%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:05:26 PM UTC 2026
% Result : Unsatisfiable 19.85s 4.11s
% Output : CNFRefutation 19.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 65 ( 29 unt; 0 nHn; 39 RR)
% Number of literals : 133 ( 0 equ; 71 neg)
% Maximal clause size : 5 ( 2 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 : 174 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(product_substitution2,axiom,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).
cnf(symmetry,axiom,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(product_substitution1,axiom,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(product_substitution3,axiom,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(prove_multiplicative_identity_axiom,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_16,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
c_0_15 ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_18,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution2]) ).
cnf(c_0_19,plain,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
inference(fof_simplification,[status(thm)],[symmetry]) ).
cnf(c_0_20,plain,
( ~ sum(additive_identity,X2,X1)
| equalish(X1,X2) ),
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(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
cnf(c_0_23,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_24,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
c_0_18 ).
cnf(c_0_25,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_26,plain,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
c_0_19 ).
cnf(c_0_27,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_22 ).
cnf(c_0_29,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_30,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_23 ).
cnf(c_0_31,plain,
( ~ equalish(X3,X2)
| product(X1,X2,multiply(X1,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_34,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_35,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_29 ).
cnf(c_0_36,plain,
( ~ sum(X6,X5,X4)
| ~ product(X3,X6,X1)
| ~ product(X3,X5,X2)
| sum(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_37,plain,
product(X1,add(additive_identity,X2),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( ~ sum(X1,X3,X2)
| sum(additive_inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_40,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_41,plain,
( ~ sum(X5,add(additive_identity,X3),X4)
| ~ product(X2,X5,X1)
| sum(X1,multiply(X2,X3),multiply(X2,X4)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
sum(additive_inverse(X1),add(X2,X1),X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_44,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution1]) ).
cnf(c_0_45,plain,
( ~ sum(X1,X3,X4)
| ~ sum(X3,additive_inverse(X4),X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_46,plain,
( ~ product(X2,additive_inverse(X3),X1)
| sum(X1,multiply(X2,X3),multiply(X2,additive_identity)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
product(X1,additive_inverse(additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_48,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
c_0_44 ).
cnf(c_0_49,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_50,plain,
( ~ sum(X1,X2,X2)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_51,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_53,plain,
( ~ equalish(X3,X1)
| product(X1,X2,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_54,plain,
( ~ sum(X2,additive_identity,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_55,plain,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_52 ).
cnf(c_0_57,plain,
product(X1,X2,multiply(add(additive_identity,X1),X2)),
inference(spm,[status(thm)],[c_0_53,c_0_27]) ).
cnf(c_0_58,plain,
equalish(additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
~ product(a,additive_identity,additive_identity),
inference(fof_simplification,[status(thm)],[prove_multiplicative_identity_axiom]) ).
cnf(c_0_60,plain,
( ~ equalish(multiply(add(additive_identity,X1),X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
equalish(multiply(X1,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_26,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
~ product(a,additive_identity,additive_identity),
c_0_59 ).
cnf(c_0_63,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:14:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 19.85/4.11 % Version: 3.5.1
% 19.85/4.11 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.85/4.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.85/4.11 % Starting new_bool_3 with 300s (1) cores
% 19.85/4.11 % Starting new_bool_1 with 300s (1) cores
% 19.85/4.11 % Starting sh5l with 300s (1) cores
% 19.85/4.11 % new_bool_1 with pid 2163976 completed with status 9
% 19.85/4.11 % new_bool_3 with pid 2163975 completed with status 9
% 19.85/4.11 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2163974 completed with status 0
% 19.85/4.11 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 19.85/4.11 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.85/4.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.85/4.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.85/4.11 % No SInE strategy applied
% 19.85/4.11 % Search class: FHUNM-FFMF21-SFFFFFNN
% 19.85/4.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.85/4.11 % Starting SubtermCWHack with 136s (1) cores
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 19.85/4.11 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 19.85/4.11 % Starting new_bool_3 with 136s (1) cores
% 19.85/4.11 % G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with pid 2163984 completed with status 0
% 19.85/4.11 % Result found by G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A
% 19.85/4.11 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.85/4.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.85/4.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.85/4.11 % No SInE strategy applied
% 19.85/4.11 % Search class: FHUNM-FFMF21-SFFFFFNN
% 19.85/4.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.85/4.11 % Starting SubtermCWHack with 136s (1) cores
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.85/4.11 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 19.85/4.11 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 19.85/4.11 % Preprocessing time : 0.001 s
% 19.85/4.11 % Presaturation interreduction done
% 19.85/4.11
% 19.85/4.11 % Proof found!
% 19.85/4.11 % SZS status Unsatisfiable
% 19.85/4.11 % SZS output start CNFRefutation
% See solution above
% 19.85/4.11 % Parsed axioms : 30
% 19.85/4.11 % Removed by relevancy pruning/SinE : 0
% 19.85/4.11 % Initial clauses : 30
% 19.85/4.11 % Removed in clause preprocessing : 0
% 19.85/4.11 % Initial clauses in saturation : 30
% 19.85/4.11 % Processed clauses : 8701
% 19.85/4.11 % ...of these trivial : 3697
% 19.85/4.11 % ...subsumed : 1522
% 19.85/4.11 % ...remaining for further processing : 3482
% 19.85/4.11 % Other redundant clauses eliminated : 0
% 19.85/4.11 % Clauses deleted for lack of memory : 0
% 19.85/4.11 % Backward-subsumed : 241
% 19.85/4.11 % Backward-rewritten : 298
% 19.85/4.11 % Generated clauses : 353089
% 19.85/4.11 % ...of the previous two non-redundant : 320729
% 19.85/4.11 % ...aggressively subsumed : 0
% 19.85/4.11 % Contextual simplify-reflections : 0
% 19.85/4.11 % Paramodulations : 353089
% 19.85/4.11 % Factorizations : 0
% 19.85/4.11 % NegExts : 0
% 19.85/4.11 % Equation resolutions : 0
% 19.85/4.11 % Disequality decompositions : 0
% 19.85/4.11 % Total rewrite steps : 35987
% 19.85/4.11 % ...of those cached : 31023
% 19.85/4.11 % Propositional unsat checks : 0
% 19.85/4.11 % Propositional check models : 0
% 19.85/4.11 % Propositional check unsatisfiable : 0
% 19.85/4.11 % Propositional clauses : 0
% 19.85/4.11 % Propositional clauses after purity: 0
% 19.85/4.11 % Propositional unsat core size : 0
% 19.85/4.11 % Propositional preprocessing time : 0.000
% 19.85/4.11 % Propositional encoding time : 0.000
% 19.85/4.11 % Propositional solver time : 0.000
% 19.85/4.11 % Success case prop preproc time : 0.000
% 19.85/4.11 % Success case prop encoding time : 0.000
% 19.85/4.11 % Success case prop solver time : 0.000
% 19.85/4.11 % Current number of processed clauses : 2913
% 19.85/4.11 % Positive orientable unit clauses : 994
% 19.85/4.11 % Positive unorientable unit clauses: 0
% 19.85/4.11 % Negative unit clauses : 0
% 19.85/4.11 % Non-unit-clauses : 1919
% 19.85/4.11 % Current number of unprocessed clauses: 309691
% 19.85/4.11 % ...number of literals in the above : 368609
% 19.85/4.11 % Current number of archived formulas : 0
% 19.85/4.11 % Current number of archived clauses : 569
% 19.85/4.11 % Clause-clause subsumption calls (NU) : 260922
% 19.85/4.11 % Rec. Clause-clause subsumption calls : 251564
% 19.85/4.11 % Non-unit clause-clause subsumptions : 1763
% 19.85/4.11 % Unit Clause-clause subsumption calls : 5517
% 19.85/4.11 % Rewrite failures with RHS unbound : 0
% 19.85/4.11 % BW rewrite match attempts : 30731
% 19.85/4.11 % BW rewrite match successes : 241
% 19.85/4.11 % Condensation attempts : 0
% 19.85/4.11 % Condensation successes : 0
% 19.85/4.11 % Termbank termtop insertions : 4757390
% 19.85/4.11 % Search garbage collected termcells : 95
% 19.85/4.11
% 19.85/4.11 % -------------------------------------------------
% 19.85/4.11 % User time : 3.309 s
% 19.85/4.11 % System time : 0.198 s
% 19.85/4.11 % Total time : 3.507 s
% 19.85/4.11 % Maximum resident set size: 3400 pages
% 19.85/4.11
% 19.85/4.11 % -------------------------------------------------
% 19.85/4.11 % User time : 18.932 s
% 19.85/4.11 % System time : 0.922 s
% 19.85/4.11 % Total time : 19.855 s
% 19.85/4.11 % Maximum resident set size: 4608 pages
% 19.85/4.11 % E exiting
%------------------------------------------------------------------------------