TSTP Solution File: SYN270-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN270-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 12:19:52 EDT 2022
% Result : Unsatisfiable 0.39s 0.60s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 49
% Syntax : Number of clauses : 116 ( 52 unt; 0 nHn; 116 RR)
% Number of literals : 221 ( 0 equ; 109 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 32 ( 31 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,
~ p4(b,b,c),
file('SYN270-1.p',unknown),
[] ).
cnf(2,axiom,
s0(d),
file('SYN270-1.p',unknown),
[] ).
cnf(4,axiom,
n0(d,e),
file('SYN270-1.p',unknown),
[] ).
cnf(6,axiom,
s0(b),
file('SYN270-1.p',unknown),
[] ).
cnf(10,axiom,
r0(b),
file('SYN270-1.p',unknown),
[] ).
cnf(12,axiom,
n0(e,b),
file('SYN270-1.p',unknown),
[] ).
cnf(14,axiom,
r0(e),
file('SYN270-1.p',unknown),
[] ).
cnf(15,axiom,
p0(b,u),
file('SYN270-1.p',unknown),
[] ).
cnf(16,axiom,
n0(a,b),
file('SYN270-1.p',unknown),
[] ).
cnf(18,axiom,
q0(u,d),
file('SYN270-1.p',unknown),
[] ).
cnf(20,axiom,
m0(u,d,v),
file('SYN270-1.p',unknown),
[] ).
cnf(25,axiom,
l0(c),
file('SYN270-1.p',unknown),
[] ).
cnf(27,axiom,
n0(d,c),
file('SYN270-1.p',unknown),
[] ).
cnf(29,axiom,
k0(e),
file('SYN270-1.p',unknown),
[] ).
cnf(32,axiom,
m0(b,b,e),
file('SYN270-1.p',unknown),
[] ).
cnf(33,axiom,
k0(b),
file('SYN270-1.p',unknown),
[] ).
cnf(35,axiom,
n0(c,d),
file('SYN270-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ n0(u,v)
| k1(v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ n0(u,v)
| l1(v,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(68,axiom,
( ~ s0(u)
| ~ p0(u,v)
| m1(u,v,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(75,axiom,
( ~ m0(b,u,v)
| n1(v,v,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(124,axiom,
( ~ p0(u,v)
| p1(v,v,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(146,axiom,
( ~ m0(u,d,u)
| ~ m0(e,d,u)
| q1(e,u,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(160,axiom,
( ~ m0(u,v,w)
| q1(w,w,w) ),
file('SYN270-1.p',unknown),
[] ).
cnf(163,axiom,
( ~ q0(u,v)
| ~ s0(d)
| ~ q1(d,v,d)
| r1(u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(164,axiom,
( ~ p0(u,u)
| s1(u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(165,axiom,
( ~ s1(u)
| ~ q0(v,w)
| s1(v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(166,axiom,
( ~ k1(u)
| ~ k2(u,v)
| ~ m1(w,v,x)
| k2(x,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(168,axiom,
( ~ q1(u,v,v)
| k2(v,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ s1(u)
| ~ l2(v,v)
| ~ n0(e,v)
| l2(u,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(172,axiom,
( ~ s1(u)
| ~ p0(v,v)
| ~ m0(w,u,x)
| l2(x,x) ),
file('SYN270-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ k1(b)
| m2(b) ),
file('SYN270-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ p1(u,v,w)
| n2(w) ),
file('SYN270-1.p',unknown),
[] ).
cnf(213,axiom,
( ~ n2(u)
| ~ k1(e)
| p2(u,u,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(220,axiom,
( ~ p1(u,u,u)
| q2(u,u,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(222,axiom,
( ~ k1(u)
| ~ l0(c)
| ~ l2(u,v)
| q2(v,c,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(225,axiom,
( ~ l1(u,v)
| q2(v,v,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(226,axiom,
( ~ k0(u)
| ~ r1(u)
| ~ q2(u,u,u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
file('SYN270-1.p',unknown),
[] ).
cnf(227,axiom,
( ~ l0(u)
| ~ r1(u)
| r2(u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(228,axiom,
( ~ s1(b)
| ~ q2(b,u,b)
| s2(u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(279,axiom,
( ~ p2(u,v,w)
| n3(w) ),
file('SYN270-1.p',unknown),
[] ).
cnf(283,axiom,
( ~ n2(u)
| p3(u,u,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(294,axiom,
( ~ n0(u,v)
| ~ q2(u,v,w)
| q3(v,w) ),
file('SYN270-1.p',unknown),
[] ).
cnf(296,axiom,
( ~ s2(u)
| ~ q3(v,u)
| ~ n1(w,u,v)
| q3(u,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(306,axiom,
( ~ p2(u,v,w)
| r3(u,w,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(311,axiom,
( ~ r2(u)
| ~ k2(v,u)
| ~ r3(u,w,w)
| r3(w,v,u) ),
file('SYN270-1.p',unknown),
[] ).
cnf(313,axiom,
( ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e)
| k4(c) ),
file('SYN270-1.p',unknown),
[] ).
cnf(324,axiom,
( ~ r0(u)
| ~ r3(v,u,v)
| p4(u,u,v) ),
file('SYN270-1.p',unknown),
[] ).
cnf(338,axiom,
( ~ l1(u,v)
| ~ p3(w,v,x)
| s4(u) ),
file('SYN270-1.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(419,plain,
( ~ r0(b)
| ~ r3(c,b,c) ),
inference(res,[status(thm),theory(equality)],[324,1]),
[iquote('0:Res:324.2,1.0')] ).
cnf(420,plain,
~ r3(c,b,c),
inference(mrr,[status(thm)],[419,10]),
[iquote('0:MRR:419.0,10.0')] ).
cnf(455,plain,
s1(b),
inference(res,[status(thm),theory(equality)],[15,164]),
[iquote('0:Res:15.0,164.0')] ).
cnf(456,plain,
( ~ q2(b,u,b)
| s2(u) ),
inference(mrr,[status(thm)],[228,455]),
[iquote('0:MRR:228.0,455.0')] ).
cnf(459,plain,
k1(c),
inference(res,[status(thm),theory(equality)],[27,40]),
[iquote('0:Res:27.0,40.0')] ).
cnf(460,plain,
k1(e),
inference(res,[status(thm),theory(equality)],[4,40]),
[iquote('0:Res:4.0,40.0')] ).
cnf(461,plain,
k1(b),
inference(res,[status(thm),theory(equality)],[16,40]),
[iquote('0:Res:16.0,40.0')] ).
cnf(468,plain,
( ~ n2(u)
| p2(u,u,u) ),
inference(mrr,[status(thm)],[213,460]),
[iquote('0:MRR:213.1,460.0')] ).
cnf(469,plain,
m2(b),
inference(mrr,[status(thm)],[175,461]),
[iquote('0:MRR:175.0,461.0')] ).
cnf(474,plain,
l1(c,c),
inference(res,[status(thm),theory(equality)],[27,41]),
[iquote('0:Res:27.0,41.0')] ).
cnf(475,plain,
l1(e,e),
inference(res,[status(thm),theory(equality)],[4,41]),
[iquote('0:Res:4.0,41.0')] ).
cnf(476,plain,
l1(b,b),
inference(res,[status(thm),theory(equality)],[16,41]),
[iquote('0:Res:16.0,41.0')] ).
cnf(492,plain,
( ~ n2(u)
| n3(u) ),
inference(res,[status(thm),theory(equality)],[468,279]),
[iquote('0:Res:468.1,279.0')] ).
cnf(502,plain,
q2(b,b,b),
inference(res,[status(thm),theory(equality)],[476,225]),
[iquote('0:Res:476.0,225.0')] ).
cnf(506,plain,
s2(b),
inference(res,[status(thm),theory(equality)],[502,456]),
[iquote('0:Res:502.0,456.0')] ).
cnf(542,plain,
p1(u,u,u),
inference(res,[status(thm),theory(equality)],[15,124]),
[iquote('0:Res:15.0,124.0')] ).
cnf(543,plain,
q2(u,u,u),
inference(mrr,[status(thm)],[220,542]),
[iquote('0:MRR:220.0,542.0')] ).
cnf(545,plain,
( ~ k0(u)
| ~ r1(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[226,543]),
[iquote('0:MRR:226.2,543.0')] ).
cnf(546,plain,
n2(u),
inference(res,[status(thm),theory(equality)],[542,176]),
[iquote('0:Res:542.0,176.0')] ).
cnf(548,plain,
p3(u,u,u),
inference(mrr,[status(thm)],[283,546]),
[iquote('0:MRR:283.0,546.0')] ).
cnf(552,plain,
p2(u,u,u),
inference(mrr,[status(thm)],[468,546]),
[iquote('0:MRR:468.0,546.0')] ).
cnf(553,plain,
n3(u),
inference(mrr,[status(thm)],[492,546]),
[iquote('0:MRR:492.0,546.0')] ).
cnf(564,plain,
( ~ q3(e,b)
| k4(c) ),
inference(mrr,[status(thm)],[394,553]),
[iquote('0:MRR:394.0,553.0')] ).
cnf(578,plain,
k2(u,u),
inference(res,[status(thm),theory(equality)],[403,168]),
[iquote('0:Res:403.0,168.0')] ).
cnf(603,plain,
( ~ q0(u,v)
| s1(u) ),
inference(ems,[status(thm)],[165,455]),
[iquote('0:EmS:165.0,455.0')] ).
cnf(609,plain,
s1(u),
inference(res,[status(thm),theory(equality)],[18,603]),
[iquote('0:Res:18.0,603.0')] ).
cnf(615,plain,
( ~ l2(u,u)
| ~ n0(e,u)
| l2(v,u) ),
inference(mrr,[status(thm)],[170,609]),
[iquote('0:MRR:170.0,609.0')] ).
cnf(616,plain,
( ~ p0(u,u)
| ~ m0(v,w,x)
| l2(x,x) ),
inference(mrr,[status(thm)],[172,609]),
[iquote('0:MRR:172.0,609.0')] ).
cnf(623,plain,
n1(e,e,b),
inference(res,[status(thm),theory(equality)],[32,75]),
[iquote('0:Res:32.0,75.0')] ).
cnf(642,plain,
r3(u,u,u),
inference(res,[status(thm),theory(equality)],[552,306]),
[iquote('0:Res:552.0,306.0')] ).
cnf(652,plain,
q1(u,u,u),
inference(res,[status(thm),theory(equality)],[20,160]),
[iquote('0:Res:20.0,160.0')] ).
cnf(680,plain,
( ~ q0(u,d)
| r1(u) ),
inference(res,[status(thm),theory(equality)],[652,401]),
[iquote('0:Res:652.0,401.1')] ).
cnf(681,plain,
r1(u),
inference(mrr,[status(thm)],[680,18]),
[iquote('0:MRR:680.0,18.0')] ).
cnf(682,plain,
( ~ l0(u)
| r2(u) ),
inference(mrr,[status(thm)],[227,681]),
[iquote('0:MRR:227.1,681.0')] ).
cnf(685,plain,
( ~ k0(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[545,681]),
[iquote('0:MRR:545.1,681.0')] ).
cnf(708,plain,
( ~ s0(b)
| m1(b,u,b) ),
inference(res,[status(thm),theory(equality)],[15,68]),
[iquote('0:Res:15.0,68.1')] ).
cnf(709,plain,
m1(b,u,b),
inference(ssi,[status(thm)],[708,6,33,10,469,461,506]),
[iquote('0:SSi:708.0,6.0,33.0,10.0,469.0,461.0,506.0')] ).
cnf(734,plain,
( ~ l1(u,v)
| s4(u) ),
inference(res,[status(thm),theory(equality)],[548,338]),
[iquote('0:Res:548.0,338.1')] ).
cnf(735,plain,
s4(c),
inference(res,[status(thm),theory(equality)],[474,734]),
[iquote('0:Res:474.0,734.0')] ).
cnf(738,plain,
s4(e),
inference(res,[status(thm),theory(equality)],[475,734]),
[iquote('0:Res:475.0,734.0')] ).
cnf(739,plain,
s4(b),
inference(res,[status(thm),theory(equality)],[476,734]),
[iquote('0:Res:476.0,734.0')] ).
cnf(992,plain,
( ~ p0(u,u)
| l2(v,v) ),
inference(res,[status(thm),theory(equality)],[20,616]),
[iquote('0:Res:20.0,616.1')] ).
cnf(993,plain,
l2(u,u),
inference(res,[status(thm),theory(equality)],[15,992]),
[iquote('0:Res:15.0,992.0')] ).
cnf(996,plain,
( ~ n0(e,u)
| l2(v,u) ),
inference(mrr,[status(thm)],[615,993]),
[iquote('0:MRR:615.0,993.0')] ).
cnf(1001,plain,
l2(u,b),
inference(res,[status(thm),theory(equality)],[12,996]),
[iquote('0:Res:12.0,996.0')] ).
cnf(1004,plain,
( ~ k1(u)
| q2(b,c,u) ),
inference(res,[status(thm),theory(equality)],[1001,400]),
[iquote('0:Res:1001.0,400.1')] ).
cnf(1011,plain,
( ~ k1(b)
| s2(c) ),
inference(res,[status(thm),theory(equality)],[1004,456]),
[iquote('0:Res:1004.1,456.0')] ).
cnf(1014,plain,
s2(c),
inference(ssi,[status(thm)],[1011,6,33,10,469,461,506,739]),
[iquote('0:SSi:1011.0,6.0,33.0,10.0,469.0,461.0,506.0,739.0')] ).
cnf(1040,plain,
( ~ k0(u)
| q2(v,u,v) ),
inference(res,[status(thm),theory(equality)],[20,685]),
[iquote('0:Res:20.0,685.1')] ).
cnf(1041,plain,
( ~ k0(u)
| s2(u) ),
inference(res,[status(thm),theory(equality)],[1040,456]),
[iquote('0:Res:1040.1,456.0')] ).
cnf(1042,plain,
( ~ k0(u)
| ~ n0(v,u)
| q3(u,v) ),
inference(res,[status(thm),theory(equality)],[1040,294]),
[iquote('0:Res:1040.1,294.1')] ).
cnf(1095,plain,
( ~ k0(b)
| q3(b,e) ),
inference(res,[status(thm),theory(equality)],[12,1042]),
[iquote('0:Res:12.0,1042.1')] ).
cnf(1100,plain,
q3(b,e),
inference(ssi,[status(thm)],[1095,6,33,10,469,461,506,739]),
[iquote('0:SSi:1095.0,6.0,33.0,10.0,469.0,461.0,506.0,739.0')] ).
cnf(1403,plain,
( ~ s2(e)
| ~ q3(b,e)
| q3(e,b) ),
inference(res,[status(thm),theory(equality)],[623,296]),
[iquote('0:Res:623.0,296.2')] ).
cnf(1419,plain,
( ~ q3(b,e)
| q3(e,b) ),
inference(ssi,[status(thm)],[1403,1041,29,14,460,738]),
[iquote('0:SSi:1403.0,1041.0,29.0,14.0,460.0,738.1')] ).
cnf(1420,plain,
q3(e,b),
inference(mrr,[status(thm)],[1419,1100]),
[iquote('0:MRR:1419.0,1100.0')] ).
cnf(1421,plain,
k4(c),
inference(mrr,[status(thm)],[564,1420]),
[iquote('0:MRR:564.0,1420.0')] ).
cnf(1454,plain,
( ~ k1(u)
| ~ k2(u,v)
| k2(b,v) ),
inference(res,[status(thm),theory(equality)],[709,166]),
[iquote('0:Res:709.0,166.2')] ).
cnf(1500,plain,
( ~ r2(u)
| ~ k2(v,u)
| r3(u,v,u) ),
inference(res,[status(thm),theory(equality)],[642,311]),
[iquote('0:Res:642.0,311.2')] ).
cnf(2129,plain,
( ~ k1(u)
| k2(b,u) ),
inference(res,[status(thm),theory(equality)],[578,1454]),
[iquote('0:Res:578.0,1454.1')] ).
cnf(2216,plain,
( ~ k1(u)
| ~ r2(u)
| r3(u,b,u) ),
inference(res,[status(thm),theory(equality)],[2129,1500]),
[iquote('0:Res:2129.1,1500.1')] ).
cnf(2633,plain,
( ~ k1(c)
| ~ r2(c) ),
inference(res,[status(thm),theory(equality)],[2216,420]),
[iquote('0:Res:2216.2,420.0')] ).
cnf(2637,plain,
$false,
inference(ssi,[status(thm)],[2633,682,25,459,735,1014,1421]),
[iquote('0:SSi:2633.1,2633.0,682.0,25.0,459.0,735.0,1014.0,1421.0,25.0,459.0,735.0,1014.0,1421.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN270-1 : TPTP v8.1.0. Released v1.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n004.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 : Tue Jul 12 01:50:37 EDT 2022
% 0.12/0.35 % 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 1978 clauses, backtracked 0 clauses, performed 0 splits and kept 1200 clauses.
% 0.39/0.60 SPASS allocated 77321 KBytes.
% 0.39/0.60 SPASS spent 0:00:00.23 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 5, length 116 :
% 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_267 rule_272 rule_274 rule_285 rule_299
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