TSTP Solution File: RNG111+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG111+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : Mon Jul 18 20:41:30 EDT 2022
% Result : Theorem 0.42s 0.59s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 32 ( 14 unt; 5 nHn; 32 RR)
% Number of literals : 70 ( 0 equ; 38 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
aElementOf0(skc4,xI),
file('RNG111+1.p',unknown),
[] ).
cnf(7,axiom,
aElementOf0(skc3,xI),
file('RNG111+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(skf18(u),xI),
file('RNG111+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(sz00,skc3),
file('RNG111+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aElementOf0(u,xI)
| ~ equal(skf18(u),sz00)
| equal(u,sz00) ),
file('RNG111+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ aElementOf0(u,xI)
| equal(u,sz00)
| iLess0(sbrdtbr0(skf18(u)),sbrdtbr0(u)) ),
file('RNG111+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ aElementOf0(u,xI)
| ~ equal(sz00,skc4)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| equal(u,sz00) ),
file('RNG111+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ aElementOf0(u,xI)
| ~ aElementOf0(v,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| ~ iLess0(sbrdtbr0(v),sbrdtbr0(skc4))
| equal(u,sz00)
| equal(v,sz00) ),
file('RNG111+1.p',unknown),
[] ).
cnf(110,plain,
( iLess0(sbrdtbr0(skf18(skc3)),sbrdtbr0(skc3))
| equal(sz00,skc3) ),
inference(res,[status(thm),theory(equality)],[7,57]),
[iquote('0:Res:7.0,57.0')] ).
cnf(111,plain,
( ~ equal(skf18(skc3),sz00)
| equal(sz00,skc3) ),
inference(res,[status(thm),theory(equality)],[7,55]),
[iquote('0:Res:7.0,55.1')] ).
cnf(127,plain,
( equal(sz00,skc4)
| iLess0(sbrdtbr0(skf18(skc4)),sbrdtbr0(skc4)) ),
inference(res,[status(thm),theory(equality)],[6,57]),
[iquote('0:Res:6.0,57.0')] ).
cnf(128,plain,
( ~ equal(skf18(skc4),sz00)
| equal(sz00,skc4) ),
inference(res,[status(thm),theory(equality)],[6,55]),
[iquote('0:Res:6.0,55.1')] ).
cnf(197,plain,
( ~ aElementOf0(u,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc4))
| ~ iLess0(sbrdtbr0(skc4),sbrdtbr0(skc3))
| equal(u,sz00)
| equal(sz00,skc4) ),
inference(res,[status(thm),theory(equality)],[6,102]),
[iquote('0:Res:6.0,102.2')] ).
cnf(206,plain,
~ equal(skf18(skc3),sz00),
inference(mrr,[status(thm)],[111,10]),
[iquote('0:MRR:111.1,10.0')] ).
cnf(208,plain,
iLess0(sbrdtbr0(skf18(skc3)),sbrdtbr0(skc3)),
inference(mrr,[status(thm)],[110,10]),
[iquote('0:MRR:110.1,10.0')] ).
cnf(282,plain,
equal(sz00,skc4),
inference(spt,[spt(split,[position(s1)])],[197]),
[iquote('1:Spt:197.4')] ).
cnf(292,plain,
( ~ aElementOf0(u,xI)
| ~ equal(sz00,skc4)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| equal(u,skc4) ),
inference(rew,[status(thm),theory(equality)],[282,71]),
[iquote('1:Rew:282.0,71.3')] ).
cnf(309,plain,
~ equal(skf18(skc3),skc4),
inference(rew,[status(thm),theory(equality)],[282,206]),
[iquote('1:Rew:282.0,206.0')] ).
cnf(330,plain,
( ~ aElementOf0(u,xI)
| ~ equal(skc4,skc4)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| equal(u,skc4) ),
inference(rew,[status(thm),theory(equality)],[282,292]),
[iquote('1:Rew:282.0,292.1')] ).
cnf(331,plain,
( ~ aElementOf0(u,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| equal(u,skc4) ),
inference(obv,[status(thm),theory(equality)],[330]),
[iquote('1:Obv:330.1')] ).
cnf(507,plain,
( ~ aElementOf0(skf18(skc3),xI)
| equal(skf18(skc3),skc4) ),
inference(res,[status(thm),theory(equality)],[208,331]),
[iquote('1:Res:208.0,331.1')] ).
cnf(509,plain,
$false,
inference(mrr,[status(thm)],[507,9,309]),
[iquote('1:MRR:507.0,507.1,9.0,309.0')] ).
cnf(511,plain,
~ equal(sz00,skc4),
inference(spt,[spt(split,[position(sa)])],[509,282]),
[iquote('1:Spt:509.0,197.4,282.0')] ).
cnf(512,plain,
( ~ aElementOf0(u,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc4))
| ~ iLess0(sbrdtbr0(skc4),sbrdtbr0(skc3))
| equal(u,sz00) ),
inference(spt,[spt(split,[position(s2)])],[197]),
[iquote('1:Spt:509.0,197.0,197.1,197.2,197.3')] ).
cnf(514,plain,
~ equal(skf18(skc4),sz00),
inference(mrr,[status(thm)],[128,511]),
[iquote('1:MRR:128.1,511.0')] ).
cnf(515,plain,
iLess0(sbrdtbr0(skf18(skc4)),sbrdtbr0(skc4)),
inference(mrr,[status(thm)],[127,511]),
[iquote('1:MRR:127.0,511.0')] ).
cnf(522,plain,
( ~ aElementOf0(u,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc4))
| equal(u,sz00) ),
inference(spt,[spt(split,[position(s2s1)])],[102]),
[iquote('2:Spt:102.1,102.3,102.5')] ).
cnf(525,plain,
( ~ aElementOf0(skf18(skc4),xI)
| equal(skf18(skc4),sz00) ),
inference(res,[status(thm),theory(equality)],[515,522]),
[iquote('2:Res:515.0,522.1')] ).
cnf(526,plain,
$false,
inference(mrr,[status(thm)],[525,9,514]),
[iquote('2:MRR:525.0,525.1,9.0,514.0')] ).
cnf(527,plain,
( ~ aElementOf0(u,xI)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc3))
| equal(u,sz00) ),
inference(spt,[spt(split,[position(s2s2)])],[102]),
[iquote('2:Spt:526.0,102.0,102.2,102.4')] ).
cnf(528,plain,
( ~ aElementOf0(skf18(skc3),xI)
| equal(skf18(skc3),sz00) ),
inference(res,[status(thm),theory(equality)],[208,527]),
[iquote('2:Res:208.0,527.1')] ).
cnf(529,plain,
$false,
inference(mrr,[status(thm)],[528,9,206]),
[iquote('2:MRR:528.0,528.1,9.0,206.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG111+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.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 May 30 21:38:06 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/0.59
% 0.42/0.59 SPASS V 3.9
% 0.42/0.59 SPASS beiseite: Proof found.
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.59 SPASS derived 317 clauses, backtracked 63 clauses, performed 2 splits and kept 318 clauses.
% 0.42/0.59 SPASS allocated 99329 KBytes.
% 0.42/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.42/0.59 0:00:00.03 for the input.
% 0.42/0.59 0:00:00.13 for the FLOTTER CNF translation.
% 0.42/0.59 0:00:00.00 for inferences.
% 0.42/0.59 0:00:00.00 for the backtracking.
% 0.42/0.59 0:00:00.04 for the reduction.
% 0.42/0.59
% 0.42/0.59
% 0.42/0.59 Here is a proof with depth 2, length 32 :
% 0.42/0.59 % SZS output start Refutation
% See solution above
% 0.42/0.59 Formulae used in the proof : m__
% 0.42/0.59
%------------------------------------------------------------------------------