TSTP Solution File: NUN081+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN081+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 16:38:47 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 10 unt; 2 nHn; 21 RR)
% Number of literals : 40 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN081+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN081+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN081+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN081+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN081+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN081+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN081+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r2(v,w)
| ~ r2(x,v)
| ~ r3(y,z,w)
| ~ r2(u,x) ),
file('NUN081+2.p',unknown),
[] ).
cnf(37,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(x,y,skf20(z,w)) ),
inference(res,[status(thm),theory(equality)],[6,33]),
[iquote('0:Res:6.0,33.1')] ).
cnf(50,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(52,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[50,1]),
[iquote('0:EmS:50.0,1.0')] ).
cnf(55,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[52,1]),
[iquote('0:Rew:52.0,1.0')] ).
cnf(56,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[52,7]),
[iquote('0:Rew:52.0,7.0')] ).
cnf(84,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(85,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,84]),
[iquote('0:Res:6.0,84.0')] ).
cnf(92,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[85,6]),
[iquote('0:Rew:85.0,6.0')] ).
cnf(93,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w)
| ~ r3(x,y,skf13(w)) ),
inference(rew,[status(thm),theory(equality)],[85,37]),
[iquote('0:Rew:85.0,37.3')] ).
cnf(616,plain,
( ~ r1(u)
| ~ r2(u,v)
| ~ r2(v,w) ),
inference(res,[status(thm),theory(equality)],[56,93]),
[iquote('0:Res:56.0,93.3')] ).
cnf(797,plain,
( ~ r1(u)
| ~ r2(skf13(u),v) ),
inference(res,[status(thm),theory(equality)],[92,616]),
[iquote('0:Res:92.0,616.1')] ).
cnf(810,plain,
~ r1(u),
inference(res,[status(thm),theory(equality)],[92,797]),
[iquote('0:Res:92.0,797.1')] ).
cnf(813,plain,
$false,
inference(unc,[status(thm)],[810,55]),
[iquote('0:UnC:810.0,55.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN081+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 : Thu Jun 2 10:02:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 619 clauses, backtracked 0 clauses, performed 0 splits and kept 326 clauses.
% 0.19/0.51 SPASS allocated 98259 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.06 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 4, length 21 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : axiom_4a axiom_2a axiom_1 axiom_2 xplusyeqthree
% 0.19/0.51
%------------------------------------------------------------------------------