%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD025-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : 600s
% DateTime : Sat Jul 16 02:28:22 EDT 2022
% Result : Unsatisfiable 0.15s 0.53s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 44 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
defined(u__dfg),
file('FLD025-5.p',unknown),
[] ).
cnf(7,axiom,
product(multiplicative_identity,a,b),
file('FLD025-5.p',unknown),
[] ).
cnf(8,axiom,
product(multiplicative_identity,c,d),
file('FLD025-5.p',unknown),
[] ).
cnf(9,axiom,
product(a,c,u__dfg),
file('FLD025-5.p',unknown),
[] ).
cnf(10,axiom,
product(d,b,v__dfg),
file('FLD025-5.p',unknown),
[] ).
cnf(11,axiom,
~ product(multiplicative_identity,u__dfg,v__dfg),
file('FLD025-5.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD025-5.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD025-5.p',unknown),
[] ).
cnf(19,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD025-5.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD025-5.p',unknown),
[] ).
cnf(54,plain,
product(c,a,u__dfg),
inference(res,[status(thm),theory(equality)],[9,21]),
[iquote('0:Res:9.0,21.0')] ).
cnf(65,plain,
( ~ product(d,u,v)
| ~ product(c,u,w)
| product(multiplicative_identity,w,v) ),
inference(res,[status(thm),theory(equality)],[8,17]),
[iquote('0:Res:8.0,17.0')] ).
cnf(66,plain,
( ~ product(multiplicative_identity,u,v)
| ~ product(c,w,u)
| product(d,w,v) ),
inference(res,[status(thm),theory(equality)],[8,18]),
[iquote('0:Res:8.0,18.0')] ).
cnf(70,plain,
( ~ product(u,d,v)
| ~ product(u,multiplicative_identity,w)
| product(w,c,v) ),
inference(res,[status(thm),theory(equality)],[8,18]),
[iquote('0:Res:8.0,18.1')] ).
cnf(97,plain,
product(a,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[7,21]),
[iquote('0:Res:7.0,21.0')] ).
cnf(113,plain,
( ~ defined(u)
| ~ product(c,v,u)
| product(d,v,u) ),
inference(res,[status(thm),theory(equality)],[19,66]),
[iquote('0:Res:19.1,66.0')] ).
cnf(144,plain,
( ~ defined(u__dfg)
| product(d,a,u__dfg) ),
inference(res,[status(thm),theory(equality)],[54,113]),
[iquote('0:Res:54.0,113.1')] ).
cnf(149,plain,
product(d,a,u__dfg),
inference(ssi,[status(thm)],[144,5]),
[iquote('0:SSi:144.0,5.0')] ).
cnf(155,plain,
product(a,d,u__dfg),
inference(res,[status(thm),theory(equality)],[149,21]),
[iquote('0:Res:149.0,21.0')] ).
cnf(361,plain,
( ~ product(c,b,u)
| product(multiplicative_identity,u,v__dfg) ),
inference(res,[status(thm),theory(equality)],[10,65]),
[iquote('0:Res:10.0,65.0')] ).
cnf(645,plain,
( ~ product(a,multiplicative_identity,u)
| product(u,c,u__dfg) ),
inference(res,[status(thm),theory(equality)],[155,70]),
[iquote('0:Res:155.0,70.0')] ).
cnf(1015,plain,
product(b,c,u__dfg),
inference(res,[status(thm),theory(equality)],[97,645]),
[iquote('0:Res:97.0,645.0')] ).
cnf(1025,plain,
product(c,b,u__dfg),
inference(res,[status(thm),theory(equality)],[1015,21]),
[iquote('0:Res:1015.0,21.0')] ).
cnf(1030,plain,
product(multiplicative_identity,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[1025,361]),
[iquote('0:Res:1025.0,361.0')] ).
cnf(1038,plain,
$false,
inference(mrr,[status(thm)],[1030,11]),
[iquote('0:MRR:1030.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : FLD025-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.10 % Command : run_spass %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Mon Jun 6 12:32:19 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.53
% 0.15/0.53 SPASS V 3.9
% 0.15/0.53 SPASS beiseite: Proof found.
% 0.15/0.53 % SZS status Theorem
% 0.15/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.53 SPASS derived 874 clauses, backtracked 0 clauses, performed 2 splits and kept 714 clauses.
% 0.15/0.53 SPASS allocated 76488 KBytes.
% 0.15/0.53 SPASS spent 0:00:00.21 on the problem.
% 0.15/0.53 0:00:00.03 for the input.
% 0.15/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.53 0:00:00.01 for inferences.
% 0.15/0.53 0:00:00.00 for the backtracking.
% 0.15/0.53 0:00:00.15 for the reduction.
% 0.15/0.53
% 0.15/0.53
% 0.15/0.53 Here is a proof with depth 8, length 25 :
% 0.15/0.53 % SZS output start Refutation
% See solution above
% 0.15/0.53 Formulae used in the proof : u_is_defined product_7 product_8 product_9 product_10 not_product_11 associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication commutativity_multiplication
% 0.15/0.53
%------------------------------------------------------------------------------