0.47  # Maximum resident set size: 1684 pages
% 0.17/0.47  % E---3.1 exiting
% 0.17/0.48  % E---3.1 exiting
%------------------------------------------------------------------------------