TSTP Solution File: SYN191-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN191-1 : TPTP v8.1.0. Released v1.1.0.
% 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 : Thu Jul 21 12:19:20 EDT 2022
% Result : Unsatisfiable 0.39s 0.60s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 48
% Syntax : Number of clauses : 113 ( 51 unt; 0 nHn; 113 RR)
% Number of literals : 215 ( 0 equ; 109 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ r3(c,b,c),
file('SYN191-1.p',unknown),
[] ).
cnf(2,axiom,
s0(d),
file('SYN191-1.p',unknown),
[] ).
cnf(4,axiom,
n0(d,e),
file('SYN191-1.p',unknown),
[] ).
cnf(6,axiom,
s0(b),
file('SYN191-1.p',unknown),
[] ).
cnf(10,axiom,
r0(b),
file('SYN191-1.p',unknown),
[] ).
cnf(12,axiom,
n0(e,b),
file('SYN191-1.p',unknown),
[] ).
cnf(14,axiom,
r0(e),
file('SYN191-1.p',unknown),
[] ).
cnf(15,axiom,
p0(b,u),
file('SYN191-1.p',unknown),
[] ).
cnf(16,axiom,
n0(a,b),
file('SYN191-1.p',unknown),
[] ).
cnf(18,axiom,
q0(u,d),
file('SYN191-1.p',unknown),
[] ).
cnf(20,axiom,
m0(u,d,v),
file('SYN191-1.p',unknown),
[] ).
cnf(25,axiom,
l0(c),
file('SYN191-1.p',unknown),
[] ).
cnf(27,axiom,
n0(d,c),
file('SYN191-1.p',unknown),
[] ).
cnf(29,axiom,
k0(e),
file('SYN191-1.p',unknown),
[] ).
cnf(32,axiom,
m0(b,b,e),
file('SYN191-1.p',unknown),
[] ).
cnf(33,axiom,
k0(b),
file('SYN191-1.p',unknown),
[] ).
cnf(35,axiom,
n0(c,d),
file('SYN191-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ n0(u,v)
| k1(v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ n0(u,v)
| l1(v,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(68,axiom,
( ~ s0(u)
| ~ p0(u,v)
| m1(u,v,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(75,axiom,
( ~ m0(b,u,v)
| n1(v,v,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(124,axiom,
( ~ p0(u,v)
| p1(v,v,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(146,axiom,
( ~ m0(u,d,u)
| ~ m0(e,d,u)
| q1(e,u,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(160,axiom,
( ~ m0(u,v,w)
| q1(w,w,w) ),
file('SYN191-1.p',unknown),
[] ).
cnf(163,axiom,
( ~ q0(u,v)
| ~ s0(d)
| ~ q1(d,v,d)
| r1(u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(164,axiom,
( ~ p0(u,u)
| s1(u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(165,axiom,
( ~ s1(u)
| ~ q0(v,w)
| s1(v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(166,axiom,
( ~ k1(u)
| ~ k2(u,v)
| ~ m1(w,v,x)
| k2(x,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(168,axiom,
( ~ q1(u,v,v)
| k2(v,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ s1(u)
| ~ l2(v,v)
| ~ n0(e,v)
| l2(u,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(172,axiom,
( ~ s1(u)
| ~ p0(v,v)
| ~ m0(w,u,x)
| l2(x,x) ),
file('SYN191-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ k1(b)
| m2(b) ),
file('SYN191-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ p1(u,v,w)
| n2(w) ),
file('SYN191-1.p',unknown),
[] ).
cnf(213,axiom,
( ~ n2(u)
| ~ k1(e)
| p2(u,u,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(220,axiom,
( ~ p1(u,u,u)
| q2(u,u,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(222,axiom,
( ~ k1(u)
| ~ l0(c)
| ~ l2(u,v)
| q2(v,c,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(225,axiom,
( ~ l1(u,v)
| q2(v,v,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(226,axiom,
( ~ k0(u)
| ~ r1(u)
| ~ q2(u,u,u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
file('SYN191-1.p',unknown),
[] ).
cnf(227,axiom,
( ~ l0(u)
| ~ r1(u)
| r2(u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(228,axiom,
( ~ s1(b)
| ~ q2(b,u,b)
| s2(u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(279,axiom,
( ~ p2(u,v,w)
| n3(w) ),
file('SYN191-1.p',unknown),
[] ).
cnf(283,axiom,
( ~ n2(u)
| p3(u,u,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(294,axiom,
( ~ n0(u,v)
| ~ q2(u,v,w)
| q3(v,w) ),
file('SYN191-1.p',unknown),
[] ).
cnf(296,axiom,
( ~ s2(u)
| ~ q3(v,u)
| ~ n1(w,u,v)
| q3(u,v) ),
file('SYN191-1.p',unknown),
[] ).
cnf(305,axiom,
( ~ r2(u)
| r3(u,u,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(311,axiom,
( ~ r2(u)
| ~ k2(v,u)
| ~ r3(u,w,w)
| r3(w,v,u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(313,axiom,
( ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e)
| k4(c) ),
file('SYN191-1.p',unknown),
[] ).
cnf(338,axiom,
( ~ l1(u,v)
| ~ p3(w,v,x)
| s4(u) ),
file('SYN191-1.p',unknown),
[] ).
cnf(394,plain,
( ~ n3(e)
| ~ q3(e,b)
| k4(c) ),
inference(mrr,[status(thm)],[313,35]),
[iquote('0:MRR:313.0,35.0')] ).
cnf(400,plain,
( ~ k1(u)
| ~ l2(u,v)
| q2(v,c,u) ),
inference(mrr,[status(thm)],[222,25]),
[iquote('0:MRR:222.1,25.0')] ).
cnf(401,plain,
( ~ q0(u,v)
| ~ q1(d,v,d)
| r1(u) ),
inference(mrr,[status(thm)],[163,2]),
[iquote('0:MRR:163.1,2.0')] ).
cnf(403,plain,
q1(e,u,u),
inference(mrr,[status(thm)],[146,20]),
[iquote('0:MRR:146.0,146.1,20.0,20.0')] ).
cnf(421,plain,
( ~ r2(c)
| ~ k2(b,c)
| ~ r3(c,c,c) ),
inference(res,[status(thm),theory(equality)],[311,1]),
[iquote('0:Res:311.3,1.0')] ).
cnf(422,plain,
( ~ r2(c)
| ~ k2(b,c) ),
inference(mrr,[status(thm)],[421,305]),
[iquote('0:MRR:421.2,305.1')] ).
cnf(457,plain,
s1(b),
inference(res,[status(thm),theory(equality)],[15,164]),
[iquote('0:Res:15.0,164.0')] ).
cnf(458,plain,
( ~ q2(b,u,b)
| s2(u) ),
inference(mrr,[status(thm)],[228,457]),
[iquote('0:MRR:228.0,457.0')] ).
cnf(461,plain,
k1(c),
inference(res,[status(thm),theory(equality)],[27,40]),
[iquote('0:Res:27.0,40.0')] ).
cnf(462,plain,
k1(e),
inference(res,[status(thm),theory(equality)],[4,40]),
[iquote('0:Res:4.0,40.0')] ).
cnf(463,plain,
k1(b),
inference(res,[status(thm),theory(equality)],[16,40]),
[iquote('0:Res:16.0,40.0')] ).
cnf(470,plain,
( ~ n2(u)
| p2(u,u,u) ),
inference(mrr,[status(thm)],[213,462]),
[iquote('0:MRR:213.1,462.0')] ).
cnf(471,plain,
m2(b),
inference(mrr,[status(thm)],[175,463]),
[iquote('0:MRR:175.0,463.0')] ).
cnf(476,plain,
l1(c,c),
inference(res,[status(thm),theory(equality)],[27,41]),
[iquote('0:Res:27.0,41.0')] ).
cnf(477,plain,
l1(e,e),
inference(res,[status(thm),theory(equality)],[4,41]),
[iquote('0:Res:4.0,41.0')] ).
cnf(478,plain,
l1(b,b),
inference(res,[status(thm),theory(equality)],[16,41]),
[iquote('0:Res:16.0,41.0')] ).
cnf(494,plain,
( ~ n2(u)
| n3(u) ),
inference(res,[status(thm),theory(equality)],[470,279]),
[iquote('0:Res:470.1,279.0')] ).
cnf(495,plain,
( ~ r1(c)
| ~ l0(c)
| ~ k2(b,c) ),
inference(sor,[status(thm)],[422,227]),
[iquote('0:SoR:422.0,227.2')] ).
cnf(498,plain,
( ~ r1(c)
| ~ k2(b,c) ),
inference(ssi,[status(thm)],[495,25,461]),
[iquote('0:SSi:495.1,25.0,461.0')] ).
cnf(506,plain,
q2(b,b,b),
inference(res,[status(thm),theory(equality)],[478,225]),
[iquote('0:Res:478.0,225.0')] ).
cnf(508,plain,
s2(b),
inference(res,[status(thm),theory(equality)],[506,458]),
[iquote('0:Res:506.0,458.0')] ).
cnf(546,plain,
p1(u,u,u),
inference(res,[status(thm),theory(equality)],[15,124]),
[iquote('0:Res:15.0,124.0')] ).
cnf(547,plain,
q2(u,u,u),
inference(mrr,[status(thm)],[220,546]),
[iquote('0:MRR:220.0,546.0')] ).
cnf(549,plain,
( ~ k0(u)
| ~ r1(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[226,547]),
[iquote('0:MRR:226.2,547.0')] ).
cnf(550,plain,
n2(u),
inference(res,[status(thm),theory(equality)],[546,176]),
[iquote('0:Res:546.0,176.0')] ).
cnf(552,plain,
p3(u,u,u),
inference(mrr,[status(thm)],[283,550]),
[iquote('0:MRR:283.0,550.0')] ).
cnf(557,plain,
n3(u),
inference(mrr,[status(thm)],[494,550]),
[iquote('0:MRR:494.0,550.0')] ).
cnf(568,plain,
( ~ q3(e,b)
| k4(c) ),
inference(mrr,[status(thm)],[394,557]),
[iquote('0:MRR:394.0,557.0')] ).
cnf(582,plain,
k2(u,u),
inference(res,[status(thm),theory(equality)],[403,168]),
[iquote('0:Res:403.0,168.0')] ).
cnf(607,plain,
( ~ q0(u,v)
| s1(u) ),
inference(ems,[status(thm)],[165,457]),
[iquote('0:EmS:165.0,457.0')] ).
cnf(613,plain,
s1(u),
inference(res,[status(thm),theory(equality)],[18,607]),
[iquote('0:Res:18.0,607.0')] ).
cnf(619,plain,
( ~ l2(u,u)
| ~ n0(e,u)
| l2(v,u) ),
inference(mrr,[status(thm)],[170,613]),
[iquote('0:MRR:170.0,613.0')] ).
cnf(620,plain,
( ~ p0(u,u)
| ~ m0(v,w,x)
| l2(x,x) ),
inference(mrr,[status(thm)],[172,613]),
[iquote('0:MRR:172.0,613.0')] ).
cnf(627,plain,
n1(e,e,b),
inference(res,[status(thm),theory(equality)],[32,75]),
[iquote('0:Res:32.0,75.0')] ).
cnf(656,plain,
q1(u,u,u),
inference(res,[status(thm),theory(equality)],[20,160]),
[iquote('0:Res:20.0,160.0')] ).
cnf(684,plain,
( ~ q0(u,d)
| r1(u) ),
inference(res,[status(thm),theory(equality)],[656,401]),
[iquote('0:Res:656.0,401.1')] ).
cnf(685,plain,
r1(u),
inference(mrr,[status(thm)],[684,18]),
[iquote('0:MRR:684.0,18.0')] ).
cnf(688,plain,
~ k2(b,c),
inference(mrr,[status(thm)],[498,685]),
[iquote('0:MRR:498.0,685.0')] ).
cnf(690,plain,
( ~ k0(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[549,685]),
[iquote('0:MRR:549.1,685.0')] ).
cnf(713,plain,
( ~ s0(b)
| m1(b,u,b) ),
inference(res,[status(thm),theory(equality)],[15,68]),
[iquote('0:Res:15.0,68.1')] ).
cnf(714,plain,
m1(b,u,b),
inference(ssi,[status(thm)],[713,6,33,10,471,463,508]),
[iquote('0:SSi:713.0,6.0,33.0,10.0,471.0,463.0,508.0')] ).
cnf(740,plain,
( ~ l1(u,v)
| s4(u) ),
inference(res,[status(thm),theory(equality)],[552,338]),
[iquote('0:Res:552.0,338.1')] ).
cnf(741,plain,
s4(c),
inference(res,[status(thm),theory(equality)],[476,740]),
[iquote('0:Res:476.0,740.0')] ).
cnf(744,plain,
s4(e),
inference(res,[status(thm),theory(equality)],[477,740]),
[iquote('0:Res:477.0,740.0')] ).
cnf(745,plain,
s4(b),
inference(res,[status(thm),theory(equality)],[478,740]),
[iquote('0:Res:478.0,740.0')] ).
cnf(998,plain,
( ~ p0(u,u)
| l2(v,v) ),
inference(res,[status(thm),theory(equality)],[20,620]),
[iquote('0:Res:20.0,620.1')] ).
cnf(1006,plain,
( ~ k0(u)
| q2(v,u,v) ),
inference(res,[status(thm),theory(equality)],[20,690]),
[iquote('0:Res:20.0,690.1')] ).
cnf(1007,plain,
l2(u,u),
inference(res,[status(thm),theory(equality)],[15,998]),
[iquote('0:Res:15.0,998.0')] ).
cnf(1010,plain,
( ~ n0(e,u)
| l2(v,u) ),
inference(mrr,[status(thm)],[619,1007]),
[iquote('0:MRR:619.0,1007.0')] ).
cnf(1015,plain,
l2(u,b),
inference(res,[status(thm),theory(equality)],[12,1010]),
[iquote('0:Res:12.0,1010.0')] ).
cnf(1018,plain,
( ~ k1(u)
| q2(b,c,u) ),
inference(res,[status(thm),theory(equality)],[1015,400]),
[iquote('0:Res:1015.0,400.1')] ).
cnf(1022,plain,
( ~ k1(b)
| s2(c) ),
inference(res,[status(thm),theory(equality)],[1018,458]),
[iquote('0:Res:1018.1,458.0')] ).
cnf(1025,plain,
s2(c),
inference(ssi,[status(thm)],[1022,6,33,10,471,463,508,745]),
[iquote('0:SSi:1022.0,6.0,33.0,10.0,471.0,463.0,508.0,745.0')] ).
cnf(1046,plain,
( ~ k0(u)
| s2(u) ),
inference(res,[status(thm),theory(equality)],[1006,458]),
[iquote('0:Res:1006.1,458.0')] ).
cnf(1047,plain,
( ~ k0(u)
| ~ n0(v,u)
| q3(u,v) ),
inference(res,[status(thm),theory(equality)],[1006,294]),
[iquote('0:Res:1006.1,294.1')] ).
cnf(1106,plain,
( ~ k0(b)
| q3(b,e) ),
inference(res,[status(thm),theory(equality)],[12,1047]),
[iquote('0:Res:12.0,1047.1')] ).
cnf(1111,plain,
q3(b,e),
inference(ssi,[status(thm)],[1106,6,33,10,471,463,508,745]),
[iquote('0:SSi:1106.0,6.0,33.0,10.0,471.0,463.0,508.0,745.0')] ).
cnf(1418,plain,
( ~ s2(e)
| ~ q3(b,e)
| q3(e,b) ),
inference(res,[status(thm),theory(equality)],[627,296]),
[iquote('0:Res:627.0,296.2')] ).
cnf(1425,plain,
( ~ q3(b,e)
| q3(e,b) ),
inference(ssi,[status(thm)],[1418,1046,29,14,462,744]),
[iquote('0:SSi:1418.0,1046.0,29.0,14.0,462.0,744.1')] ).
cnf(1426,plain,
q3(e,b),
inference(mrr,[status(thm)],[1425,1111]),
[iquote('0:MRR:1425.0,1111.0')] ).
cnf(1427,plain,
k4(c),
inference(mrr,[status(thm)],[568,1426]),
[iquote('0:MRR:568.0,1426.0')] ).
cnf(1458,plain,
( ~ k1(u)
| ~ k2(u,v)
| k2(b,v) ),
inference(res,[status(thm),theory(equality)],[714,166]),
[iquote('0:Res:714.0,166.2')] ).
cnf(2108,plain,
( ~ k1(u)
| k2(b,u) ),
inference(res,[status(thm),theory(equality)],[582,1458]),
[iquote('0:Res:582.0,1458.1')] ).
cnf(2116,plain,
~ k1(c),
inference(res,[status(thm),theory(equality)],[2108,688]),
[iquote('0:Res:2108.1,688.0')] ).
cnf(2118,plain,
$false,
inference(ssi,[status(thm)],[2116,25,461,741,1025,1427]),
[iquote('0:SSi:2116.0,25.0,461.0,741.0,1025.0,1427.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN191-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 12 08:29:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.39/0.60
% 0.39/0.60 SPASS V 3.9
% 0.39/0.60 SPASS beiseite: Proof found.
% 0.39/0.60 % SZS status Theorem
% 0.39/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.60 SPASS derived 1520 clauses, backtracked 0 clauses, performed 0 splits and kept 1063 clauses.
% 0.39/0.60 SPASS allocated 77030 KBytes.
% 0.39/0.60 SPASS spent 0:00:00.24 on the problem.
% 0.39/0.60 0:00:00.04 for the input.
% 0.39/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.60 0:00:00.02 for inferences.
% 0.39/0.60 0:00:00.00 for the backtracking.
% 0.39/0.60 0:00:00.13 for the reduction.
% 0.39/0.60
% 0.39/0.60
% 0.39/0.60 Here is a proof with depth 4, length 113 :
% 0.39/0.60 % SZS output start Refutation
% See solution above
% 0.39/0.60 Formulae used in the proof : prove_this axiom_1 axiom_3 axiom_5 axiom_9 axiom_11 axiom_13 axiom_14 axiom_15 axiom_17 axiom_19 axiom_24 axiom_26 axiom_28 axiom_31 axiom_32 axiom_34 rule_001 rule_002 rule_029 rule_036 rule_085 rule_107 rule_121 rule_124 rule_125 rule_126 rule_127 rule_129 rule_131 rule_133 rule_136 rule_137 rule_174 rule_181 rule_183 rule_186 rule_187 rule_188 rule_189 rule_240 rule_244 rule_255 rule_257 rule_266 rule_272 rule_274 rule_299
% 0.39/0.60
%------------------------------------------------------------------------------