TSTP Solution File: RNG001-1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 1.22s 0.67s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 67 ( 34 unt; 0 nHn; 35 RR)
% Number of literals : 132 ( 28 equ; 67 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 190 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',additive_identity1) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',closure_of_addition) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',left_inverse) ).
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/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',distributivity4) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',closure_of_multiplication) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',multiplication_is_well_defined) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',associativity_of_multiplication2) ).
cnf(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',distributivity2) ).
cnf(prove_a_times_0_is_0,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.L3XTsiN8pP/E---3.1_12660.p',prove_a_times_0_is_0) ).
cnf(c_0_12,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_13,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_14,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_15,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_16,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_17,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_18,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_21]) ).
cnf(c_0_23,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_24,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_25,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_26,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_27,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_28,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_29,plain,
( X1 = X2
| ~ sum(add(X2,additive_inverse(X3)),X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_30,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,multiply(X6,X2),X3)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( X1 = X2
| ~ sum(add(X2,X3),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_34,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X2),multiply(X5,X2),X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ sum(add(X3,X2),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_37,plain,
( product(X1,X2,X3)
| ~ sum(multiply(additive_identity,X2),multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_38,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_15]),c_0_33]) ).
cnf(c_0_39,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_15]),c_0_33]) ).
cnf(c_0_40,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_41,plain,
product(X1,X2,add(multiply(additive_identity,X2),multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_42,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_43,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_44,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33]) ).
cnf(c_0_45,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_48,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity2 ).
cnf(c_0_50,plain,
( product(multiply(X1,X2),X3,X4)
| ~ product(X1,multiply(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
cnf(c_0_51,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_48]),c_0_21]) ).
cnf(c_0_52,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X5,multiply(X1,X6),X3)
| ~ sum(X4,X6,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_28]) ).
cnf(c_0_53,plain,
( product(multiply(X1,additive_identity),X2,X3)
| ~ product(X1,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X1,X4),multiply(X1,X5),X3)
| ~ sum(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_55,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_53,c_0_28]) ).
cnf(c_0_56,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X1,additive_identity),multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_13]) ).
cnf(c_0_57,plain,
( X1 = multiply(X2,additive_identity)
| ~ product(multiply(X2,additive_identity),X3,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_55]) ).
cnf(c_0_58,plain,
product(X1,X2,add(multiply(X1,additive_identity),multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_59,plain,
multiply(multiply(X1,additive_identity),X2) = multiply(X1,additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_55]) ).
cnf(c_0_60,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_38]),c_0_33]) ).
cnf(c_0_61,plain,
add(multiply(X1,additive_identity),multiply(X1,additive_identity)) = multiply(X1,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_59]) ).
cnf(c_0_62,plain,
additive_inverse(multiply(X1,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_46]) ).
cnf(c_0_63,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_62]),c_0_21]) ).
cnf(c_0_64,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_a_times_0_is_0 ).
cnf(c_0_65,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_28,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Oct 2 19:47:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 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.L3XTsiN8pP/E---3.1_12660.p
% 1.22/0.67 # Version: 3.1pre001
% 1.22/0.67 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.67 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.67 # Starting new_bool_3 with 300s (1) cores
% 1.22/0.67 # Starting new_bool_1 with 300s (1) cores
% 1.22/0.67 # Starting sh5l with 300s (1) cores
% 1.22/0.67 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 12738 completed with status 0
% 1.22/0.67 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.22/0.67 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.67 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.67 # No SInE strategy applied
% 1.22/0.67 # Search class: FHUSM-FFMF21-SFFFFFNN
% 1.22/0.67 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.22/0.67 # Starting new_bool_3 with 136s (1) cores
% 1.22/0.67 # Starting new_bool_1 with 136s (1) cores
% 1.22/0.67 # Starting sh5l with 136s (1) cores
% 1.22/0.67 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 12742 completed with status 0
% 1.22/0.67 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 1.22/0.67 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.67 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.67 # No SInE strategy applied
% 1.22/0.67 # Search class: FHUSM-FFMF21-SFFFFFNN
% 1.22/0.67 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.67 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 1.22/0.67 # Preprocessing time : 0.001 s
% 1.22/0.67 # Presaturation interreduction done
% 1.22/0.67
% 1.22/0.67 # Proof found!
% 1.22/0.67 # SZS status Unsatisfiable
% 1.22/0.67 # SZS output start CNFRefutation
% See solution above
% 1.22/0.67 # Parsed axioms : 18
% 1.22/0.67 # Removed by relevancy pruning/SinE : 0
% 1.22/0.67 # Initial clauses : 18
% 1.22/0.67 # Removed in clause preprocessing : 0
% 1.22/0.67 # Initial clauses in saturation : 18
% 1.22/0.67 # Processed clauses : 2589
% 1.22/0.67 # ...of these trivial : 247
% 1.22/0.67 # ...subsumed : 1801
% 1.22/0.67 # ...remaining for further processing : 541
% 1.22/0.67 # Other redundant clauses eliminated : 0
% 1.22/0.67 # Clauses deleted for lack of memory : 0
% 1.22/0.67 # Backward-subsumed : 13
% 1.22/0.67 # Backward-rewritten : 37
% 1.22/0.67 # Generated clauses : 12161
% 1.22/0.67 # ...of the previous two non-redundant : 7910
% 1.22/0.67 # ...aggressively subsumed : 0
% 1.22/0.67 # Contextual simplify-reflections : 0
% 1.22/0.67 # Paramodulations : 12161
% 1.22/0.67 # Factorizations : 0
% 1.22/0.67 # NegExts : 0
% 1.22/0.67 # Equation resolutions : 0
% 1.22/0.67 # Total rewrite steps : 13144
% 1.22/0.67 # Propositional unsat checks : 0
% 1.22/0.67 # Propositional check models : 0
% 1.22/0.67 # Propositional check unsatisfiable : 0
% 1.22/0.67 # Propositional clauses : 0
% 1.22/0.67 # Propositional clauses after purity: 0
% 1.22/0.67 # Propositional unsat core size : 0
% 1.22/0.67 # Propositional preprocessing time : 0.000
% 1.22/0.67 # Propositional encoding time : 0.000
% 1.22/0.67 # Propositional solver time : 0.000
% 1.22/0.67 # Success case prop preproc time : 0.000
% 1.22/0.67 # Success case prop encoding time : 0.000
% 1.22/0.67 # Success case prop solver time : 0.000
% 1.22/0.67 # Current number of processed clauses : 473
% 1.22/0.67 # Positive orientable unit clauses : 53
% 1.22/0.67 # Positive unorientable unit clauses: 1
% 1.22/0.67 # Negative unit clauses : 0
% 1.22/0.67 # Non-unit-clauses : 419
% 1.22/0.67 # Current number of unprocessed clauses: 5157
% 1.22/0.67 # ...number of literals in the above : 8151
% 1.22/0.67 # Current number of archived formulas : 0
% 1.22/0.67 # Current number of archived clauses : 68
% 1.22/0.67 # Clause-clause subsumption calls (NU) : 127902
% 1.22/0.67 # Rec. Clause-clause subsumption calls : 80731
% 1.22/0.67 # Non-unit clause-clause subsumptions : 1770
% 1.22/0.67 # Unit Clause-clause subsumption calls : 12
% 1.22/0.67 # Rewrite failures with RHS unbound : 0
% 1.22/0.67 # BW rewrite match attempts : 829
% 1.22/0.67 # BW rewrite match successes : 34
% 1.22/0.67 # Condensation attempts : 0
% 1.22/0.67 # Condensation successes : 0
% 1.22/0.67 # Termbank termtop insertions : 119226
% 1.22/0.67
% 1.22/0.67 # -------------------------------------------------
% 1.22/0.67 # User time : 0.129 s
% 1.22/0.67 # System time : 0.009 s
% 1.22/0.67 # Total time : 0.138 s
% 1.22/0.67 # Maximum resident set size: 1632 pages
% 1.22/0.67
% 1.22/0.67 # -------------------------------------------------
% 1.22/0.67 # User time : 0.717 s
% 1.22/0.67 # System time : 0.022 s
% 1.22/0.67 # Total time : 0.739 s
% 1.22/0.67 # Maximum resident set size: 1688 pages
% 1.22/0.67 % E---3.1 exiting
% 1.22/0.67 % E---3.1 exiting
%------------------------------------------------------------------------------