%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 16:38:42 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 22 unt; 3 nHn; 36 RR)
% Number of literals : 62 ( 0 equ; 32 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skf22(u)),
file('NUN054+2.p',unknown),
[] ).
cnf(5,axiom,
r2(u,skf17(v,u)),
file('NUN054+2.p',unknown),
[] ).
cnf(6,axiom,
r2(u,skf20(v,u)),
file('NUN054+2.p',unknown),
[] ).
cnf(7,axiom,
r3(u,skf22(u),u),
file('NUN054+2.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,skc1)
| skP0(skc1,u) ),
file('NUN054+2.p',unknown),
[] ).
cnf(9,axiom,
r3(u,v,skf18(v,u)),
file('NUN054+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ r1(u)
| ~ skP0(v,u) ),
file('NUN054+2.p',unknown),
[] ).
cnf(14,axiom,
r2(skf18(u,v),skf16(v,u)),
file('NUN054+2.p',unknown),
[] ).
cnf(18,axiom,
r3(u,skf17(u,v),skf16(u,v)),
file('NUN054+2.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,skf13(v))
| skP1(skf13(v),u,v) ),
file('NUN054+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ r2(u,v)
| ~ skP1(w,v,u) ),
file('NUN054+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ r3(u,v,w)
| ~ skP2(x,w,v,u) ),
file('NUN054+2.p',unknown),
[] ).
cnf(31,axiom,
( equal(u,skf14(v,w))
| skP2(skf14(v,w),u,w,v) ),
file('NUN054+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ r1(u)
| ~ r1(v)
| ~ r1(w)
| ~ r2(u,x)
| ~ r2(v,y)
| ~ r3(w,y,x) ),
file('NUN054+2.p',unknown),
[] ).
cnf(36,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r3(skf22(y),x,w) ),
inference(res,[status(thm),theory(equality)],[1,33]),
[iquote('0:Res:1.0,33.0')] ).
cnf(53,plain,
( ~ r1(u)
| equal(u,skc1) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.1,13.1')] ).
cnf(55,plain,
equal(skf22(u),skc1),
inference(ems,[status(thm)],[53,1]),
[iquote('0:EmS:53.0,1.0')] ).
cnf(58,plain,
r1(skc1),
inference(rew,[status(thm),theory(equality)],[55,1]),
[iquote('0:Rew:55.0,1.0')] ).
cnf(59,plain,
r3(u,skc1,u),
inference(rew,[status(thm),theory(equality)],[55,7]),
[iquote('0:Rew:55.0,7.0')] ).
cnf(62,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,w)
| ~ r2(v,x)
| ~ r3(skc1,x,w) ),
inference(rew,[status(thm),theory(equality)],[55,36]),
[iquote('0:Rew:55.0,36.4')] ).
cnf(93,plain,
( ~ r2(u,v)
| equal(v,skf13(u)) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.1,22.1')] ).
cnf(94,plain,
equal(skf20(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[6,93]),
[iquote('0:Res:6.0,93.0')] ).
cnf(95,plain,
equal(skf17(u,v),skf13(v)),
inference(res,[status(thm),theory(equality)],[5,93]),
[iquote('0:Res:5.0,93.0')] ).
cnf(101,plain,
r2(u,skf13(u)),
inference(rew,[status(thm),theory(equality)],[94,6]),
[iquote('0:Rew:94.0,6.0')] ).
cnf(105,plain,
r3(u,skf13(v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[95,18]),
[iquote('0:Rew:95.0,18.0')] ).
cnf(384,plain,
( ~ r3(u,v,w)
| equal(w,skf14(u,v)) ),
inference(res,[status(thm),theory(equality)],[31,27]),
[iquote('0:Res:31.1,27.1')] ).
cnf(420,plain,
equal(skf18(u,v),skf14(v,u)),
inference(res,[status(thm),theory(equality)],[9,384]),
[iquote('0:Res:9.0,384.0')] ).
cnf(421,plain,
equal(skf14(u,skc1),u),
inference(res,[status(thm),theory(equality)],[59,384]),
[iquote('0:Res:59.0,384.0')] ).
cnf(430,plain,
r2(skf14(u,v),skf16(u,v)),
inference(rew,[status(thm),theory(equality)],[420,14]),
[iquote('0:Rew:420.0,14.0')] ).
cnf(463,plain,
r2(u,skf16(u,skc1)),
inference(spr,[status(thm),theory(equality)],[421,430]),
[iquote('0:SpR:421.0,430.0')] ).
cnf(470,plain,
equal(skf16(u,skc1),skf13(u)),
inference(res,[status(thm),theory(equality)],[463,93]),
[iquote('0:Res:463.0,93.0')] ).
cnf(477,plain,
r3(u,skf13(skc1),skf13(u)),
inference(spr,[status(thm),theory(equality)],[470,105]),
[iquote('0:SpR:470.0,105.0')] ).
cnf(633,plain,
( ~ r1(u)
| ~ r1(v)
| ~ r2(u,skf13(skc1))
| ~ r2(v,skf13(skc1)) ),
inference(res,[status(thm),theory(equality)],[477,62]),
[iquote('0:Res:477.0,62.4')] ).
cnf(636,plain,
( ~ r1(u)
| ~ r2(u,skf13(skc1)) ),
inference(con,[status(thm)],[633]),
[iquote('0:Con:633.1')] ).
cnf(653,plain,
~ r1(skc1),
inference(res,[status(thm),theory(equality)],[101,636]),
[iquote('0:Res:101.0,636.1')] ).
cnf(658,plain,
$false,
inference(ssi,[status(thm)],[653,58]),
[iquote('0:SSi:653.0,58.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN054+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n027.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Thu Jun 2 07:49:04 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 510 clauses, backtracked 0 clauses, performed 0 splits and kept 276 clauses.
% 0.18/0.47 SPASS allocated 98123 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.47 0:00:00.03 for the input.
% 0.18/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.04 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 7, length 36 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.47 Formulae used in the proof : axiom_4a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 zeroplusoneeqone
% 0.18/0.47
%------------------------------------------------------------------------------