%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:05:27 PM UTC 2026
% Result : Unsatisfiable 34.35s 5.53s
% Output : CNFRefutation 34.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 22 unt; 0 nHn; 34 RR)
% Number of literals : 96 ( 0 equ; 52 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(sum_substitution3,axiom,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(sum_substitution2,axiom,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
cnf(distributivity3,axiom,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(product_substitution1,axiom,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
cnf(additive_inverse_substitution,axiom,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_substitution) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(a_inverse_times_b,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(c_0_13,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_14,plain,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[sum_substitution3]) ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
c_0_13 ).
cnf(c_0_16,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_17,plain,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ sum(additive_identity,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_20,plain,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[sum_substitution2]) ).
cnf(c_0_21,plain,
( ~ equalish(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity3]) ).
cnf(c_0_24,plain,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
c_0_20 ).
cnf(c_0_25,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_26,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution1]) ).
cnf(c_0_27,plain,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
inference(fof_simplification,[status(thm)],[additive_inverse_substitution]) ).
cnf(c_0_28,plain,
sum(additive_identity,add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_23 ).
cnf(c_0_30,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_31,plain,
( ~ equalish(X1,X2)
| sum(additive_inverse(X1),X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
c_0_26 ).
cnf(c_0_33,hypothesis,
product(additive_inverse(a),b,c),
a_inverse_times_b ).
cnf(c_0_34,plain,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
c_0_27 ).
cnf(c_0_35,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_36,plain,
( ~ sum(X5,X3,additive_identity)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_38,hypothesis,
( ~ equalish(additive_inverse(a),X1)
| product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
equalish(additive_inverse(X1),additive_inverse(add(additive_identity,X1))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ product(X3,X4,X2)
| ~ product(additive_inverse(add(additive_identity,X3)),X4,X1)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,hypothesis,
product(additive_inverse(add(additive_identity,a)),b,c),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
~ sum(c,d,additive_identity),
inference(fof_simplification,[status(thm)],[prove_sum_is_additive_identity]) ).
cnf(c_0_43,hypothesis,
( ~ product(a,b,X1)
| sum(c,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_45,negated_conjecture,
~ sum(c,d,additive_identity),
c_0_42 ).
cnf(c_0_46,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 04:09:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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/benchmark/theBenchmark.p
% 34.35/5.53 % Version: 3.5.1
% 34.35/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 34.35/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 34.35/5.53 % Starting new_bool_3 with 300s (1) cores
% 34.35/5.53 % Starting new_bool_1 with 300s (1) cores
% 34.35/5.53 % Starting sh5l with 300s (1) cores
% 34.35/5.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 941871 completed with status 0
% 34.35/5.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 34.35/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 34.35/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 34.35/5.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 34.35/5.53 % No SInE strategy applied
% 34.35/5.53 % Search class: FHUNM-FFMF21-SFFFFFNN
% 34.35/5.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 34.35/5.53 % Starting SubtermCWHack with 136s (1) cores
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 34.35/5.53 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 34.35/5.53 % Starting new_bool_3 with 136s (1) cores
% 34.35/5.53 % G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with pid 941878 completed with status 0
% 34.35/5.53 % Result found by G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A
% 34.35/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 34.35/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 34.35/5.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 34.35/5.53 % No SInE strategy applied
% 34.35/5.53 % Search class: FHUNM-FFMF21-SFFFFFNN
% 34.35/5.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 34.35/5.53 % Starting SubtermCWHack with 136s (1) cores
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 34.35/5.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 34.35/5.53 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 34.35/5.53 % Preprocessing time : 0.001 s
% 34.35/5.53 % Presaturation interreduction done
% 34.35/5.53
% 34.35/5.53 % Proof found!
% 34.35/5.53 % SZS status Unsatisfiable
% 34.35/5.53 % SZS output start CNFRefutation
% See solution above
% 34.35/5.53 % Parsed axioms : 31
% 34.35/5.53 % Removed by relevancy pruning/SinE : 0
% 34.35/5.53 % Initial clauses : 31
% 34.35/5.53 % Removed in clause preprocessing : 0
% 34.35/5.53 % Initial clauses in saturation : 31
% 34.35/5.53 % Processed clauses : 10463
% 34.35/5.53 % ...of these trivial : 3716
% 34.35/5.53 % ...subsumed : 3300
% 34.35/5.53 % ...remaining for further processing : 3447
% 34.35/5.53 % Other redundant clauses eliminated : 0
% 34.35/5.53 % Clauses deleted for lack of memory : 0
% 34.35/5.53 % Backward-subsumed : 241
% 34.35/5.53 % Backward-rewritten : 272
% 34.35/5.53 % Generated clauses : 337662
% 34.35/5.53 % ...of the previous two non-redundant : 294597
% 34.35/5.53 % ...aggressively subsumed : 0
% 34.35/5.53 % Contextual simplify-reflections : 0
% 34.35/5.53 % Paramodulations : 337662
% 34.35/5.53 % Factorizations : 0
% 34.35/5.53 % NegExts : 0
% 34.35/5.53 % Equation resolutions : 0
% 34.35/5.53 % Disequality decompositions : 0
% 34.35/5.53 % Total rewrite steps : 48195
% 34.35/5.53 % ...of those cached : 42753
% 34.35/5.53 % Propositional unsat checks : 0
% 34.35/5.53 % Propositional check models : 0
% 34.35/5.53 % Propositional check unsatisfiable : 0
% 34.35/5.53 % Propositional clauses : 0
% 34.35/5.53 % Propositional clauses after purity: 0
% 34.35/5.53 % Propositional unsat core size : 0
% 34.35/5.53 % Propositional preprocessing time : 0.000
% 34.35/5.53 % Propositional encoding time : 0.000
% 34.35/5.53 % Propositional solver time : 0.000
% 34.35/5.53 % Success case prop preproc time : 0.000
% 34.35/5.53 % Success case prop encoding time : 0.000
% 34.35/5.53 % Success case prop solver time : 0.000
% 34.35/5.53 % Current number of processed clauses : 2903
% 34.35/5.53 % Positive orientable unit clauses : 1063
% 34.35/5.53 % Positive unorientable unit clauses: 0
% 34.35/5.53 % Negative unit clauses : 1
% 34.35/5.53 % Non-unit-clauses : 1839
% 34.35/5.53 % Current number of unprocessed clauses: 282464
% 34.35/5.53 % ...number of literals in the above : 361896
% 34.35/5.53 % Current number of archived formulas : 0
% 34.35/5.53 % Current number of archived clauses : 544
% 34.35/5.53 % Clause-clause subsumption calls (NU) : 750704
% 34.35/5.53 % Rec. Clause-clause subsumption calls : 657286
% 34.35/5.53 % Non-unit clause-clause subsumptions : 3541
% 34.35/5.53 % Unit Clause-clause subsumption calls : 4339
% 34.35/5.53 % Rewrite failures with RHS unbound : 0
% 34.35/5.53 % BW rewrite match attempts : 30771
% 34.35/5.53 % BW rewrite match successes : 272
% 34.35/5.53 % Condensation attempts : 0
% 34.35/5.53 % Condensation successes : 0
% 34.35/5.53 % Termbank termtop insertions : 4102648
% 34.35/5.53 % Search garbage collected termcells : 90
% 34.35/5.53
% 34.35/5.53 % -------------------------------------------------
% 34.35/5.53 % User time : 4.673 s
% 34.35/5.53 % System time : 0.211 s
% 34.35/5.53 % Total time : 4.884 s
% 34.35/5.53 % Maximum resident set size: 3604 pages
% 34.35/5.53
% 34.35/5.53 % -------------------------------------------------
% 34.35/5.53 % User time : 23.216 s
% 34.35/5.53 % System time : 1.052 s
% 34.35/5.53 % Total time : 24.268 s
% 34.35/5.53 % Maximum resident set size: 4864 pages
% 34.35/5.53 % E exiting
%------------------------------------------------------------------------------