%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 18:03:06 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 9 unt; 5 nHn; 16 RR)
% Number of literals : 32 ( 0 equ; 12 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
m1_subset_1(skc12,skc10),
file('ALG227+1.p',unknown),
[] ).
cnf(19,axiom,
m1_pboole(skc11,skc10),
file('ALG227+1.p',unknown),
[] ).
cnf(20,axiom,
~ v1_xboole_0(skc10),
file('ALG227+1.p',unknown),
[] ).
cnf(28,axiom,
~ r2_hidden(skc12,k1_closure3(skc10,skc11)),
file('ALG227+1.p',unknown),
[] ).
cnf(29,axiom,
~ equal(k1_funct_1(skc11,skc12),k1_xboole_0),
file('ALG227+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ m1_pboole(u,v)
| ~ equal(w,a_2_0_closure3(v,u))
| v1_xboole_0(v)
| equal(w,k1_closure3(v,u)) ),
file('ALG227+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ m1_pboole(u,v)
| ~ m1_subset_1(w,v)
| v1_xboole_0(v)
| r2_hidden(w,a_2_0_closure3(v,u))
| equal(k1_funct_1(u,w),k1_xboole_0) ),
file('ALG227+1.p',unknown),
[] ).
cnf(57,plain,
( ~ equal(u,a_2_0_closure3(skc10,skc11))
| equal(u,k1_closure3(skc10,skc11))
| v1_xboole_0(skc10) ),
inference(res,[status(thm),theory(equality)],[19,43]),
[iquote('0:Res:19.0,43.1')] ).
cnf(60,plain,
( ~ m1_pboole(u,skc10)
| equal(k1_funct_1(u,skc12),k1_xboole_0)
| r2_hidden(skc12,a_2_0_closure3(skc10,u))
| v1_xboole_0(skc10) ),
inference(res,[status(thm),theory(equality)],[18,45]),
[iquote('0:Res:18.0,45.0')] ).
cnf(72,plain,
( ~ equal(u,a_2_0_closure3(skc10,skc11))
| equal(u,k1_closure3(skc10,skc11)) ),
inference(mrr,[status(thm)],[57,20]),
[iquote('0:MRR:57.2,20.0')] ).
cnf(75,plain,
( ~ m1_pboole(u,skc10)
| r2_hidden(skc12,a_2_0_closure3(skc10,u))
| equal(k1_funct_1(u,skc12),k1_xboole_0) ),
inference(mrr,[status(thm)],[60,20]),
[iquote('0:MRR:60.3,20.0')] ).
cnf(88,plain,
( ~ m1_pboole(skc11,skc10)
| r2_hidden(skc12,a_2_0_closure3(skc10,skc11)) ),
inference(res,[status(thm),theory(equality)],[75,29]),
[iquote('0:Res:75.1,29.0')] ).
cnf(91,plain,
r2_hidden(skc12,a_2_0_closure3(skc10,skc11)),
inference(mrr,[status(thm)],[88,19]),
[iquote('0:MRR:88.0,19.0')] ).
cnf(155,plain,
equal(a_2_0_closure3(skc10,skc11),k1_closure3(skc10,skc11)),
inference(eqr,[status(thm),theory(equality)],[72]),
[iquote('0:EqR:72.0')] ).
cnf(156,plain,
r2_hidden(skc12,k1_closure3(skc10,skc11)),
inference(rew,[status(thm),theory(equality)],[155,91]),
[iquote('0:Rew:155.0,91.0')] ).
cnf(169,plain,
$false,
inference(mrr,[status(thm)],[156,28]),
[iquote('0:MRR:156.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 08:32:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 111 clauses, backtracked 0 clauses, performed 0 splits and kept 113 clauses.
% 0.19/0.45 SPASS allocated 97785 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.01 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 2, length 16 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : t8_closure3 d3_closure3 fraenkel_a_2_0_closure3
% 0.19/0.45
%------------------------------------------------------------------------------