TSTP Solution File: SYN180-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN180-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 12:19:15 EDT 2022
% Result : Unsatisfiable 0.45s 0.63s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 44
% Syntax : Number of clauses : 97 ( 49 unt; 0 nHn; 97 RR)
% Number of literals : 174 ( 0 equ; 82 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ q4(a,e),
file('SYN180-1.p',unknown),
[] ).
cnf(2,axiom,
s0(d),
file('SYN180-1.p',unknown),
[] ).
cnf(4,axiom,
n0(d,e),
file('SYN180-1.p',unknown),
[] ).
cnf(6,axiom,
s0(b),
file('SYN180-1.p',unknown),
[] ).
cnf(10,axiom,
r0(b),
file('SYN180-1.p',unknown),
[] ).
cnf(13,axiom,
m0(a,u,a),
file('SYN180-1.p',unknown),
[] ).
cnf(14,axiom,
r0(e),
file('SYN180-1.p',unknown),
[] ).
cnf(15,axiom,
p0(b,u),
file('SYN180-1.p',unknown),
[] ).
cnf(16,axiom,
n0(a,b),
file('SYN180-1.p',unknown),
[] ).
cnf(18,axiom,
q0(u,d),
file('SYN180-1.p',unknown),
[] ).
cnf(20,axiom,
m0(u,d,v),
file('SYN180-1.p',unknown),
[] ).
cnf(21,axiom,
l0(a),
file('SYN180-1.p',unknown),
[] ).
cnf(29,axiom,
k0(e),
file('SYN180-1.p',unknown),
[] ).
cnf(33,axiom,
k0(b),
file('SYN180-1.p',unknown),
[] ).
cnf(37,axiom,
q0(a,b),
file('SYN180-1.p',unknown),
[] ).
cnf(38,axiom,
n0(b,a),
file('SYN180-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ n0(u,v)
| k1(v) ),
file('SYN180-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ n0(u,v)
| l1(v,v) ),
file('SYN180-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ m1(u,v,w)
| ~ m1(u,w,x)
| m1(x,w,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(60,axiom,
( ~ k0(u)
| ~ l0(v)
| m1(v,u,v) ),
file('SYN180-1.p',unknown),
[] ).
cnf(63,axiom,
( ~ m0(a,u,a)
| ~ q0(v,w)
| ~ m1(w,c,w)
| m1(v,a,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(68,axiom,
( ~ s0(u)
| ~ p0(u,v)
| m1(u,v,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(124,axiom,
( ~ p0(u,v)
| p1(v,v,v) ),
file('SYN180-1.p',unknown),
[] ).
cnf(152,axiom,
( ~ r0(u)
| ~ m1(v,w,w)
| q1(v,v,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(160,axiom,
( ~ m0(u,v,w)
| q1(w,w,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(163,axiom,
( ~ q0(u,v)
| ~ s0(d)
| ~ q1(d,v,d)
| r1(u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(164,axiom,
( ~ p0(u,u)
| s1(u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ k1(b)
| m2(b) ),
file('SYN180-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ p1(u,v,w)
| n2(w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(194,axiom,
( ~ k1(u)
| ~ p2(e,v,w)
| p2(v,w,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(215,axiom,
( ~ m1(u,v,u)
| p2(v,u,v) ),
file('SYN180-1.p',unknown),
[] ).
cnf(216,axiom,
( ~ k0(u)
| ~ p1(v,v,v)
| q2(v,u,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(220,axiom,
( ~ p1(u,u,u)
| q2(u,u,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(225,axiom,
( ~ l1(u,v)
| q2(v,v,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(226,axiom,
( ~ k0(u)
| ~ r1(u)
| ~ q2(u,u,u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
file('SYN180-1.p',unknown),
[] ).
cnf(228,axiom,
( ~ s1(b)
| ~ q2(b,u,b)
| s2(u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(249,axiom,
( ~ n2(u)
| k3(u,u,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(275,axiom,
( ~ n2(u)
| m3(u,u,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(283,axiom,
( ~ n2(u)
| p3(u,u,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(294,axiom,
( ~ n0(u,v)
| ~ q2(u,v,w)
| q3(v,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(306,axiom,
( ~ p2(u,v,w)
| r3(u,w,u) ),
file('SYN180-1.p',unknown),
[] ).
cnf(315,axiom,
( ~ q3(u,u)
| ~ r3(u,e,v)
| ~ q1(a,a,v)
| k4(e) ),
file('SYN180-1.p',unknown),
[] ).
cnf(334,axiom,
( ~ m3(u,v,u)
| ~ q2(u,w,x)
| ~ k3(y,y,x)
| q4(x,w) ),
file('SYN180-1.p',unknown),
[] ).
cnf(338,axiom,
( ~ l1(u,v)
| ~ p3(w,v,x)
| s4(u) ),
file('SYN180-1.p',unknown),
[] ).
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(416,plain,
( ~ q0(u,v)
| ~ m1(v,c,v)
| m1(u,a,v) ),
inference(mrr,[status(thm)],[63,13]),
[iquote('0:MRR:63.0,13.0')] ).
cnf(419,plain,
( ~ m3(u,v,u)
| ~ k3(w,w,a)
| ~ q2(u,e,a) ),
inference(res,[status(thm),theory(equality)],[334,1]),
[iquote('0:Res:334.3,1.0')] ).
cnf(454,plain,
s1(b),
inference(res,[status(thm),theory(equality)],[15,164]),
[iquote('0:Res:15.0,164.0')] ).
cnf(455,plain,
( ~ q2(b,u,b)
| s2(u) ),
inference(mrr,[status(thm)],[228,454]),
[iquote('0:MRR:228.0,454.0')] ).
cnf(456,plain,
k1(a),
inference(res,[status(thm),theory(equality)],[38,40]),
[iquote('0:Res:38.0,40.0')] ).
cnf(459,plain,
k1(e),
inference(res,[status(thm),theory(equality)],[4,40]),
[iquote('0:Res:4.0,40.0')] ).
cnf(460,plain,
k1(b),
inference(res,[status(thm),theory(equality)],[16,40]),
[iquote('0:Res:16.0,40.0')] ).
cnf(468,plain,
m2(b),
inference(mrr,[status(thm)],[175,460]),
[iquote('0:MRR:175.0,460.0')] ).
cnf(471,plain,
l1(a,a),
inference(res,[status(thm),theory(equality)],[38,41]),
[iquote('0:Res:38.0,41.0')] ).
cnf(474,plain,
l1(e,e),
inference(res,[status(thm),theory(equality)],[4,41]),
[iquote('0:Res:4.0,41.0')] ).
cnf(475,plain,
l1(b,b),
inference(res,[status(thm),theory(equality)],[16,41]),
[iquote('0:Res:16.0,41.0')] ).
cnf(501,plain,
q2(b,b,b),
inference(res,[status(thm),theory(equality)],[475,225]),
[iquote('0:Res:475.0,225.0')] ).
cnf(503,plain,
s2(b),
inference(res,[status(thm),theory(equality)],[501,455]),
[iquote('0:Res:501.0,455.0')] ).
cnf(541,plain,
p1(u,u,u),
inference(res,[status(thm),theory(equality)],[15,124]),
[iquote('0:Res:15.0,124.0')] ).
cnf(542,plain,
q2(u,u,u),
inference(mrr,[status(thm)],[220,541]),
[iquote('0:MRR:220.0,541.0')] ).
cnf(543,plain,
( ~ k0(u)
| q2(v,u,u) ),
inference(mrr,[status(thm)],[216,541]),
[iquote('0:MRR:216.1,541.0')] ).
cnf(544,plain,
( ~ k0(u)
| ~ r1(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[226,542]),
[iquote('0:MRR:226.2,542.0')] ).
cnf(545,plain,
n2(u),
inference(res,[status(thm),theory(equality)],[541,176]),
[iquote('0:Res:541.0,176.0')] ).
cnf(547,plain,
p3(u,u,u),
inference(mrr,[status(thm)],[283,545]),
[iquote('0:MRR:283.0,545.0')] ).
cnf(548,plain,
m3(u,u,u),
inference(mrr,[status(thm)],[275,545]),
[iquote('0:MRR:275.0,545.0')] ).
cnf(549,plain,
k3(u,u,u),
inference(mrr,[status(thm)],[249,545]),
[iquote('0:MRR:249.0,545.0')] ).
cnf(651,plain,
q1(u,u,u),
inference(res,[status(thm),theory(equality)],[20,160]),
[iquote('0:Res:20.0,160.0')] ).
cnf(679,plain,
( ~ q0(u,d)
| r1(u) ),
inference(res,[status(thm),theory(equality)],[651,401]),
[iquote('0:Res:651.0,401.1')] ).
cnf(680,plain,
r1(u),
inference(mrr,[status(thm)],[679,18]),
[iquote('0:MRR:679.0,18.0')] ).
cnf(684,plain,
( ~ k0(u)
| ~ m0(v,w,x)
| q2(x,u,x) ),
inference(mrr,[status(thm)],[544,680]),
[iquote('0:MRR:544.1,680.0')] ).
cnf(707,plain,
( ~ s0(b)
| m1(b,u,b) ),
inference(res,[status(thm),theory(equality)],[15,68]),
[iquote('0:Res:15.0,68.1')] ).
cnf(708,plain,
m1(b,u,b),
inference(ssi,[status(thm)],[707,6,33,10,468,460,503]),
[iquote('0:SSi:707.0,6.0,33.0,10.0,468.0,460.0,503.0')] ).
cnf(709,plain,
p2(u,b,u),
inference(res,[status(thm),theory(equality)],[708,215]),
[iquote('0:Res:708.0,215.0')] ).
cnf(733,plain,
( ~ l1(u,v)
| s4(u) ),
inference(res,[status(thm),theory(equality)],[547,338]),
[iquote('0:Res:547.0,338.1')] ).
cnf(737,plain,
s4(a),
inference(res,[status(thm),theory(equality)],[471,733]),
[iquote('0:Res:471.0,733.0')] ).
cnf(739,plain,
s4(e),
inference(res,[status(thm),theory(equality)],[474,733]),
[iquote('0:Res:474.0,733.0')] ).
cnf(740,plain,
s4(b),
inference(res,[status(thm),theory(equality)],[475,733]),
[iquote('0:Res:475.0,733.0')] ).
cnf(783,plain,
( ~ p2(e,u,v)
| p2(u,v,v) ),
inference(ems,[status(thm)],[194,460]),
[iquote('0:EmS:194.0,460.0')] ).
cnf(789,plain,
p2(b,e,e),
inference(res,[status(thm),theory(equality)],[709,783]),
[iquote('0:Res:709.0,783.0')] ).
cnf(798,plain,
r3(b,e,b),
inference(res,[status(thm),theory(equality)],[789,306]),
[iquote('0:Res:789.0,306.0')] ).
cnf(890,plain,
( ~ m1(u,v,v)
| q1(u,u,v) ),
inference(ems,[status(thm)],[152,10]),
[iquote('0:EmS:152.0,10.0')] ).
cnf(939,plain,
( ~ k0(u)
| ~ n0(v,u)
| q3(u,u) ),
inference(res,[status(thm),theory(equality)],[543,294]),
[iquote('0:Res:543.1,294.1')] ).
cnf(999,plain,
( ~ k0(u)
| q2(v,u,v) ),
inference(res,[status(thm),theory(equality)],[20,684]),
[iquote('0:Res:20.0,684.1')] ).
cnf(1082,plain,
( ~ k0(b)
| q3(b,b) ),
inference(res,[status(thm),theory(equality)],[16,939]),
[iquote('0:Res:16.0,939.1')] ).
cnf(1086,plain,
q3(b,b),
inference(ssi,[status(thm)],[1082,6,33,10,468,460,503,740]),
[iquote('0:SSi:1082.0,6.0,33.0,10.0,468.0,460.0,503.0,740.0')] ).
cnf(1121,plain,
( ~ q0(u,b)
| m1(u,a,b) ),
inference(res,[status(thm),theory(equality)],[708,416]),
[iquote('0:Res:708.0,416.1')] ).
cnf(1123,plain,
m1(a,a,b),
inference(res,[status(thm),theory(equality)],[37,1121]),
[iquote('0:Res:37.0,1121.0')] ).
cnf(1312,plain,
( ~ m1(a,b,u)
| m1(u,b,b) ),
inference(res,[status(thm),theory(equality)],[1123,55]),
[iquote('0:Res:1123.0,55.0')] ).
cnf(1385,plain,
( ~ k0(b)
| ~ l0(a)
| m1(a,b,b) ),
inference(res,[status(thm),theory(equality)],[60,1312]),
[iquote('0:Res:60.2,1312.0')] ).
cnf(1386,plain,
m1(a,b,b),
inference(ssi,[status(thm)],[1385,21,456,737,6,33,10,468,460,503,740]),
[iquote('0:SSi:1385.1,1385.0,21.0,456.0,737.0,6.0,33.0,10.0,468.0,460.0,503.0,740.0')] ).
cnf(1433,plain,
q1(a,a,b),
inference(res,[status(thm),theory(equality)],[1386,890]),
[iquote('0:Res:1386.0,890.0')] ).
cnf(1485,plain,
( ~ q3(b,b)
| ~ q1(a,a,b)
| k4(e) ),
inference(res,[status(thm),theory(equality)],[798,315]),
[iquote('0:Res:798.0,315.1')] ).
cnf(1488,plain,
k4(e),
inference(mrr,[status(thm)],[1485,1086,1433]),
[iquote('0:MRR:1485.0,1485.1,1086.0,1433.0')] ).
cnf(2000,plain,
( ~ k3(u,u,a)
| ~ q2(v,e,a) ),
inference(res,[status(thm),theory(equality)],[548,419]),
[iquote('0:Res:548.0,419.0')] ).
cnf(2115,plain,
~ q2(u,e,a),
inference(res,[status(thm),theory(equality)],[549,2000]),
[iquote('0:Res:549.0,2000.0')] ).
cnf(2122,plain,
~ k0(e),
inference(res,[status(thm),theory(equality)],[999,2115]),
[iquote('0:Res:999.1,2115.0')] ).
cnf(2123,plain,
$false,
inference(ssi,[status(thm)],[2122,29,14,459,739,1488]),
[iquote('0:SSi:2122.0,29.0,14.0,459.0,739.0,1488.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN180-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n008.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 Jul 11 23:23:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.63
% 0.45/0.63 SPASS V 3.9
% 0.45/0.63 SPASS beiseite: Proof found.
% 0.45/0.63 % SZS status Theorem
% 0.45/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.63 SPASS derived 1525 clauses, backtracked 0 clauses, performed 0 splits and kept 1064 clauses.
% 0.45/0.63 SPASS allocated 77032 KBytes.
% 0.45/0.63 SPASS spent 0:00:00.27 on the problem.
% 0.45/0.63 0:00:00.04 for the input.
% 0.45/0.63 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.63 0:00:00.02 for inferences.
% 0.45/0.63 0:00:00.00 for the backtracking.
% 0.45/0.63 0:00:00.14 for the reduction.
% 0.45/0.63
% 0.45/0.63
% 0.45/0.63 Here is a proof with depth 6, length 97 :
% 0.45/0.63 % SZS output start Refutation
% See solution above
% 0.45/0.63 Formulae used in the proof : prove_this axiom_1 axiom_3 axiom_5 axiom_9 axiom_12 axiom_13 axiom_14 axiom_15 axiom_17 axiom_19 axiom_20 axiom_28 axiom_32 axiom_36 axiom_37 rule_001 rule_002 rule_016 rule_021 rule_024 rule_029 rule_085 rule_113 rule_121 rule_124 rule_125 rule_136 rule_137 rule_155 rule_176 rule_177 rule_181 rule_186 rule_187 rule_189 rule_210 rule_236 rule_244 rule_255 rule_267 rule_276 rule_295 rule_299
% 0.45/0.63
%------------------------------------------------------------------------------