%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Thu Jul 14 23:49:25 EDT 2022
% Result : Unsatisfiable 12.12s 12.36s
% Output : Refutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 32 ( 19 unt; 0 nHn; 32 RR)
% Number of literals : 55 ( 0 equ; 28 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sum__dfg(x__dfg,y__dfg,multiplicative_identity),
file('BOO013-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(x__dfg,z__dfg,multiplicative_identity),
file('BOO013-1.p',unknown),
[] ).
cnf(3,axiom,
product(x__dfg,y__dfg,additive_identity),
file('BOO013-1.p',unknown),
[] ).
cnf(4,axiom,
product(x__dfg,z__dfg,additive_identity),
file('BOO013-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(z__dfg,y__dfg),
file('BOO013-1.p',unknown),
[] ).
cnf(7,axiom,
product(u,v,multiply(u,v)),
file('BOO013-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('BOO013-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('BOO013-1.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(additive_identity,u,u),
file('BOO013-1.p',unknown),
[] ).
cnf(11,axiom,
sum__dfg(u,additive_identity,u),
file('BOO013-1.p',unknown),
[] ).
cnf(12,axiom,
product(multiplicative_identity,u,u),
file('BOO013-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(y,x1,v)
| ~ product(x,x1,u)
| product(z,x1,w) ),
file('BOO013-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('BOO013-1.p',unknown),
[] ).
cnf(29,plain,
( ~ product(u,v,y__dfg)
| ~ product(u,v,z__dfg) ),
inference(res,[status(thm),theory(equality)],[27,5]),
[iquote('0:Res:27.2,5.0')] ).
cnf(65,plain,
( ~ sum__dfg(u,additive_identity,v)
| ~ sum__dfg(w,x__dfg,x)
| ~ product(w,y__dfg,u)
| product(x,y__dfg,v) ),
inference(res,[status(thm),theory(equality)],[3,17]),
[iquote('0:Res:3.0,17.1')] ).
cnf(82,plain,
product(u,v,multiply(v,u)),
inference(res,[status(thm),theory(equality)],[7,9]),
[iquote('0:Res:7.0,9.0')] ).
cnf(95,plain,
sum__dfg(z__dfg,x__dfg,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(114,plain,
( ~ product(multiplicative_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[12,27]),
[iquote('0:Res:12.0,27.0')] ).
cnf(116,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,27]),
[iquote('0:Res:7.0,27.0')] ).
cnf(163,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,additive_identity)
| product(w,x,y) ),
inference(res,[status(thm),theory(equality)],[10,17]),
[iquote('0:Res:10.0,17.0')] ).
cnf(310,plain,
~ product(multiplicative_identity,z__dfg,y__dfg),
inference(res,[status(thm),theory(equality)],[12,29]),
[iquote('0:Res:12.0,29.1')] ).
cnf(333,plain,
equal(multiply(u,v),multiply(v,u)),
inference(res,[status(thm),theory(equality)],[82,116]),
[iquote('0:Res:82.0,116.0')] ).
cnf(934,plain,
( ~ sum__dfg(u,x__dfg,v)
| ~ product(u,y__dfg,w)
| product(v,y__dfg,w) ),
inference(res,[status(thm),theory(equality)],[11,65]),
[iquote('0:Res:11.0,65.0')] ).
cnf(4451,plain,
( ~ product(y__dfg,u,v)
| ~ product(x__dfg,u,additive_identity)
| product(multiplicative_identity,u,v) ),
inference(res,[status(thm),theory(equality)],[1,163]),
[iquote('0:Res:1.0,163.0')] ).
cnf(15167,plain,
( ~ product(y__dfg,z__dfg,y__dfg)
| ~ product(x__dfg,z__dfg,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4451,310]),
[iquote('0:Res:4451.2,310.0')] ).
cnf(15179,plain,
~ product(y__dfg,z__dfg,y__dfg),
inference(mrr,[status(thm)],[15167,4]),
[iquote('0:MRR:15167.1,4.0')] ).
cnf(16596,plain,
( ~ product(z__dfg,y__dfg,u)
| product(multiplicative_identity,y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[95,934]),
[iquote('0:Res:95.0,934.0')] ).
cnf(16630,plain,
product(multiplicative_identity,y__dfg,multiply(z__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[7,16596]),
[iquote('0:Res:7.0,16596.0')] ).
cnf(16642,plain,
product(multiplicative_identity,y__dfg,multiply(y__dfg,z__dfg)),
inference(rew,[status(thm),theory(equality)],[333,16630]),
[iquote('0:Rew:333.0,16630.0')] ).
cnf(16677,plain,
equal(multiply(y__dfg,z__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[16642,114]),
[iquote('0:Res:16642.0,114.0')] ).
cnf(16710,plain,
product(y__dfg,z__dfg,y__dfg),
inference(spr,[status(thm),theory(equality)],[16677,7]),
[iquote('0:SpR:16677.0,7.0')] ).
cnf(16713,plain,
$false,
inference(mrr,[status(thm)],[16710,15179]),
[iquote('0:MRR:16710.0,15179.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n023.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 : Wed Jun 1 16:30:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 12.12/12.36
% 12.12/12.36 SPASS V 3.9
% 12.12/12.36 SPASS beiseite: Proof found.
% 12.12/12.36 % SZS status Theorem
% 12.12/12.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.12/12.36 SPASS derived 13119 clauses, backtracked 0 clauses, performed 0 splits and kept 7189 clauses.
% 12.12/12.36 SPASS allocated 73795 KBytes.
% 12.12/12.36 SPASS spent 0:0:11.95 on the problem.
% 12.12/12.36 0:00:00.03 for the input.
% 12.12/12.36 0:00:00.00 for the FLOTTER CNF translation.
% 12.12/12.36 0:00:00.16 for inferences.
% 12.12/12.36 0:00:00.00 for the backtracking.
% 12.12/12.36 0:0:11.65 for the reduction.
% 12.12/12.36
% 12.12/12.36
% 12.12/12.36 Here is a proof with depth 6, length 32 :
% 12.12/12.36 % SZS output start Refutation
% See solution above
% 12.12/12.36 Formulae used in the proof : sum_to_multiplicative_identity1 sum_to_multiplicative_identity2 product_to_additive_identity1 product_to_additive_identity2 prove_both_inverse_are_equal closure_of_multiplication commutativity_of_addition commutativity_of_multiplication additive_identity1 additive_identity2 multiplicative_identity1 distributivity4 multiplication_is_well_defined
% 12.12/12.36
%------------------------------------------------------------------------------