%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Tue Jul 19 05:30:03 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 6 unt; 1 nHn; 14 RR)
% Number of literals : 25 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ subset(skc6,skc7),
file('SET956+1.p',unknown),
[] ).
cnf(5,axiom,
subset(skc6,cartesian_product2(skc8,skc9)),
file('SET956+1.p',unknown),
[] ).
cnf(9,axiom,
( subset(u,v)
| in(skf3(v,u),u) ),
file('SET956+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(skf3(u,v),u)
| subset(w,u) ),
file('SET956+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(ordered_pair(u,v),skc6)
| in(ordered_pair(u,v),skc7) ),
file('SET956+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(u,v)
| ~ subset(v,cartesian_product2(w,x))
| equal(ordered_pair(skf5(w,x,u),skf4(x,u,w)),u) ),
file('SET956+1.p',unknown),
[] ).
cnf(18,plain,
in(skf3(skc7,skc6),skc6),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.1,4.0')] ).
cnf(19,plain,
~ in(skf3(skc7,u),skc7),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.1,4.0')] ).
cnf(21,plain,
( ~ in(u,skc6)
| equal(ordered_pair(skf5(skc8,skc9,u),skf4(skc9,u,skc8)),u) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(152,plain,
( ~ in(u,skc6)
| ~ in(ordered_pair(skf5(skc8,skc9,u),skf4(skc9,u,skc8)),skc6)
| in(u,skc7) ),
inference(spr,[status(thm),theory(equality)],[21,12]),
[iquote('0:SpR:21.1,12.1')] ).
cnf(157,plain,
( ~ in(u,skc6)
| ~ in(u,skc6)
| in(u,skc7) ),
inference(rew,[status(thm),theory(equality)],[21,152]),
[iquote('0:Rew:21.1,152.1')] ).
cnf(158,plain,
( ~ in(u,skc6)
| in(u,skc7) ),
inference(obv,[status(thm),theory(equality)],[157]),
[iquote('0:Obv:157.0')] ).
cnf(170,plain,
~ in(skf3(skc7,u),skc6),
inference(res,[status(thm),theory(equality)],[158,19]),
[iquote('0:Res:158.1,19.0')] ).
cnf(175,plain,
$false,
inference(unc,[status(thm)],[170,18]),
[iquote('0:UnC:170.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 01:49:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 141 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.19/0.47 SPASS allocated 85351 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.01 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 3, length 14 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : t109_zfmisc_1 d3_tarski t103_zfmisc_1
% 0.19/0.47
%------------------------------------------------------------------------------