TSTP Solution File: RNG001-5 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 19:14:38 EDT 2023
% Result : Unsatisfiable 20.45s 3.12s
% Output : CNFRefutation 20.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 56 ( 28 unt; 0 nHn; 30 RR)
% Number of literals : 107 ( 0 equ; 53 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 140 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',closure_of_addition) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',product_substitution2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',closure_of_multiplication) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',symmetry) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',associativity_of_addition1) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',distributivity1) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',left_inverse) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',commutativity_of_addition) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',right_inverse) ).
cnf(product_substitution1,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',product_substitution1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',additive_identity2) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',product_substitution3) ).
cnf(prove_multiplicative_identity_axiom,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.a1VEmdRnJT/E---3.1_8502.p',prove_multiplicative_identity_axiom) ).
cnf(c_0_15,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_16,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_17,plain,
( equalish(X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_19,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_20,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_21,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_22,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_24,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_25,plain,
( product(X1,X2,multiply(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_29,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_30,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_31,plain,
product(X1,add(additive_identity,X2),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_34,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_35,plain,
( sum(X1,multiply(X2,X3),multiply(X2,X4))
| ~ product(X2,X5,X1)
| ~ sum(X5,add(additive_identity,X3),X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
sum(additive_inverse(X1),add(X2,X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_38,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(X4),X2)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_39,plain,
( sum(X1,multiply(X2,X3),multiply(X2,additive_identity))
| ~ product(X2,additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
product(X1,additive_inverse(additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_41,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_42,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_43,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_44,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( product(X1,X2,multiply(X3,X2))
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_46,plain,
( equalish(X1,X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_42]) ).
cnf(c_0_47,plain,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_49,plain,
product(X1,X2,multiply(add(additive_identity,X1),X2)),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_50,plain,
equalish(additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(add(additive_identity,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
equalish(multiply(X1,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_multiplicative_identity_axiom ).
cnf(c_0_54,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 2400
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Oct 2 19:41:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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.a1VEmdRnJT/E---3.1_8502.p
% 20.45/3.12 # Version: 3.1pre001
% 20.45/3.12 # Preprocessing class: FSMSSMSSSSSNFFN.
% 20.45/3.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.45/3.12 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.45/3.12 # Starting new_bool_3 with 300s (1) cores
% 20.45/3.12 # Starting new_bool_1 with 300s (1) cores
% 20.45/3.12 # Starting sh5l with 300s (1) cores
% 20.45/3.12 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8583 completed with status 0
% 20.45/3.12 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 20.45/3.12 # Preprocessing class: FSMSSMSSSSSNFFN.
% 20.45/3.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.45/3.12 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.45/3.12 # No SInE strategy applied
% 20.45/3.12 # Search class: FHUNM-FFMF21-SFFFFFNN
% 20.45/3.12 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 20.45/3.12 # Starting G-E--_107_C12_02_nc_F1_PI_AE_Q4_CS_SP_PS_S064A with 811s (1) cores
% 20.45/3.12 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 20.45/3.12 # Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 20.45/3.12 # Starting new_bool_3 with 136s (1) cores
% 20.45/3.12 # Starting new_bool_1 with 136s (1) cores
% 20.45/3.12 # G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with pid 8593 completed with status 0
% 20.45/3.12 # Result found by G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A
% 20.45/3.12 # Preprocessing class: FSMSSMSSSSSNFFN.
% 20.45/3.12 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.45/3.12 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 20.45/3.12 # No SInE strategy applied
% 20.45/3.12 # Search class: FHUNM-FFMF21-SFFFFFNN
% 20.45/3.12 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 20.45/3.12 # Starting G-E--_107_C12_02_nc_F1_PI_AE_Q4_CS_SP_PS_S064A with 811s (1) cores
% 20.45/3.12 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 20.45/3.12 # Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 20.45/3.12 # Preprocessing time : 0.001 s
% 20.45/3.12 # Presaturation interreduction done
% 20.45/3.12
% 20.45/3.12 # Proof found!
% 20.45/3.12 # SZS status Unsatisfiable
% 20.45/3.12 # SZS output start CNFRefutation
% See solution above
% 20.45/3.13 # Parsed axioms : 30
% 20.45/3.13 # Removed by relevancy pruning/SinE : 0
% 20.45/3.13 # Initial clauses : 30
% 20.45/3.13 # Removed in clause preprocessing : 0
% 20.45/3.13 # Initial clauses in saturation : 30
% 20.45/3.13 # Processed clauses : 8701
% 20.45/3.13 # ...of these trivial : 3697
% 20.45/3.13 # ...subsumed : 1522
% 20.45/3.13 # ...remaining for further processing : 3482
% 20.45/3.13 # Other redundant clauses eliminated : 0
% 20.45/3.13 # Clauses deleted for lack of memory : 0
% 20.45/3.13 # Backward-subsumed : 241
% 20.45/3.13 # Backward-rewritten : 298
% 20.45/3.13 # Generated clauses : 353089
% 20.45/3.13 # ...of the previous two non-redundant : 320729
% 20.45/3.13 # ...aggressively subsumed : 0
% 20.45/3.13 # Contextual simplify-reflections : 0
% 20.45/3.13 # Paramodulations : 353089
% 20.45/3.13 # Factorizations : 0
% 20.45/3.13 # NegExts : 0
% 20.45/3.13 # Equation resolutions : 0
% 20.45/3.13 # Total rewrite steps : 35987
% 20.45/3.13 # Propositional unsat checks : 0
% 20.45/3.13 # Propositional check models : 0
% 20.45/3.13 # Propositional check unsatisfiable : 0
% 20.45/3.13 # Propositional clauses : 0
% 20.45/3.13 # Propositional clauses after purity: 0
% 20.45/3.13 # Propositional unsat core size : 0
% 20.45/3.13 # Propositional preprocessing time : 0.000
% 20.45/3.13 # Propositional encoding time : 0.000
% 20.45/3.13 # Propositional solver time : 0.000
% 20.45/3.13 # Success case prop preproc time : 0.000
% 20.45/3.13 # Success case prop encoding time : 0.000
% 20.45/3.13 # Success case prop solver time : 0.000
% 20.45/3.13 # Current number of processed clauses : 2913
% 20.45/3.13 # Positive orientable unit clauses : 994
% 20.45/3.13 # Positive unorientable unit clauses: 0
% 20.45/3.13 # Negative unit clauses : 0
% 20.45/3.13 # Non-unit-clauses : 1919
% 20.45/3.13 # Current number of unprocessed clauses: 309691
% 20.45/3.13 # ...number of literals in the above : 368609
% 20.45/3.13 # Current number of archived formulas : 0
% 20.45/3.13 # Current number of archived clauses : 569
% 20.45/3.13 # Clause-clause subsumption calls (NU) : 260922
% 20.45/3.13 # Rec. Clause-clause subsumption calls : 251564
% 20.45/3.13 # Non-unit clause-clause subsumptions : 1763
% 20.45/3.13 # Unit Clause-clause subsumption calls : 5517
% 20.45/3.13 # Rewrite failures with RHS unbound : 0
% 20.45/3.13 # BW rewrite match attempts : 30731
% 20.45/3.13 # BW rewrite match successes : 241
% 20.45/3.13 # Condensation attempts : 0
% 20.45/3.13 # Condensation successes : 0
% 20.45/3.13 # Termbank termtop insertions : 4757000
% 20.45/3.13
% 20.45/3.13 # -------------------------------------------------
% 20.45/3.13 # User time : 2.452 s
% 20.45/3.13 # System time : 0.132 s
% 20.45/3.13 # Total time : 2.584 s
% 20.45/3.13 # Maximum resident set size: 1664 pages
% 20.45/3.13
% 20.45/3.13 # -------------------------------------------------
% 20.45/3.13 # User time : 12.467 s
% 20.45/3.13 # System time : 0.362 s
% 20.45/3.13 # Total time : 12.829 s
% 20.45/3.13 # Maximum resident set size: 1696 pages
% 20.45/3.13 % E---3.1 exiting
% 20.45/3.13 % E---3.1 exiting
%------------------------------------------------------------------------------