TSTP Solution File: NUM007-1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.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 : Thu Aug 31 11:28:16 EDT 2023
% Result : Unsatisfiable 143.45s 19.74s
% Output : CNFRefutation 143.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of clauses : 61 ( 16 unt; 4 nHn; 49 RR)
% Number of literals : 148 ( 21 equ; 84 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_50,plain,
( ~ divides(X0,X1)
| ~ divides(X1,X2)
| divides(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_divides) ).
cnf(c_51,plain,
divides(X0,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operand_divides_product) ).
cnf(c_52,plain,
( ~ divides(X0,X1)
| divides(multiply(X2,X0),multiply(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_and_multiply) ).
cnf(c_55,plain,
( ~ divides(multiply(X0,X1),X2)
| ~ divides(X1,X2)
| divides(X0,quotient(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply2) ).
cnf(c_56,plain,
( ~ divides(X0,multiply(X1,X2))
| ~ divides(X1,X0)
| divides(quotient(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_quotient_multiply3) ).
cnf(c_57,plain,
( ~ gcd(X0,X1,X2)
| divides(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides1) ).
cnf(c_58,plain,
( ~ gcd(X0,X1,X2)
| divides(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_divides2) ).
cnf(c_59,plain,
( ~ gcd(X0,X1,X2)
| ~ divides(X3,X0)
| ~ divides(X3,X1)
| divides(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd1) ).
cnf(c_63,plain,
( ~ gcd(X0,X1,X2)
| gcd(multiply(X3,X0),multiply(X3,X1),multiply(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_gcd) ).
cnf(c_64,plain,
( ~ divides(X0,X1)
| ~ divides(X2,X1)
| divides(X0,k(X2,X0,X1))
| lcm(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm1) ).
cnf(c_65,plain,
( ~ divides(X0,X1)
| ~ divides(X2,X1)
| divides(X2,k(X2,X0,X1))
| lcm(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm2) ).
cnf(c_66,plain,
( ~ divides(X0,k(X1,X2,X0))
| ~ divides(X1,X0)
| ~ divides(X2,X0)
| lcm(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcm3) ).
cnf(c_69,plain,
multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c_70,plain,
( ~ lcm(X0,X1,X2)
| lcm(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_lcm) ).
cnf(c_72,negated_conjecture,
gcd(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_gcd_of_a_and_b) ).
cnf(c_73,negated_conjecture,
~ lcm(a,b,quotient(multiply(a,b),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lcm) ).
cnf(c_239,plain,
X0 = X0,
theory(equality) ).
cnf(c_242,plain,
( X0 != X1
| X2 != X3
| ~ divides(X1,X3)
| divides(X0,X2) ),
theory(equality) ).
cnf(c_636,plain,
( ~ lcm(b,a,quotient(multiply(a,b),c))
| lcm(a,b,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_646,plain,
( ~ divides(multiply(X0,X1),multiply(X2,X3))
| ~ divides(X1,multiply(X2,X3))
| divides(X0,quotient(multiply(X2,X3),X1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_658,plain,
( multiply(X0,X1) != X2
| X3 != X4
| ~ divides(X2,X4)
| divides(multiply(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_242]) ).
cnf(c_660,plain,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(a,k(a,b,quotient(multiply(a,b),c)))
| lcm(b,a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_661,plain,
( ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| divides(b,k(a,b,quotient(multiply(a,b),c)))
| lcm(b,a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_662,plain,
( ~ divides(quotient(multiply(a,b),c),k(a,b,quotient(multiply(a,b),c)))
| ~ divides(a,quotient(multiply(a,b),c))
| ~ divides(b,quotient(multiply(a,b),c))
| lcm(b,a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_721,plain,
( multiply(X0,X1) != multiply(X0,X1)
| X2 != X3
| ~ divides(multiply(X0,X1),X3)
| divides(multiply(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_658]) ).
cnf(c_722,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(instantiation,[status(thm)],[c_239]) ).
cnf(c_737,plain,
( ~ divides(multiply(b,c),multiply(a,b))
| ~ divides(c,multiply(a,b))
| divides(b,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_646]) ).
cnf(c_806,plain,
( ~ divides(multiply(a,b),multiply(c,k(a,b,quotient(multiply(a,b),c))))
| ~ divides(c,multiply(a,b))
| divides(quotient(multiply(a,b),c),k(a,b,quotient(multiply(a,b),c))) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_1222,plain,
divides(c,b),
inference(superposition,[status(thm)],[c_72,c_57]) ).
cnf(c_1230,plain,
divides(c,a),
inference(superposition,[status(thm)],[c_72,c_58]) ).
cnf(c_1231,plain,
divides(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_69,c_51]) ).
cnf(c_1267,plain,
( ~ divides(b,X0)
| divides(c,X0) ),
inference(superposition,[status(thm)],[c_1222,c_50]) ).
cnf(c_1268,plain,
( ~ divides(multiply(X0,X1),X2)
| divides(X1,X2) ),
inference(superposition,[status(thm)],[c_1231,c_50]) ).
cnf(c_1281,plain,
divides(c,multiply(X0,b)),
inference(superposition,[status(thm)],[c_1231,c_1267]) ).
cnf(c_1282,plain,
divides(c,multiply(a,b)),
inference(instantiation,[status(thm)],[c_1281]) ).
cnf(c_1355,plain,
( ~ divides(X0,X1)
| divides(multiply(X0,X2),multiply(X2,X1)) ),
inference(superposition,[status(thm)],[c_69,c_52]) ).
cnf(c_1357,plain,
( ~ divides(X0,X1)
| divides(multiply(X2,X0),multiply(X1,X2)) ),
inference(superposition,[status(thm)],[c_69,c_52]) ).
cnf(c_1748,plain,
( ~ divides(X0,X1)
| divides(multiply(b,X0),multiply(b,X1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_2316,plain,
( ~ divides(X0,X1)
| divides(multiply(X0,X2),multiply(X1,X2)) ),
inference(superposition,[status(thm)],[c_69,c_1355]) ).
cnf(c_3639,plain,
( ~ divides(multiply(X0,X1),X2)
| divides(X0,quotient(X2,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_55,c_1268]) ).
cnf(c_3644,plain,
( ~ divides(X0,X1)
| divides(X2,quotient(multiply(X2,X1),X0)) ),
inference(superposition,[status(thm)],[c_52,c_3639]) ).
cnf(c_5560,plain,
( ~ divides(X0,multiply(X1,X2))
| ~ divides(X0,multiply(X1,X3))
| ~ gcd(X2,X3,X4)
| divides(X0,multiply(X1,X4)) ),
inference(superposition,[status(thm)],[c_63,c_59]) ).
cnf(c_6168,plain,
multiply(a,b) = multiply(b,a),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_7158,plain,
( ~ divides(c,X0)
| divides(multiply(b,c),multiply(b,X0)) ),
inference(instantiation,[status(thm)],[c_1748]) ).
cnf(c_7159,plain,
( ~ divides(c,a)
| divides(multiply(b,c),multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_7158]) ).
cnf(c_8158,plain,
( multiply(a,b) != X0
| multiply(b,c) != multiply(b,c)
| ~ divides(multiply(b,c),X0)
| divides(multiply(b,c),multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_721]) ).
cnf(c_8164,plain,
( multiply(c,k(a,b,quotient(multiply(a,b),c))) != X0
| multiply(a,b) != multiply(a,b)
| ~ divides(multiply(a,b),X0)
| divides(multiply(a,b),multiply(c,k(a,b,quotient(multiply(a,b),c)))) ),
inference(instantiation,[status(thm)],[c_721]) ).
cnf(c_14346,plain,
multiply(b,c) = multiply(b,c),
inference(instantiation,[status(thm)],[c_722]) ).
cnf(c_14908,plain,
multiply(a,b) = multiply(a,b),
inference(instantiation,[status(thm)],[c_722]) ).
cnf(c_15785,plain,
multiply(c,k(a,b,quotient(multiply(a,b),c))) = multiply(k(a,b,quotient(multiply(a,b),c)),c),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_28168,plain,
( multiply(a,b) != multiply(b,a)
| multiply(b,c) != multiply(b,c)
| ~ divides(multiply(b,c),multiply(b,a))
| divides(multiply(b,c),multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_8158]) ).
cnf(c_42655,plain,
( multiply(c,k(a,b,quotient(multiply(a,b),c))) != multiply(k(a,b,quotient(multiply(a,b),c)),c)
| multiply(a,b) != multiply(a,b)
| ~ divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),c))
| divides(multiply(a,b),multiply(c,k(a,b,quotient(multiply(a,b),c)))) ),
inference(instantiation,[status(thm)],[c_8164]) ).
cnf(c_136893,plain,
( ~ divides(b,X0)
| divides(multiply(a,b),multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_1357]) ).
cnf(c_136941,plain,
( ~ divides(a,X0)
| divides(multiply(a,b),multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_2316]) ).
cnf(c_138892,plain,
( ~ divides(multiply(X0,X1),multiply(X2,X3))
| ~ divides(multiply(X0,X1),multiply(X2,X4))
| ~ gcd(X3,X4,X5)
| divides(multiply(X0,X1),multiply(X2,X5)) ),
inference(instantiation,[status(thm)],[c_5560]) ).
cnf(c_139062,plain,
( ~ divides(c,b)
| divides(a,quotient(multiply(a,b),c)) ),
inference(instantiation,[status(thm)],[c_3644]) ).
cnf(c_168960,plain,
( ~ divides(b,k(a,b,quotient(multiply(a,b),c)))
| divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),a)) ),
inference(instantiation,[status(thm)],[c_136893]) ).
cnf(c_372100,plain,
( ~ divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),X0))
| ~ divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),X1))
| ~ gcd(X0,X1,c)
| divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),c)) ),
inference(instantiation,[status(thm)],[c_138892]) ).
cnf(c_383469,plain,
( ~ divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),a))
| ~ divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),b))
| ~ gcd(a,b,c)
| divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),c)) ),
inference(instantiation,[status(thm)],[c_372100]) ).
cnf(c_393285,plain,
( ~ divides(a,k(a,b,quotient(multiply(a,b),c)))
| divides(multiply(a,b),multiply(k(a,b,quotient(multiply(a,b),c)),b)) ),
inference(instantiation,[status(thm)],[c_136941]) ).
cnf(c_393286,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_393285,c_383469,c_168960,c_139062,c_42655,c_28168,c_15785,c_14908,c_14346,c_7159,c_6168,c_1282,c_1230,c_1222,c_806,c_737,c_662,c_660,c_661,c_636,c_73,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Aug 25 17:30:13 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 143.45/19.74 % SZS status Started for theBenchmark.p
% 143.45/19.74 % SZS status Unsatisfiable for theBenchmark.p
% 143.45/19.74
% 143.45/19.74 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 143.45/19.74
% 143.45/19.74 ------ iProver source info
% 143.45/19.74
% 143.45/19.74 git: date: 2023-05-31 18:12:56 +0000
% 143.45/19.74 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 143.45/19.74 git: non_committed_changes: false
% 143.45/19.74 git: last_make_outside_of_git: false
% 143.45/19.74
% 143.45/19.74 ------ Parsing...successful
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 143.45/19.74
% 143.45/19.74 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 143.45/19.74
% 143.45/19.74 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 143.45/19.74 ------ Proving...
% 143.45/19.74 ------ Problem Properties
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74 clauses 25
% 143.45/19.74 conjectures 2
% 143.45/19.74 EPR 8
% 143.45/19.74 Horn 21
% 143.45/19.74 unary 8
% 143.45/19.74 binary 6
% 143.45/19.74 lits 60
% 143.45/19.74 lits eq 3
% 143.45/19.74 fd_pure 0
% 143.45/19.74 fd_pseudo 0
% 143.45/19.74 fd_cond 0
% 143.45/19.74 fd_pseudo_cond 0
% 143.45/19.74 AC symbols 0
% 143.45/19.74
% 143.45/19.74 ------ Input Options Time Limit: Unbounded
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74 ------
% 143.45/19.74 Current options:
% 143.45/19.74 ------
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74 ------ Proving...
% 143.45/19.74
% 143.45/19.74
% 143.45/19.74 % SZS status Unsatisfiable for theBenchmark.p
% 143.45/19.74
% 143.45/19.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 143.45/19.74
% 143.45/19.74
%------------------------------------------------------------------------------