TSTP Solution File: SEU131+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:34:11 EDT 2022
% Result : Theorem 1.85s 2.04s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 10 unt; 12 nHn; 30 RR)
% Number of literals : 63 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(set_difference(empty_set,u),empty_set),
file('SEU131+1.p',unknown),
[] ).
cnf(9,axiom,
( subset(skc4,skc5)
| equal(set_difference(skc4,skc5),empty_set) ),
file('SEU131+1.p',unknown),
[] ).
cnf(11,axiom,
( subset(u,v)
| in(skf3(v,u),u) ),
file('SEU131+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(skf3(u,v),u)
| subset(w,u) ),
file('SEU131+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ subset(skc4,skc5)
| ~ equal(set_difference(skc4,skc5),empty_set) ),
file('SEU131+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU131+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SEU131+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SEU131+1.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,set_difference(v,w))
| in(skf4(w,v,u),u)
| in(skf4(w,v,u),v) ),
file('SEU131+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ in(skf4(u,v,w),u)
| equal(w,set_difference(v,u))
| in(skf4(u,v,w),w) ),
file('SEU131+1.p',unknown),
[] ).
cnf(31,plain,
subset(skc4,skc5),
inference(spt,[spt(split,[position(s1)])],[9]),
[iquote('1:Spt:9.0')] ).
cnf(32,plain,
~ equal(set_difference(skc4,skc5),empty_set),
inference(mrr,[status(thm)],[14,31]),
[iquote('1:MRR:14.0,31.0')] ).
cnf(80,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[18]),
[iquote('0:EqR:18.2')] ).
cnf(130,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[20]),
[iquote('0:EqR:20.1')] ).
cnf(158,plain,
( ~ subset(u,v)
| equal(w,set_difference(u,x))
| in(skf4(x,u,w),w)
| in(skf4(x,u,w),v) ),
inference(res,[status(thm),theory(equality)],[21,15]),
[iquote('0:Res:21.2,15.0')] ).
cnf(163,plain,
( ~ in(u,empty_set)
| ~ in(u,v) ),
inference(spl,[status(thm),theory(equality)],[6,80]),
[iquote('0:SpL:6.0,80.0')] ).
cnf(175,plain,
~ in(u,empty_set),
inference(con,[status(thm)],[163]),
[iquote('0:Con:163.1')] ).
cnf(845,plain,
( equal(u,set_difference(skc4,v))
| in(skf4(v,skc4,u),u)
| in(skf4(v,skc4,u),skc5) ),
inference(res,[status(thm),theory(equality)],[31,158]),
[iquote('1:Res:31.0,158.0')] ).
cnf(3881,plain,
( equal(u,set_difference(skc4,skc5))
| in(skf4(skc5,skc4,u),u)
| equal(u,set_difference(skc4,skc5))
| in(skf4(skc5,skc4,u),u) ),
inference(res,[status(thm),theory(equality)],[845,22]),
[iquote('1:Res:845.2,22.0')] ).
cnf(3887,plain,
( equal(u,set_difference(skc4,skc5))
| in(skf4(skc5,skc4,u),u) ),
inference(obv,[status(thm),theory(equality)],[3881]),
[iquote('1:Obv:3881.1')] ).
cnf(3905,plain,
equal(set_difference(skc4,skc5),empty_set),
inference(res,[status(thm),theory(equality)],[3887,175]),
[iquote('1:Res:3887.1,175.0')] ).
cnf(3924,plain,
$false,
inference(mrr,[status(thm)],[3905,32]),
[iquote('1:MRR:3905.0,32.0')] ).
cnf(3927,plain,
~ subset(skc4,skc5),
inference(spt,[spt(split,[position(sa)])],[3924,31]),
[iquote('1:Spt:3924.0,9.0,31.0')] ).
cnf(3928,plain,
equal(set_difference(skc4,skc5),empty_set),
inference(spt,[spt(split,[position(s2)])],[9]),
[iquote('1:Spt:3924.0,9.1')] ).
cnf(3940,plain,
( ~ in(u,skc4)
| in(u,empty_set)
| in(u,skc5) ),
inference(spr,[status(thm),theory(equality)],[3928,130]),
[iquote('1:SpR:3928.0,130.1')] ).
cnf(3975,plain,
( ~ in(u,skc4)
| in(u,skc5) ),
inference(mrr,[status(thm)],[3940,175]),
[iquote('1:MRR:3940.1,175.0')] ).
cnf(3989,plain,
( ~ in(skf3(skc5,u),skc4)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[3975,12]),
[iquote('1:Res:3975.1,12.0')] ).
cnf(4096,plain,
( subset(skc4,skc5)
| subset(u,skc5) ),
inference(res,[status(thm),theory(equality)],[11,3989]),
[iquote('1:Res:11.1,3989.0')] ).
cnf(4100,plain,
subset(skc4,skc5),
inference(con,[status(thm)],[4096]),
[iquote('1:Con:4096.1')] ).
cnf(4101,plain,
$false,
inference(mrr,[status(thm)],[4100,3927]),
[iquote('1:MRR:4100.0,3927.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n003.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 : Sun Jun 19 07:08:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.85/2.04
% 1.85/2.04 SPASS V 3.9
% 1.85/2.04 SPASS beiseite: Proof found.
% 1.85/2.04 % SZS status Theorem
% 1.85/2.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.85/2.04 SPASS derived 3570 clauses, backtracked 20 clauses, performed 2 splits and kept 1694 clauses.
% 1.85/2.04 SPASS allocated 101072 KBytes.
% 1.85/2.04 SPASS spent 0:00:01.68 on the problem.
% 1.85/2.04 0:00:00.04 for the input.
% 1.85/2.04 0:00:00.05 for the FLOTTER CNF translation.
% 1.85/2.04 0:00:00.05 for inferences.
% 1.85/2.04 0:00:00.03 for the backtracking.
% 1.85/2.04 0:00:01.49 for the reduction.
% 1.85/2.04
% 1.85/2.04
% 1.85/2.04 Here is a proof with depth 4, length 30 :
% 1.85/2.04 % SZS output start Refutation
% See solution above
% 1.85/2.04 Formulae used in the proof : t4_boole l32_xboole_1 d3_tarski d4_xboole_0
% 1.85/2.04
%------------------------------------------------------------------------------