%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG038-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : 600s
% DateTime : Mon Jul 18 20:41:17 EDT 2022
% Result : Unsatisfiable 2.06s 2.25s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 57 ( 25 unt; 0 nHn; 57 RR)
% Number of literals : 119 ( 0 equ; 71 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(u,additive_identity)
| product(u,h(u,v),v) ),
file('RNG038-1.p',unknown),
[] ).
cnf(2,axiom,
product(a,b,additive_identity),
file('RNG038-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(b,additive_identity),
file('RNG038-1.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(additive_identity,u,u),
file('RNG038-1.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(u,additive_identity,u),
file('RNG038-1.p',unknown),
[] ).
cnf(7,axiom,
product(u,v,multiply(u,v)),
file('RNG038-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(u,v,add(u,v)),
file('RNG038-1.p',unknown),
[] ).
cnf(9,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG038-1.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG038-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG038-1.p',unknown),
[] ).
cnf(22,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(u,v,b) ),
inference(res,[status(thm),theory(equality)],[20,4]),
[iquote('0:Res:20.2,4.0')] ).
cnf(34,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.0,13.0')] ).
cnf(53,plain,
( ~ sum__dfg(u,additive_identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[6,20]),
[iquote('0:Res:6.0,20.0')] ).
cnf(56,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(u,v)) ),
inference(res,[status(thm),theory(equality)],[8,20]),
[iquote('0:Res:8.0,20.0')] ).
cnf(98,plain,
( ~ equal(u,additive_identity)
| ~ product(v,h(u,w),x)
| ~ product(y,v,u)
| product(y,x,w) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.1,14.0')] ).
cnf(109,plain,
equal(add(u,v),add(v,u)),
inference(res,[status(thm),theory(equality)],[34,56]),
[iquote('0:Res:34.0,56.0')] ).
cnf(131,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[6,12]),
[iquote('0:Res:6.0,12.0')] ).
cnf(133,plain,
( ~ sum__dfg(u,v,additive_inverse(w))
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[10,12]),
[iquote('0:Res:10.0,12.0')] ).
cnf(134,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,y)
| sum__dfg(y,v,add(x,w)) ),
inference(res,[status(thm),theory(equality)],[8,12]),
[iquote('0:Res:8.0,12.0')] ).
cnf(139,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,additive_identity)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(175,plain,
( ~ sum__dfg(u,v,a)
| ~ product(v,b,w)
| ~ product(u,b,x)
| sum__dfg(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(260,plain,
( ~ sum__dfg(u,v,b)
| ~ product(a,v,w)
| ~ product(a,u,x)
| sum__dfg(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,16]),
[iquote('0:Res:2.0,16.0')] ).
cnf(317,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[9,131]),
[iquote('0:Res:9.0,131.0')] ).
cnf(381,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| sum__dfg(u,additive_identity,v) ),
inference(res,[status(thm),theory(equality)],[9,139]),
[iquote('0:Res:9.0,139.0')] ).
cnf(398,plain,
sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u),
inference(res,[status(thm),theory(equality)],[9,381]),
[iquote('0:Res:9.0,381.0')] ).
cnf(418,plain,
equal(additive_inverse(additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[398,53]),
[iquote('0:Res:398.0,53.0')] ).
cnf(592,plain,
( ~ sum__dfg(u,additive_identity,v)
| sum__dfg(v,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,133]),
[iquote('0:Res:5.0,133.0')] ).
cnf(955,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_identity,add(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,134]),
[iquote('0:Res:6.0,134.0')] ).
cnf(1232,plain,
( ~ product(a,b,u)
| ~ product(additive_identity,b,v)
| sum__dfg(v,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,175]),
[iquote('0:Res:5.0,175.0')] ).
cnf(1311,plain,
( ~ product(a,b,u)
| ~ product(a,additive_identity,v)
| sum__dfg(v,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,260]),
[iquote('0:Res:5.0,260.0')] ).
cnf(1326,plain,
sum__dfg(add(u,additive_inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[8,317]),
[iquote('0:Res:8.0,317.0')] ).
cnf(1366,plain,
~ sum__dfg(add(b,additive_inverse(u)),u,additive_identity),
inference(res,[status(thm),theory(equality)],[1326,22]),
[iquote('0:Res:1326.0,22.1')] ).
cnf(1974,plain,
~ sum__dfg(u,additive_identity,add(b,additive_inverse(additive_inverse(u)))),
inference(res,[status(thm),theory(equality)],[592,1366]),
[iquote('0:Res:592.1,1366.0')] ).
cnf(1978,plain,
~ sum__dfg(u,additive_identity,add(b,u)),
inference(rew,[status(thm),theory(equality)],[418,1974]),
[iquote('0:Rew:418.0,1974.0')] ).
cnf(1981,plain,
~ sum__dfg(u,additive_identity,add(u,b)),
inference(spl,[status(thm),theory(equality)],[109,1978]),
[iquote('0:SpL:109.0,1978.0')] ).
cnf(1990,plain,
( ~ equal(u,additive_identity)
| ~ equal(u,additive_identity)
| ~ product(v,u,u)
| product(v,w,w) ),
inference(res,[status(thm),theory(equality)],[1,98]),
[iquote('0:Res:1.1,98.1')] ).
cnf(1991,plain,
( ~ equal(u,additive_identity)
| ~ product(v,u,u)
| product(v,w,w) ),
inference(obv,[status(thm),theory(equality)],[1990]),
[iquote('0:Obv:1990.0')] ).
cnf(4237,plain,
~ sum__dfg(u,b,u),
inference(res,[status(thm),theory(equality)],[955,1981]),
[iquote('0:Res:955.1,1981.0')] ).
cnf(6736,plain,
( ~ product(a,b,additive_identity)
| ~ product(additive_identity,b,u)
| equal(additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[1232,53]),
[iquote('0:Res:1232.2,53.0')] ).
cnf(6756,plain,
( ~ product(a,b,b)
| ~ product(additive_identity,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1232,4237]),
[iquote('0:Res:1232.2,4237.0')] ).
cnf(6806,plain,
( ~ product(additive_identity,b,u)
| equal(additive_identity,u) ),
inference(mrr,[status(thm)],[6736,2]),
[iquote('0:MRR:6736.0,2.0')] ).
cnf(6957,plain,
equal(multiply(additive_identity,b),additive_identity),
inference(res,[status(thm),theory(equality)],[7,6806]),
[iquote('0:Res:7.0,6806.0')] ).
cnf(6960,plain,
product(additive_identity,b,additive_identity),
inference(spr,[status(thm),theory(equality)],[6957,7]),
[iquote('0:SpR:6957.0,7.0')] ).
cnf(6969,plain,
~ product(a,b,b),
inference(mrr,[status(thm)],[6756,6960]),
[iquote('0:MRR:6756.1,6960.0')] ).
cnf(7050,plain,
( ~ product(a,b,additive_identity)
| ~ product(a,additive_identity,u)
| equal(additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[1311,53]),
[iquote('0:Res:1311.2,53.0')] ).
cnf(7119,plain,
( ~ product(a,additive_identity,u)
| equal(additive_identity,u) ),
inference(mrr,[status(thm)],[7050,2]),
[iquote('0:MRR:7050.0,2.0')] ).
cnf(7276,plain,
equal(multiply(a,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[7,7119]),
[iquote('0:Res:7.0,7119.0')] ).
cnf(7279,plain,
product(a,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[7276,7]),
[iquote('0:SpR:7276.0,7.0')] ).
cnf(7294,plain,
( ~ equal(additive_identity,additive_identity)
| product(a,u,u) ),
inference(res,[status(thm),theory(equality)],[7279,1991]),
[iquote('0:Res:7279.0,1991.1')] ).
cnf(7295,plain,
product(a,u,u),
inference(obv,[status(thm),theory(equality)],[7294]),
[iquote('0:Obv:7294.0')] ).
cnf(7296,plain,
$false,
inference(unc,[status(thm)],[7295,6969]),
[iquote('0:UnC:7295.0,6969.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG038-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 08:30:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.06/2.25
% 2.06/2.25 SPASS V 3.9
% 2.06/2.25 SPASS beiseite: Proof found.
% 2.06/2.25 % SZS status Theorem
% 2.06/2.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.06/2.25 SPASS derived 5833 clauses, backtracked 0 clauses, performed 0 splits and kept 2035 clauses.
% 2.06/2.25 SPASS allocated 67401 KBytes.
% 2.06/2.25 SPASS spent 0:00:01.88 on the problem.
% 2.06/2.25 0:00:00.04 for the input.
% 2.06/2.25 0:00:00.00 for the FLOTTER CNF translation.
% 2.06/2.25 0:00:00.06 for inferences.
% 2.06/2.25 0:00:00.00 for the backtracking.
% 2.06/2.25 0:00:01.75 for the reduction.
% 2.06/2.25
% 2.06/2.25
% 2.06/2.25 Here is a proof with depth 8, length 57 :
% 2.06/2.25 % SZS output start Refutation
% See solution above
% 2.06/2.25 Formulae used in the proof : some_property a_times_b prove_b_is_additive_identity additive_identity1 additive_identity2 closure_of_multiplication closure_of_addition left_inverse right_inverse associativity_of_addition1 associativity_of_addition2 commutativity_of_addition associativity_of_multiplication1 distributivity1 distributivity3 addition_is_well_defined
% 2.06/2.25
%------------------------------------------------------------------------------