%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM017-1 : 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 : n008.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 01:44:15 PM UTC 2026
% Result : Unsatisfiable 186.63s 27.94s
% Output : CNFRefutation 186.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 53 ( 11 unt; 0 nHn; 43 RR)
% Number of literals : 123 ( 0 equ; 74 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 147 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_divisible_by_operand,axiom,
( ~ product(X1,X2,X3)
| divides(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_divisible_by_operand) ).
cnf(primes_lemma1,axiom,
( ~ prime(X1)
| ~ product(X3,X3,X2)
| ~ divides(X1,X2)
| divides(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',primes_lemma1) ).
cnf(closure_of_product,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
cnf(product_associativity1,axiom,
( ~ product(X1,X4,X6)
| ~ product(X4,X5,X2)
| ~ product(X1,X2,X3)
| product(X6,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_associativity1) ).
cnf(divides_implies_product,axiom,
( ~ divides(X1,X2)
| product(X1,second_divided_by_1st(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_implies_product) ).
cnf(well_defined_product,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_product) ).
cnf(product_commutativity,axiom,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_commutativity) ).
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(product_left_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(divides_substitution1,axiom,
( ~ divides(X3,X1)
| ~ equalish(X1,X2)
| divides(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_substitution1) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X1,b)
| ~ divides(X1,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
cnf(c_0_12,plain,
( ~ product(X1,X2,X3)
| divides(X1,X3) ),
inference(fof_simplification,[status(thm)],[product_divisible_by_operand]) ).
cnf(c_0_13,plain,
( ~ prime(X1)
| ~ product(X3,X3,X2)
| ~ divides(X1,X2)
| divides(X1,X3) ),
inference(fof_simplification,[status(thm)],[primes_lemma1]) ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X3)
| divides(X1,X3) ),
c_0_12 ).
cnf(c_0_15,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_product ).
cnf(c_0_16,plain,
( ~ prime(X1)
| ~ product(X3,X3,X2)
| ~ divides(X1,X2)
| divides(X1,X3) ),
c_0_13 ).
cnf(c_0_17,plain,
divides(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ product(X1,X4,X6)
| ~ product(X4,X5,X2)
| ~ product(X1,X2,X3)
| product(X6,X5,X3) ),
inference(fof_simplification,[status(thm)],[product_associativity1]) ).
cnf(c_0_19,plain,
( ~ divides(X1,X2)
| product(X1,second_divided_by_1st(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[divides_implies_product]) ).
cnf(c_0_20,plain,
( ~ product(X2,X2,multiply(X1,X3))
| ~ prime(X1)
| divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X4,X3) ),
inference(fof_simplification,[status(thm)],[well_defined_product]) ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[product_commutativity]) ).
cnf(c_0_23,plain,
( ~ product(X1,X4,X6)
| ~ product(X4,X5,X2)
| ~ product(X1,X2,X3)
| product(X6,X5,X3) ),
c_0_18 ).
cnf(c_0_24,plain,
( ~ divides(X1,X2)
| product(X1,second_divided_by_1st(X1,X2),X2) ),
c_0_19 ).
cnf(c_0_25,plain,
( ~ prime(X1)
| divides(X1,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X4,X3) ),
c_0_21 ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_22 ).
cnf(c_0_28,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
( ~ prime(X1)
| product(X1,second_divided_by_1st(X1,X1),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution2]) ).
cnf(c_0_31,plain,
( ~ product(X1,X2,X3)
| equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_32,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_33,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_34,plain,
( ~ product(X1,multiply(second_divided_by_1st(X1,X1),X2),X3)
| ~ prime(X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
c_0_30 ).
cnf(c_0_36,plain,
equalish(multiply(X1,X2),multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ divides(X3,X1)
| ~ equalish(X1,X2)
| divides(X3,X2) ),
inference(fof_simplification,[status(thm)],[divides_substitution1]) ).
cnf(c_0_38,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_33 ).
cnf(c_0_39,plain,
( ~ prime(X1)
| product(X1,X2,multiply(X1,multiply(second_divided_by_1st(X1,X1),X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_40,plain,
( ~ product(X1,multiply(X3,X2),X4)
| product(X1,multiply(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( ~ divides(X3,X1)
| ~ equalish(X1,X2)
| divides(X3,X2) ),
c_0_37 ).
cnf(c_0_42,plain,
divides(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_43,plain,
( ~ product(X3,X1,multiply(X3,multiply(second_divided_by_1st(X3,X3),X2)))
| ~ prime(X3)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
product(X1,multiply(X2,X3),multiply(X1,multiply(X3,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_15]) ).
cnf(c_0_45,negated_conjecture,
( ~ divides(X1,b)
| ~ divides(X1,c) ),
inference(fof_simplification,[status(thm)],[prove_there_is_no_common_divisor]) ).
cnf(c_0_46,plain,
( ~ equalish(multiply(X3,X1),X2)
| divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( ~ prime(X2)
| equalish(multiply(X1,second_divided_by_1st(X2,X2)),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( ~ divides(X1,b)
| ~ divides(X1,c) ),
c_0_45 ).
cnf(c_0_49,plain,
( ~ prime(X1)
| divides(second_divided_by_1st(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,hypothesis,
prime(a),
a_is_prime ).
cnf(c_0_51,negated_conjecture,
~ prime(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49]) ).
cnf(c_0_52,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_50,c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.51 % Computer : n008.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 01:59:39 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.55 Running first-order theorem proving
% 0.09/0.55 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
% 186.63/27.94 % Version: 3.5.1
% 186.63/27.94 % Preprocessing class: FSMSSMSSSSSNFFN.
% 186.63/27.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 186.63/27.94 % Starting new_bool_3 with 300s (1) cores
% 186.63/27.94 % Starting new_bool_1 with 300s (1) cores
% 186.63/27.94 % Starting sh5l with 300s (1) cores
% 186.63/27.94 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4110800 completed with status 0
% 186.63/27.94 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 186.63/27.94 % Preprocessing class: FSMSSMSSSSSNFFN.
% 186.63/27.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 186.63/27.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 186.63/27.94 % No SInE strategy applied
% 186.63/27.94 % Search class: FHHNS-FFMS22-SFFFFFNN
% 186.63/27.94 % partial match(2): FGHNF-FFMS22-SFFFFFNN
% 186.63/27.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 186.63/27.94 % Starting SubtermCWHack with 136s (1) cores
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 186.63/27.94 % Starting new_bool_3 with 136s (1) cores
% 186.63/27.94 % Starting new_bool_1 with 136s (1) cores
% 186.63/27.94 % new_bool_1 with pid 4110813 completed with status 0
% 186.63/27.94 % Result found by new_bool_1
% 186.63/27.94 % Preprocessing class: FSMSSMSSSSSNFFN.
% 186.63/27.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 186.63/27.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 186.63/27.94 % No SInE strategy applied
% 186.63/27.94 % Search class: FHHNS-FFMS22-SFFFFFNN
% 186.63/27.94 % partial match(2): FGHNF-FFMS22-SFFFFFNN
% 186.63/27.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 186.63/27.94 % Starting SubtermCWHack with 136s (1) cores
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 186.63/27.94 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 186.63/27.94 % Starting new_bool_3 with 136s (1) cores
% 186.63/27.94 % Starting new_bool_1 with 136s (1) cores
% 186.63/27.94 % Preprocessing time : 0.001 s
% 186.63/27.94 % Presaturation interreduction done
% 186.63/27.94
% 186.63/27.94 % Proof found!
% 186.63/27.94 % SZS status Unsatisfiable
% 186.63/27.94 % SZS output start CNFRefutation
% See solution above
% 186.63/27.94 % Parsed axioms : 24
% 186.63/27.94 % Removed by relevancy pruning/SinE : 0
% 186.63/27.94 % Initial clauses : 24
% 186.63/27.94 % Removed in clause preprocessing : 0
% 186.63/27.94 % Initial clauses in saturation : 24
% 186.63/27.94 % Processed clauses : 22571
% 186.63/27.94 % ...of these trivial : 2723
% 186.63/27.94 % ...subsumed : 4930
% 186.63/27.94 % ...remaining for further processing : 14918
% 186.63/27.94 % Other redundant clauses eliminated : 0
% 186.63/27.94 % Clauses deleted for lack of memory : 0
% 186.63/27.94 % Backward-subsumed : 3948
% 186.63/27.94 % Backward-rewritten : 517
% 186.63/27.94 % Generated clauses : 873623
% 186.63/27.94 % ...of the previous two non-redundant : 771239
% 186.63/27.94 % ...aggressively subsumed : 0
% 186.63/27.94 % Contextual simplify-reflections : 1
% 186.63/27.94 % Paramodulations : 873619
% 186.63/27.94 % Factorizations : 0
% 186.63/27.94 % NegExts : 0
% 186.63/27.94 % Equation resolutions : 0
% 186.63/27.94 % Disequality decompositions : 0
% 186.63/27.94 % Total rewrite steps : 106183
% 186.63/27.94 % ...of those cached : 80848
% 186.63/27.94 % Propositional unsat checks : 2
% 186.63/27.94 % Propositional check models : 0
% 186.63/27.94 % Propositional check unsatisfiable : 0
% 186.63/27.94 % Propositional clauses : 0
% 186.63/27.94 % Propositional clauses after purity: 0
% 186.63/27.94 % Propositional unsat core size : 0
% 186.63/27.94 % Propositional preprocessing time : 0.000
% 186.63/27.94 % Propositional encoding time : 1.029
% 186.63/27.94 % Propositional solver time : 1.365
% 186.63/27.94 % Success case prop preproc time : 0.000
% 186.63/27.94 % Success case prop encoding time : 0.000
% 186.63/27.94 % Success case prop solver time : 0.000
% 186.63/27.94 % Current number of processed clauses : 10425
% 186.63/27.94 % Positive orientable unit clauses : 2798
% 186.63/27.94 % Positive unorientable unit clauses: 0
% 186.63/27.94 % Negative unit clauses : 4
% 186.63/27.94 % Non-unit-clauses : 7623
% 186.63/27.94 % Current number of unprocessed clauses: 747341
% 186.63/27.94 % ...number of literals in the above : 1038489
% 186.63/27.94 % Current number of archived formulas : 0
% 186.63/27.94 % Current number of archived clauses : 4493
% 186.63/27.94 % Clause-clause subsumption calls (NU) : 7407486
% 186.63/27.94 % Rec. Clause-clause subsumption calls : 6106142
% 186.63/27.94 % Non-unit clause-clause subsumptions : 6462
% 186.63/27.94 % Unit Clause-clause subsumption calls : 189963
% 186.63/27.94 % Rewrite failures with RHS unbound : 0
% 186.63/27.94 % BW rewrite match attempts : 77878
% 186.63/27.94 % BW rewrite match successes : 508
% 186.63/27.94 % Condensation attempts : 0
% 186.63/27.94 % Condensation successes : 0
% 186.63/27.94 % Termbank termtop insertions : 16395336
% 186.63/27.94 % Search garbage collected termcells : 72
% 186.63/27.94
% 186.63/27.94 % -------------------------------------------------
% 186.63/27.94 % User time : 25.690 s
% 186.63/27.94 % System time : 0.922 s
% 186.63/27.94 % Total time : 26.612 s
% 186.63/27.94 % Maximum resident set size: 3648 pages
% 186.63/27.94
% 186.63/27.94 % -------------------------------------------------
% 186.63/27.94 % User time : 128.268 s
% 186.63/27.94 % System time : 3.847 s
% 186.63/27.94 % Total time : 132.115 s
% 186.63/27.94 % Maximum resident set size: 4608 pages
% 186.63/27.94 % E exiting
%------------------------------------------------------------------------------