%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG006-2 : 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 : n007.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 02:05:28 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 21 RR)
% Number of literals : 41 ( 0 equ; 23 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
cnf(product_lemma1,axiom,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_lemma1) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
cnf(c_0_7,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_8,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X7) ),
c_0_7 ).
cnf(c_0_9,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
aPb_plus_IaPc ).
cnf(c_0_10,plain,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
inference(fof_simplification,[status(thm)],[product_lemma1]) ).
cnf(c_0_11,hypothesis,
( ~ sum(X4,X3,X2)
| ~ product(X1,X4,aPb)
| ~ product(X1,X3,additive_inverse(aPc))
| product(X1,X2,aPb_S_IaPc) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,hypothesis,
product(a,b,aPb),
a_times_b ).
cnf(c_0_13,plain,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
c_0_10 ).
cnf(c_0_14,hypothesis,
product(a,c,aPc),
a_times_c ).
cnf(c_0_15,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(fof_simplification,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c_0_16,hypothesis,
( ~ sum(b,X2,X1)
| ~ product(a,X2,additive_inverse(aPc))
| product(a,X1,aPb_S_IaPc) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
b_plus_inverse_c ).
cnf(c_0_18,hypothesis,
product(a,additive_inverse(c),additive_inverse(aPc)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
c_0_15 ).
cnf(c_0_20,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n007.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:08:20 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.52 Running first-order theorem proving
% 0.18/0.52 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
% 0.24/0.60 % Version: 3.5.1
% 0.24/0.60 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.24/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.60 % Starting sh5l with 300s (1) cores
% 0.24/0.60 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 142393 completed with status 0
% 0.24/0.60 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.24/0.60 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.24/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.60 % No SInE strategy applied
% 0.24/0.60 % Search class: FHUNM-FFMS21-SFFFFFNN
% 0.24/0.60 % partial match(1): FHUSM-FFMS21-SFFFFFNN
% 0.24/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.24/0.60 % Starting G-E--_301_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.24/0.60 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.60 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.60 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 142398 completed with status 0
% 0.24/0.60 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.24/0.60 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.24/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.60 % No SInE strategy applied
% 0.24/0.60 % Search class: FHUNM-FFMS21-SFFFFFNN
% 0.24/0.60 % partial match(1): FHUSM-FFMS21-SFFFFFNN
% 0.24/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.24/0.60 % Preprocessing time : 0.002 s
% 0.24/0.60 % Presaturation interreduction done
% 0.24/0.60
% 0.24/0.60 % Proof found!
% 0.24/0.60 % SZS status Unsatisfiable
% 0.24/0.60 % SZS output start CNFRefutation
% See solution above
% 0.24/0.60 % Parsed axioms : 36
% 0.24/0.60 % Removed by relevancy pruning/SinE : 0
% 0.24/0.60 % Initial clauses : 36
% 0.24/0.60 % Removed in clause preprocessing : 0
% 0.24/0.60 % Initial clauses in saturation : 36
% 0.24/0.60 % Processed clauses : 365
% 0.24/0.60 % ...of these trivial : 25
% 0.24/0.60 % ...subsumed : 0
% 0.24/0.60 % ...remaining for further processing : 340
% 0.24/0.60 % Other redundant clauses eliminated : 0
% 0.24/0.60 % Clauses deleted for lack of memory : 0
% 0.24/0.60 % Backward-subsumed : 0
% 0.24/0.60 % Backward-rewritten : 3
% 0.24/0.60 % Generated clauses : 2005
% 0.24/0.60 % ...of the previous two non-redundant : 1532
% 0.24/0.60 % ...aggressively subsumed : 0
% 0.24/0.60 % Contextual simplify-reflections : 0
% 0.24/0.60 % Paramodulations : 2005
% 0.24/0.60 % Factorizations : 0
% 0.24/0.60 % NegExts : 0
% 0.24/0.60 % Equation resolutions : 0
% 0.24/0.60 % Disequality decompositions : 0
% 0.24/0.60 % Total rewrite steps : 507
% 0.24/0.60 % ...of those cached : 384
% 0.24/0.60 % Propositional unsat checks : 0
% 0.24/0.60 % Propositional check models : 0
% 0.24/0.60 % Propositional check unsatisfiable : 0
% 0.24/0.60 % Propositional clauses : 0
% 0.24/0.60 % Propositional clauses after purity: 0
% 0.24/0.60 % Propositional unsat core size : 0
% 0.24/0.60 % Propositional preprocessing time : 0.000
% 0.24/0.60 % Propositional encoding time : 0.000
% 0.24/0.60 % Propositional solver time : 0.000
% 0.24/0.60 % Success case prop preproc time : 0.000
% 0.24/0.60 % Success case prop encoding time : 0.000
% 0.24/0.60 % Success case prop solver time : 0.000
% 0.24/0.60 % Current number of processed clauses : 301
% 0.24/0.60 % Positive orientable unit clauses : 84
% 0.24/0.60 % Positive unorientable unit clauses: 0
% 0.24/0.60 % Negative unit clauses : 1
% 0.24/0.60 % Non-unit-clauses : 216
% 0.24/0.60 % Current number of unprocessed clauses: 1231
% 0.24/0.60 % ...number of literals in the above : 2023
% 0.24/0.60 % Current number of archived formulas : 0
% 0.24/0.60 % Current number of archived clauses : 39
% 0.24/0.60 % Clause-clause subsumption calls (NU) : 2240
% 0.24/0.60 % Rec. Clause-clause subsumption calls : 1977
% 0.24/0.60 % Non-unit clause-clause subsumptions : 0
% 0.24/0.60 % Unit Clause-clause subsumption calls : 16
% 0.24/0.60 % Rewrite failures with RHS unbound : 0
% 0.24/0.60 % BW rewrite match attempts : 203
% 0.24/0.60 % BW rewrite match successes : 3
% 0.24/0.60 % Condensation attempts : 0
% 0.24/0.60 % Condensation successes : 0
% 0.24/0.60 % Termbank termtop insertions : 22747
% 0.24/0.60 % Search garbage collected termcells : 93
% 0.24/0.60
% 0.24/0.60 % -------------------------------------------------
% 0.24/0.60 % User time : 0.052 s
% 0.24/0.60 % System time : 0.007 s
% 0.24/0.60 % Total time : 0.059 s
% 0.24/0.60 % Maximum resident set size: 3660 pages
% 0.24/0.60
% 0.24/0.60 % -------------------------------------------------
% 0.24/0.60 % User time : 0.210 s
% 0.24/0.60 % System time : 0.029 s
% 0.24/0.60 % Total time : 0.239 s
% 0.24/0.60 % Maximum resident set size: 4608 pages
% 0.24/0.60 % E exiting
%------------------------------------------------------------------------------