%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG001-3 : 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 : n016.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 13.66s 3.93s
% Output : CNFRefutation 13.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 46 ( 19 unt; 0 nHn; 28 RR)
% Number of literals : 112 ( 0 equ; 69 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 152 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
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(additive_inverse1,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(distributivity2,axiom,
( ~ sum(X3,X5,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c_0_8,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_9,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition2]) ).
cnf(c_0_10,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_8 ).
cnf(c_0_11,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_12,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_13,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_9 ).
cnf(c_0_14,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,axiom,
sum(additive_inverse(X1),X1,additive_identity),
additive_inverse1 ).
cnf(c_0_16,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_12 ).
cnf(c_0_17,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_18,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X4,additive_identity,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_19,plain,
( ~ sum(X1,additive_inverse(X2),additive_identity)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,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_16,c_0_17]) ).
cnf(c_0_21,plain,
( ~ sum(additive_inverse(X2),additive_identity,X1)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_22,plain,
sum(additive_inverse(additive_inverse(X1)),additive_identity,X1),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_23,plain,
( ~ sum(X5,X3,X4)
| ~ product(X2,X5,X1)
| sum(X1,multiply(X2,X3),multiply(X2,X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_24,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ sum(X2,X3,X4)
| sum(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4)) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_26,plain,
sum(X1,additive_identity,X1),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_27,plain,
( ~ sum(X1,X3,X4)
| ~ sum(X3,additive_inverse(X4),X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_28,plain,
sum(multiply(X1,X2),multiply(X1,additive_identity),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X7) ),
inference(fof_simplification,[status(thm)],[distributivity2]) ).
cnf(c_0_30,plain,
( ~ sum(multiply(X1,additive_identity),additive_inverse(multiply(X1,X2)),X3)
| sum(multiply(X1,X2),X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X7) ),
c_0_29 ).
cnf(c_0_32,plain,
( ~ sum(X2,additive_identity,X1)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_33,plain,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_34,plain,
( ~ sum(X4,X6,X2)
| ~ sum(X5,multiply(X1,X6),X3)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_35,plain,
sum(additive_identity,additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_37,plain,
( ~ sum(X4,X5,X2)
| ~ sum(multiply(X1,X4),multiply(X1,X5),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_38,plain,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,multiply(X2,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_39,plain,
sum(multiply(X1,additive_identity),X2,X2),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
~ product(a,additive_identity,additive_identity),
inference(fof_simplification,[status(thm)],[prove_a_times_additive_id_is_additive_id]) ).
cnf(c_0_41,plain,
( ~ sum(multiply(X1,X2),multiply(X1,additive_identity),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_42,plain,
sum(multiply(X1,additive_identity),multiply(X2,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
~ product(a,additive_identity,additive_identity),
c_0_40 ).
cnf(c_0_44,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n016.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 04:14:23 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 13.66/3.93 % Version: 3.5.1
% 13.66/3.93 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.66/3.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.66/3.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.66/3.93 % Starting new_bool_3 with 300s (1) cores
% 13.66/3.93 % Starting new_bool_1 with 300s (1) cores
% 13.66/3.93 % Starting sh5l with 300s (1) cores
% 13.66/3.93 % new_bool_3 with pid 1527506 completed with status 9
% 13.66/3.93 % new_bool_1 with pid 1527507 completed with status 9
% 13.66/3.93 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1527502 completed with status 0
% 13.66/3.93 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.66/3.93 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.66/3.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.66/3.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.66/3.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.66/3.93 % No SInE strategy applied
% 13.66/3.93 % Search class: FHUNS-FFSF21-SFFFFFNN
% 13.66/3.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.66/3.93 % Starting SubtermCWHack with 136s (1) cores
% 13.66/3.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.66/3.93 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 13.66/3.93 % Starting new_bool_3 with 136s (1) cores
% 13.66/3.93 % Starting new_bool_1 with 136s (1) cores
% 13.66/3.93 % new_bool_3 with pid 1527509 completed with status 0
% 13.66/3.93 % Result found by new_bool_3
% 13.66/3.93 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.66/3.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.66/3.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.66/3.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.66/3.93 % No SInE strategy applied
% 13.66/3.93 % Search class: FHUNS-FFSF21-SFFFFFNN
% 13.66/3.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.66/3.93 % Starting SubtermCWHack with 136s (1) cores
% 13.66/3.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.66/3.93 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_S0Y with 136s (1) cores
% 13.66/3.93 % Starting new_bool_3 with 136s (1) cores
% 13.66/3.93 % Preprocessing time : 0.002 s
% 13.66/3.93 % Presaturation interreduction done
% 13.66/3.93
% 13.66/3.93 % Proof found!
% 13.66/3.93 % SZS status Unsatisfiable
% 13.66/3.93 % SZS output start CNFRefutation
% See solution above
% 13.66/3.93 % Parsed axioms : 8
% 13.66/3.93 % Removed by relevancy pruning/SinE : 0
% 13.66/3.93 % Initial clauses : 8
% 13.66/3.93 % Removed in clause preprocessing : 0
% 13.66/3.93 % Initial clauses in saturation : 8
% 13.66/3.93 % Processed clauses : 9066
% 13.66/3.93 % ...of these trivial : 2356
% 13.66/3.93 % ...subsumed : 3764
% 13.66/3.93 % ...remaining for further processing : 2946
% 13.66/3.93 % Other redundant clauses eliminated : 0
% 13.66/3.93 % Clauses deleted for lack of memory : 0
% 13.66/3.93 % Backward-subsumed : 221
% 13.66/3.93 % Backward-rewritten : 41
% 13.66/3.93 % Generated clauses : 140088
% 13.66/3.93 % ...of the previous two non-redundant : 83160
% 13.66/3.93 % ...aggressively subsumed : 0
% 13.66/3.93 % Contextual simplify-reflections : 0
% 13.66/3.93 % Paramodulations : 140088
% 13.66/3.93 % Factorizations : 0
% 13.66/3.93 % NegExts : 0
% 13.66/3.93 % Equation resolutions : 0
% 13.66/3.93 % Disequality decompositions : 0
% 13.66/3.93 % Total rewrite steps : 59270
% 13.66/3.93 % ...of those cached : 58209
% 13.66/3.93 % Propositional unsat checks : 0
% 13.66/3.93 % Propositional check models : 0
% 13.66/3.93 % Propositional check unsatisfiable : 0
% 13.66/3.93 % Propositional clauses : 0
% 13.66/3.93 % Propositional clauses after purity: 0
% 13.66/3.93 % Propositional unsat core size : 0
% 13.66/3.93 % Propositional preprocessing time : 0.000
% 13.66/3.93 % Propositional encoding time : 0.000
% 13.66/3.93 % Propositional solver time : 0.000
% 13.66/3.93 % Success case prop preproc time : 0.000
% 13.66/3.93 % Success case prop encoding time : 0.000
% 13.66/3.93 % Success case prop solver time : 0.000
% 13.66/3.93 % Current number of processed clauses : 2676
% 13.66/3.93 % Positive orientable unit clauses : 235
% 13.66/3.93 % Positive unorientable unit clauses: 0
% 13.66/3.93 % Negative unit clauses : 0
% 13.66/3.93 % Non-unit-clauses : 2441
% 13.66/3.93 % Current number of unprocessed clauses: 73019
% 13.66/3.93 % ...number of literals in the above : 108642
% 13.66/3.93 % Current number of archived formulas : 0
% 13.66/3.93 % Current number of archived clauses : 270
% 13.66/3.93 % Clause-clause subsumption calls (NU) : 3060723
% 13.66/3.93 % Rec. Clause-clause subsumption calls : 2612096
% 13.66/3.93 % Non-unit clause-clause subsumptions : 3985
% 13.66/3.93 % Unit Clause-clause subsumption calls : 1158
% 13.66/3.93 % Rewrite failures with RHS unbound : 0
% 13.66/3.93 % BW rewrite match attempts : 15961
% 13.66/3.93 % BW rewrite match successes : 41
% 13.66/3.93 % Condensation attempts : 0
% 13.66/3.93 % Condensation successes : 0
% 13.66/3.93 % Termbank termtop insertions : 2161144
% 13.66/3.93 % Search garbage collected termcells : 30
% 13.66/3.93
% 13.66/3.93 % -------------------------------------------------
% 13.66/3.93 % User time : 3.256 s
% 13.66/3.93 % System time : 0.081 s
% 13.66/3.93 % Total time : 3.337 s
% 13.66/3.93 % Maximum resident set size: 3380 pages
% 13.66/3.93
% 13.66/3.93 % -------------------------------------------------
% 13.66/3.93 % User time : 16.179 s
% 13.66/3.93 % System time : 0.532 s
% 13.66/3.93 % Total time : 16.711 s
% 13.66/3.93 % Maximum resident set size: 4864 pages
% 13.66/3.93 % E exiting
%------------------------------------------------------------------------------