%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG039-2 : 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 : n003.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 02:05:36 PM UTC 2026
% Result : Unsatisfiable 1.23s 0.70s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 54 ( 29 unt; 0 nHn; 35 RR)
% Number of literals : 94 ( 0 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 95 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(transitivity,axiom,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(clause43,axiom,
product(X1,multiply(X1,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
cnf(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
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(clause46,axiom,
product(a,multiply(b,c),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
cnf(clause71,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
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(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
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(clause50,axiom,
product(b,c,multiply(d,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
cnf(clause59,axiom,
product(multiply(d,b),a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_15,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_14 ).
cnf(c_0_16,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_17,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_18,plain,
( ~ product(additive_identity,X2,X1)
| equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
product(X1,multiply(X1,X2),multiply(X1,X2)),
clause43 ).
cnf(c_0_20,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_21,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_22,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
c_0_17 ).
cnf(c_0_23,plain,
equalish(multiply(additive_identity,X1),additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ product(a,multiply(b,X3),X1)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_25,axiom,
product(a,multiply(b,c),c),
clause46 ).
cnf(c_0_26,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_21 ).
cnf(c_0_27,axiom,
product(X1,X1,X1),
clause71 ).
cnf(c_0_28,plain,
( ~ equalish(X1,multiply(additive_identity,X2))
| equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
equalish(c,multiply(X1,c)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ equalish(X1,X2)
| product(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
equalish(c,additive_identity),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution2]) ).
cnf(c_0_33,plain,
( ~ product(X2,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_34,plain,
product(c,c,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
c_0_32 ).
cnf(c_0_36,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_37,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution1]) ).
cnf(c_0_38,plain,
( ~ equalish(additive_identity,X2)
| product(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_39,plain,
equalish(additive_identity,c),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,axiom,
product(b,c,multiply(d,b)),
clause50 ).
cnf(c_0_41,plain,
( ~ equalish(additive_identity,X2)
| product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( ~ product(X1,X3,X4)
| ~ equalish(X1,X2)
| product(X2,X3,X4) ),
c_0_37 ).
cnf(c_0_43,plain,
product(additive_identity,X1,c),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( ~ product(b,c,X1)
| equalish(X1,multiply(d,b)) ),
inference(spm,[status(thm)],[c_0_15,c_0_40]) ).
cnf(c_0_45,plain,
product(X1,c,additive_identity),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_46,axiom,
product(multiply(d,b),a,d),
clause59 ).
cnf(c_0_47,plain,
( ~ equalish(additive_identity,X1)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
equalish(additive_identity,multiply(d,b)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ equalish(c,d),
inference(fof_simplification,[status(thm)],[prove_c_equals_d]) ).
cnf(c_0_50,plain,
( ~ product(multiply(d,b),a,X1)
| equalish(X1,d) ),
inference(spm,[status(thm)],[c_0_15,c_0_46]) ).
cnf(c_0_51,plain,
product(multiply(d,b),X1,c),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
~ equalish(c,d),
c_0_49 ).
cnf(c_0_53,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 04:16:31 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 1.23/0.70 % Version: 3.5.1
% 1.23/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.23/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.23/0.70 % Starting new_bool_3 with 300s (1) cores
% 1.23/0.70 % Starting new_bool_1 with 300s (1) cores
% 1.23/0.70 % Starting sh5l with 300s (1) cores
% 1.23/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3382209 completed with status 0
% 1.23/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.23/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.23/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.23/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.23/0.70 % No SInE strategy applied
% 1.23/0.70 % Search class: FHUNM-FFMM22-SFFFFFNN
% 1.23/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.23/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.23/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.23/0.70 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S3S with 136s (1) cores
% 1.23/0.70 % Starting new_bool_3 with 136s (1) cores
% 1.23/0.70 % Starting new_bool_1 with 136s (1) cores
% 1.23/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3382214 completed with status 0
% 1.23/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.23/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.23/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.23/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.23/0.70 % No SInE strategy applied
% 1.23/0.70 % Search class: FHUNM-FFMM22-SFFFFFNN
% 1.23/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.23/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.23/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.23/0.70 % Preprocessing time : 0.003 s
% 1.23/0.70 % Presaturation interreduction done
% 1.23/0.70
% 1.23/0.70 % Proof found!
% 1.23/0.70 % SZS status Unsatisfiable
% 1.23/0.70 % SZS output start CNFRefutation
% See solution above
% 1.23/0.70 % Parsed axioms : 74
% 1.23/0.70 % Removed by relevancy pruning/SinE : 0
% 1.23/0.70 % Initial clauses : 74
% 1.23/0.70 % Removed in clause preprocessing : 0
% 1.23/0.70 % Initial clauses in saturation : 74
% 1.23/0.70 % Processed clauses : 555
% 1.23/0.70 % ...of these trivial : 37
% 1.23/0.70 % ...subsumed : 4
% 1.23/0.70 % ...remaining for further processing : 514
% 1.23/0.70 % Other redundant clauses eliminated : 0
% 1.23/0.70 % Clauses deleted for lack of memory : 0
% 1.23/0.70 % Backward-subsumed : 12
% 1.23/0.70 % Backward-rewritten : 37
% 1.23/0.70 % Generated clauses : 4084
% 1.23/0.70 % ...of the previous two non-redundant : 3309
% 1.23/0.70 % ...aggressively subsumed : 0
% 1.23/0.70 % Contextual simplify-reflections : 0
% 1.23/0.70 % Paramodulations : 4084
% 1.23/0.70 % Factorizations : 0
% 1.23/0.70 % NegExts : 0
% 1.23/0.70 % Equation resolutions : 0
% 1.23/0.70 % Disequality decompositions : 0
% 1.23/0.70 % Total rewrite steps : 846
% 1.23/0.70 % ...of those cached : 597
% 1.23/0.70 % Propositional unsat checks : 0
% 1.23/0.70 % Propositional check models : 0
% 1.23/0.70 % Propositional check unsatisfiable : 0
% 1.23/0.70 % Propositional clauses : 0
% 1.23/0.70 % Propositional clauses after purity: 0
% 1.23/0.70 % Propositional unsat core size : 0
% 1.23/0.70 % Propositional preprocessing time : 0.000
% 1.23/0.70 % Propositional encoding time : 0.000
% 1.23/0.70 % Propositional solver time : 0.000
% 1.23/0.70 % Success case prop preproc time : 0.000
% 1.23/0.70 % Success case prop encoding time : 0.000
% 1.23/0.70 % Success case prop solver time : 0.000
% 1.23/0.70 % Current number of processed clauses : 391
% 1.23/0.70 % Positive orientable unit clauses : 185
% 1.23/0.70 % Positive unorientable unit clauses: 0
% 1.23/0.70 % Negative unit clauses : 1
% 1.23/0.70 % Non-unit-clauses : 205
% 1.23/0.70 % Current number of unprocessed clauses: 2834
% 1.23/0.70 % ...number of literals in the above : 5031
% 1.23/0.70 % Current number of archived formulas : 0
% 1.23/0.70 % Current number of archived clauses : 123
% 1.23/0.70 % Clause-clause subsumption calls (NU) : 2297
% 1.23/0.70 % Rec. Clause-clause subsumption calls : 1984
% 1.23/0.70 % Non-unit clause-clause subsumptions : 16
% 1.23/0.70 % Unit Clause-clause subsumption calls : 4
% 1.23/0.70 % Rewrite failures with RHS unbound : 0
% 1.23/0.70 % BW rewrite match attempts : 520
% 1.23/0.70 % BW rewrite match successes : 37
% 1.23/0.70 % Condensation attempts : 0
% 1.23/0.70 % Condensation successes : 0
% 1.23/0.70 % Termbank termtop insertions : 43110
% 1.23/0.70 % Search garbage collected termcells : 103
% 1.23/0.70
% 1.23/0.70 % -------------------------------------------------
% 1.23/0.70 % User time : 0.092 s
% 1.23/0.70 % System time : 0.009 s
% 1.23/0.70 % Total time : 0.102 s
% 1.23/0.70 % Maximum resident set size: 3680 pages
% 1.23/0.70
% 1.23/0.70 % -------------------------------------------------
% 1.23/0.70 % User time : 0.697 s
% 1.23/0.70 % System time : 0.059 s
% 1.23/0.70 % Total time : 0.756 s
% 1.23/0.70 % Maximum resident set size: 4608 pages
% 1.23/0.70 % E exiting
%------------------------------------------------------------------------------