%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM017-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:52:43 PM UTC 2026
% Result : Unsatisfiable 55.44s 32.25s
% Output : CNFRefutation 55.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of clauses : 86 ( 22 unt; 0 nHn; 70 RR)
% Number of literals : 186 ( 22 equ; 110 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 178 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_associativity2,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ product(X6,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_associativity2) ).
cnf(c_squared,hypothesis,
product(c,c,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_squared) ).
cnf(product_left_cancellation,axiom,
( X2 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(closure_of_product,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
cnf(product_divisible_by_operand,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_divisible_by_operand) ).
cnf(divides_implies_product,axiom,
( product(X1,second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides_implies_product) ).
cnf(well_defined_product,axiom,
( X4 = X3
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_product) ).
cnf(product_associativity1,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ product(X1,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_associativity1) ).
cnf(product_commutativity,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_commutativity) ).
cnf(transitivity_of_divides,axiom,
( divides(X3,X2)
| ~ divides(X1,X2)
| ~ divides(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divides) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X1,c)
| ~ divides(X1,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(primes_lemma1,axiom,
( divides(X1,X3)
| ~ divides(X1,X2)
| ~ product(X3,X3,X2)
| ~ prime(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',primes_lemma1) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
cnf(c_0_13,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ product(X6,X4,X1) ),
product_associativity2 ).
cnf(c_0_14,hypothesis,
product(c,c,e),
c_squared ).
cnf(c_0_15,axiom,
( X2 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_left_cancellation ).
cnf(c_0_16,hypothesis,
( product(c,X1,X2)
| ~ product(c,X3,X1)
| ~ product(e,X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_product ).
cnf(c_0_18,hypothesis,
( X1 = c
| ~ product(c,X1,e) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,hypothesis,
( product(c,multiply(c,X1),X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
product_divisible_by_operand ).
cnf(c_0_21,plain,
( X1 = X2
| ~ product(X3,X1,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,hypothesis,
( multiply(c,X1) = c
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
divides(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_24,axiom,
( product(X1,second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
divides_implies_product ).
cnf(c_0_25,axiom,
( X4 = X3
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
well_defined_product ).
cnf(c_0_26,hypothesis,
( X1 = X2
| ~ product(c,X1,c)
| ~ product(e,X2,e) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,hypothesis,
( divides(c,c)
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_28,plain,
( X1 = second_divided_by_1st(X2,X3)
| ~ product(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_20]) ).
cnf(c_0_29,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_30,hypothesis,
( second_divided_by_1st(c,c) = X1
| ~ product(e,X1,e) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_27]) ).
cnf(c_0_31,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ product(X1,X4,X6) ),
product_associativity1 ).
cnf(c_0_32,hypothesis,
( multiply(c,X1) = second_divided_by_1st(c,X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_33,plain,
( multiply(X1,second_divided_by_1st(X1,X2)) = X2
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_34,hypothesis,
( second_divided_by_1st(e,e) = second_divided_by_1st(c,c)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_35,hypothesis,
divides(c,e),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_36,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_37,hypothesis,
second_divided_by_1st(c,multiply(e,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_38,hypothesis,
( multiply(e,second_divided_by_1st(c,c)) = e
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,hypothesis,
second_divided_by_1st(c,e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_35])]) ).
cnf(c_0_40,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
product_commutativity ).
cnf(c_0_41,plain,
( product(X1,X2,multiply(X3,multiply(X4,X2)))
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_42,hypothesis,
( multiply(c,second_divided_by_1st(c,c)) = c
| ~ divides(e,e) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( product(X1,second_divided_by_1st(X2,X3),X4)
| ~ divides(X2,X3)
| ~ product(X5,X2,X1)
| ~ product(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_44,plain,
( product(second_divided_by_1st(X1,X2),X1,X2)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_45,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_46,plain,
( multiply(X1,X2) = X2
| ~ product(X3,X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_47,hypothesis,
( product(c,second_divided_by_1st(c,c),c)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_48,hypothesis,
( product(e,second_divided_by_1st(c,X1),X2)
| ~ divides(c,X1)
| ~ product(c,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_14]) ).
cnf(c_0_49,axiom,
( divides(X3,X2)
| ~ divides(X1,X2)
| ~ divides(X3,X1) ),
transitivity_of_divides ).
cnf(c_0_50,plain,
( divides(second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_51,plain,
divides(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_52,hypothesis,
( multiply(second_divided_by_1st(c,c),X1) = X1
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,hypothesis,
( divides(e,X1)
| ~ divides(c,X2)
| ~ product(c,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_48]) ).
cnf(c_0_54,hypothesis,
( product(X1,c,X2)
| ~ product(X3,c,X1)
| ~ product(X3,e,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_55,negated_conjecture,
( ~ divides(X1,c)
| ~ divides(X1,b) ),
prove_there_is_no_common_divisor ).
cnf(c_0_56,plain,
( divides(second_divided_by_1st(X1,X2),X3)
| ~ divides(X2,X3)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,hypothesis,
( divides(X1,X1)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,hypothesis,
( divides(e,e)
| ~ divides(c,c) ),
inference(spm,[status(thm)],[c_0_53,c_0_14]) ).
cnf(c_0_59,hypothesis,
( product(multiply(X1,c),c,X2)
| ~ product(X1,e,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_17]) ).
cnf(c_0_60,negated_conjecture,
( ~ divides(second_divided_by_1st(X1,X2),b)
| ~ divides(X2,c)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,hypothesis,
( divides(second_divided_by_1st(c,c),X1)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_62,hypothesis,
( divides(X1,X1)
| ~ divides(c,c) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
( divides(c,c)
| ~ divides(c,X1)
| ~ product(c,X1,e) ),
inference(spm,[status(thm)],[c_0_27,c_0_48]) ).
cnf(c_0_64,hypothesis,
( product(c,multiply(X1,c),X2)
| ~ product(X1,e,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
~ divides(c,c),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_66,plain,
( product(second_divided_by_1st(X1,X2),X3,X4)
| ~ divides(X1,X2)
| ~ product(X1,X5,X3)
| ~ product(X2,X5,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_44]) ).
cnf(c_0_67,hypothesis,
( divides(c,X1)
| ~ divides(e,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_68,hypothesis,
~ product(X1,e,e),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_51])]),c_0_65]) ).
cnf(c_0_69,hypothesis,
( product(second_divided_by_1st(c,X1),e,X2)
| ~ divides(c,X1)
| ~ product(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_14]) ).
cnf(c_0_70,hypothesis,
second_divided_by_1st(c,multiply(X1,e)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_71,hypothesis,
divides(c,multiply(X1,e)),
inference(spm,[status(thm)],[c_0_67,c_0_51]) ).
cnf(c_0_72,plain,
( product(X1,second_divided_by_1st(second_divided_by_1st(X2,X1),X3),X4)
| ~ divides(second_divided_by_1st(X2,X1),X3)
| ~ divides(X2,X1)
| ~ product(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_73,hypothesis,
( ~ divides(c,X1)
| ~ product(X1,c,e) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,axiom,
( divides(X1,X3)
| ~ divides(X1,X2)
| ~ product(X3,X3,X2)
| ~ prime(X1) ),
primes_lemma1 ).
cnf(c_0_75,hypothesis,
product(multiply(c,X1),c,multiply(X1,e)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_70]),c_0_71])]) ).
cnf(c_0_76,plain,
( multiply(second_divided_by_1st(second_divided_by_1st(X1,X2),X3),X4) = X4
| ~ divides(second_divided_by_1st(X1,X2),X3)
| ~ product(X1,X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_72]),c_0_20]) ).
cnf(c_0_77,hypothesis,
~ product(multiply(c,X1),c,e),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_78,plain,
( divides(X1,X2)
| ~ prime(X1)
| ~ divides(X1,multiply(X2,X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_17]) ).
cnf(c_0_79,hypothesis,
( ~ divides(second_divided_by_1st(X1,X2),X3)
| ~ product(X1,X3,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_80,plain,
( divides(X1,X1)
| ~ prime(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_81,hypothesis,
prime(a),
a_is_prime ).
cnf(c_0_82,hypothesis,
~ product(X1,X2,X2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_50]),c_0_20]) ).
cnf(c_0_83,hypothesis,
divides(a,a),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,hypothesis,
~ divides(X1,X1),
inference(spm,[status(thm)],[c_0_82,c_0_44]) ).
cnf(c_0_85,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_83,c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM017-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 00:06:01 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 55.44/32.25 % Version : CSE_E---1.7
% 55.44/32.25 % Problem : theBenchmark.p
% 55.44/32.25 % SZS status Unsatisfiable for theBenchmark.p
% 55.44/32.25 % SZS output start CNFRefutation
% See solution above
% 55.64/32.47 % Total time : 24.388s
%------------------------------------------------------------------------------