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