TSTP Solution File: LAT359+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT359+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Sun Jul 17 06:51:24 EDT 2022
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of clauses : 61 ( 13 unt; 14 nHn; 61 RR)
% Number of literals : 161 ( 0 equ; 99 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
l2_altcat_1(skc14),
file('LAT359+1.p',unknown),
[] ).
cnf(5,axiom,
v1_xboole_0(k1_xboole_0),
file('LAT359+1.p',unknown),
[] ).
cnf(20,axiom,
v1_relat_1(skc25),
file('LAT359+1.p',unknown),
[] ).
cnf(21,axiom,
v1_xboole_0(skc25),
file('LAT359+1.p',unknown),
[] ).
cnf(34,axiom,
m1_subset_1(skf3(u),u),
file('LAT359+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ v1_xboole_0(u)
| v1_funct_1(u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ l2_altcat_1(u)
| l1_altcat_1(u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ m1_pboole(u,v)
| v1_relat_1(u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ m1_pboole(u,v)
| v1_funct_1(u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ v1_xboole_0(u)
| equal(u,k1_xboole_0) ),
file('LAT359+1.p',unknown),
[] ).
cnf(71,axiom,
r2_hidden(skc17,k1_binop_1(u1_altcat_1(skc14),skc15,skc16)),
file('LAT359+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ r2_hidden(u,v)
| m1_subset_1(u,v) ),
file('LAT359+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('LAT359+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ l1_altcat_1(u)
| m1_pboole(u1_altcat_1(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u))) ),
file('LAT359+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ r2_hidden(k4_tarski(u,v),k2_zfmisc_1(w,x))
| r2_hidden(u,w) ),
file('LAT359+1.p',unknown),
[] ).
cnf(116,axiom,
( ~ r2_hidden(k4_tarski(u,v),k2_zfmisc_1(w,x))
| r2_hidden(v,x) ),
file('LAT359+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ m1_pboole(u,v)
| equal(k1_relat_1(u),v) ),
file('LAT359+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| equal(k1_funct_1(u,k4_tarski(v,w)),k1_binop_1(u,v,w)) ),
file('LAT359+1.p',unknown),
[] ).
cnf(123,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ equal(v,k1_xboole_0)
| r2_hidden(w,k1_relat_1(u))
| equal(v,k1_funct_1(u,w)) ),
file('LAT359+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ r2_hidden(v,k1_relat_1(u))
| ~ equal(w,k1_funct_1(u,v))
| r2_hidden(k4_tarski(v,w),u) ),
file('LAT359+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ l1_altcat_1(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| equal(k1_binop_1(u1_altcat_1(u),w,v),k1_altcat_1(u,w,v)) ),
file('LAT359+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ m1_subset_1(u,u1_struct_0(skc14))
| ~ equal(u,skc15)
| ~ r2_hidden(skc17,k1_altcat_1(skc14,u,skc16))
| ~ m1_subset_1(skc17,k1_altcat_1(skc14,u,skc16))
| ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
file('LAT359+1.p',unknown),
[] ).
cnf(130,plain,
( ~ m1_pboole(u,v)
| equal(k1_relat_1(u),v) ),
inference(mrr,[status(thm)],[118,53,52]),
[iquote('0:MRR:118.0,118.1,53.1,52.1')] ).
cnf(131,plain,
( ~ equal(u,skc15)
| ~ m1_subset_1(u,u1_struct_0(skc14))
| ~ m1_subset_1(skc16,u1_struct_0(skc14))
| ~ r2_hidden(skc17,k1_altcat_1(skc14,u,skc16)) ),
inference(mrr,[status(thm)],[127,73]),
[iquote('0:MRR:127.3,73.1')] ).
cnf(132,plain,
l1_altcat_1(skc14),
inference(res,[status(thm),theory(equality)],[1,49]),
[iquote('0:Res:1.0,49.0')] ).
cnf(142,plain,
equal(skc25,k1_xboole_0),
inference(ems,[status(thm)],[70,21]),
[iquote('0:EmS:70.0,21.0')] ).
cnf(144,plain,
v1_relat_1(k1_xboole_0),
inference(rew,[status(thm),theory(equality)],[142,20]),
[iquote('0:Rew:142.0,20.0')] ).
cnf(235,plain,
( v1_xboole_0(u)
| r2_hidden(skf3(u),u) ),
inference(res,[status(thm),theory(equality)],[34,94]),
[iquote('0:Res:34.0,94.0')] ).
cnf(324,plain,
( ~ l1_altcat_1(u)
| equal(k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),k1_relat_1(u1_altcat_1(u))) ),
inference(res,[status(thm),theory(equality)],[114,130]),
[iquote('0:Res:114.1,130.0')] ).
cnf(325,plain,
( ~ l1_altcat_1(u)
| v1_relat_1(u1_altcat_1(u)) ),
inference(res,[status(thm),theory(equality)],[114,52]),
[iquote('0:Res:114.1,52.0')] ).
cnf(326,plain,
( ~ l1_altcat_1(u)
| v1_funct_1(u1_altcat_1(u)) ),
inference(res,[status(thm),theory(equality)],[114,53]),
[iquote('0:Res:114.1,53.0')] ).
cnf(361,plain,
( ~ l1_altcat_1(u)
| ~ r2_hidden(k4_tarski(v,w),k1_relat_1(u1_altcat_1(u)))
| r2_hidden(v,u1_struct_0(u)) ),
inference(spl,[status(thm),theory(equality)],[324,115]),
[iquote('0:SpL:324.1,115.0')] ).
cnf(362,plain,
( ~ l1_altcat_1(u)
| ~ r2_hidden(k4_tarski(v,w),k1_relat_1(u1_altcat_1(u)))
| r2_hidden(w,u1_struct_0(u)) ),
inference(spl,[status(thm),theory(equality)],[324,116]),
[iquote('0:SpL:324.1,116.0')] ).
cnf(397,plain,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| r2_hidden(v,k1_relat_1(u))
| equal(k1_funct_1(u,v),k1_xboole_0) ),
inference(eqr,[status(thm),theory(equality)],[123]),
[iquote('0:EqR:123.2')] ).
cnf(415,plain,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ v1_xboole_0(u)
| ~ r2_hidden(v,k1_relat_1(u))
| ~ equal(w,k1_funct_1(u,v)) ),
inference(res,[status(thm),theory(equality)],[125,74]),
[iquote('0:Res:125.4,74.1')] ).
cnf(421,plain,
( ~ v1_funct_1(u)
| ~ v1_relat_1(u)
| ~ v1_xboole_0(u)
| ~ r2_hidden(v,k1_relat_1(u)) ),
inference(aed,[status(thm),theory(equality)],[415]),
[iquote('0:AED:415.4')] ).
cnf(422,plain,
( ~ v1_relat_1(u)
| ~ v1_xboole_0(u)
| ~ r2_hidden(v,k1_relat_1(u)) ),
inference(ssi,[status(thm)],[421,43]),
[iquote('0:SSi:421.0,43.1')] ).
cnf(426,plain,
( ~ v1_relat_1(u)
| ~ v1_xboole_0(u)
| v1_xboole_0(k1_relat_1(u)) ),
inference(res,[status(thm),theory(equality)],[235,422]),
[iquote('0:Res:235.1,422.2')] ).
cnf(431,plain,
( ~ v1_xboole_0(u)
| ~ v1_relat_1(u)
| equal(k1_relat_1(u),k1_xboole_0) ),
inference(ems,[status(thm)],[70,426]),
[iquote('0:EmS:70.0,426.2')] ).
cnf(434,plain,
( ~ v1_relat_1(u)
| ~ v1_xboole_0(u)
| ~ r2_hidden(v,k1_xboole_0) ),
inference(rew,[status(thm),theory(equality)],[431,422]),
[iquote('0:Rew:431.2,422.2')] ).
cnf(448,plain,
~ r2_hidden(u,k1_xboole_0),
inference(ems,[status(thm)],[434,144,5]),
[iquote('0:EmS:434.0,434.1,144.0,5.0')] ).
cnf(453,plain,
( ~ l1_altcat_1(skc14)
| ~ m1_subset_1(skc16,u1_struct_0(skc14))
| ~ m1_subset_1(skc15,u1_struct_0(skc14))
| r2_hidden(skc17,k1_altcat_1(skc14,skc15,skc16)) ),
inference(spr,[status(thm),theory(equality)],[126,71]),
[iquote('0:SpR:126.3,71.0')] ).
cnf(457,plain,
( ~ m1_subset_1(skc16,u1_struct_0(skc14))
| ~ m1_subset_1(skc15,u1_struct_0(skc14))
| r2_hidden(skc17,k1_altcat_1(skc14,skc15,skc16)) ),
inference(ssi,[status(thm)],[453,1,132]),
[iquote('0:SSi:453.0,1.0,132.0')] ).
cnf(540,plain,
( ~ m1_subset_1(skc16,u1_struct_0(skc14))
| ~ m1_subset_1(skc15,u1_struct_0(skc14))
| ~ equal(skc15,skc15)
| ~ m1_subset_1(skc15,u1_struct_0(skc14))
| ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[457,131]),
[iquote('0:Res:457.2,131.3')] ).
cnf(559,plain,
( ~ m1_subset_1(skc15,u1_struct_0(skc14))
| ~ m1_subset_1(skc16,u1_struct_0(skc14)) ),
inference(obv,[status(thm),theory(equality)],[540]),
[iquote('0:Obv:540.2')] ).
cnf(560,plain,
( ~ r2_hidden(skc16,u1_struct_0(skc14))
| ~ m1_subset_1(skc15,u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[73,559]),
[iquote('0:Res:73.1,559.1')] ).
cnf(561,plain,
( ~ r2_hidden(skc15,u1_struct_0(skc14))
| ~ r2_hidden(skc16,u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[73,560]),
[iquote('0:Res:73.1,560.1')] ).
cnf(612,plain,
( ~ v1_funct_1(u1_altcat_1(u))
| ~ v1_relat_1(u1_altcat_1(u))
| ~ l1_altcat_1(u)
| equal(k1_funct_1(u1_altcat_1(u),k4_tarski(v,w)),k1_xboole_0)
| r2_hidden(v,u1_struct_0(u)) ),
inference(res,[status(thm),theory(equality)],[397,361]),
[iquote('0:Res:397.2,361.1')] ).
cnf(613,plain,
( ~ v1_funct_1(u1_altcat_1(u))
| ~ v1_relat_1(u1_altcat_1(u))
| ~ l1_altcat_1(u)
| equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
| r2_hidden(v,u1_struct_0(u)) ),
inference(rew,[status(thm),theory(equality)],[121,612]),
[iquote('0:Rew:121.2,612.3')] ).
cnf(614,plain,
( ~ l1_altcat_1(u)
| equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
| r2_hidden(v,u1_struct_0(u)) ),
inference(ssi,[status(thm)],[613,325,326]),
[iquote('0:SSi:613.1,613.0,325.1,326.1,325.1,326.1')] ).
cnf(616,plain,
( ~ l1_altcat_1(skc14)
| r2_hidden(skc15,u1_struct_0(skc14))
| r2_hidden(skc17,k1_xboole_0) ),
inference(spr,[status(thm),theory(equality)],[614,71]),
[iquote('0:SpR:614.1,71.0')] ).
cnf(622,plain,
( r2_hidden(skc15,u1_struct_0(skc14))
| r2_hidden(skc17,k1_xboole_0) ),
inference(ssi,[status(thm)],[616,1,132]),
[iquote('0:SSi:616.0,1.0,132.0')] ).
cnf(623,plain,
r2_hidden(skc15,u1_struct_0(skc14)),
inference(mrr,[status(thm)],[622,448]),
[iquote('0:MRR:622.1,448.0')] ).
cnf(624,plain,
~ r2_hidden(skc16,u1_struct_0(skc14)),
inference(mrr,[status(thm)],[561,623]),
[iquote('0:MRR:561.0,623.0')] ).
cnf(667,plain,
( ~ v1_funct_1(u1_altcat_1(u))
| ~ v1_relat_1(u1_altcat_1(u))
| ~ l1_altcat_1(u)
| equal(k1_funct_1(u1_altcat_1(u),k4_tarski(v,w)),k1_xboole_0)
| r2_hidden(w,u1_struct_0(u)) ),
inference(res,[status(thm),theory(equality)],[397,362]),
[iquote('0:Res:397.2,362.1')] ).
cnf(668,plain,
( ~ v1_funct_1(u1_altcat_1(u))
| ~ v1_relat_1(u1_altcat_1(u))
| ~ l1_altcat_1(u)
| equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
| r2_hidden(w,u1_struct_0(u)) ),
inference(rew,[status(thm),theory(equality)],[121,667]),
[iquote('0:Rew:121.2,667.3')] ).
cnf(669,plain,
( ~ l1_altcat_1(u)
| equal(k1_binop_1(u1_altcat_1(u),v,w),k1_xboole_0)
| r2_hidden(w,u1_struct_0(u)) ),
inference(ssi,[status(thm)],[668,325,326]),
[iquote('0:SSi:668.1,668.0,325.1,326.1,325.1,326.1')] ).
cnf(716,plain,
( ~ l1_altcat_1(skc14)
| r2_hidden(skc16,u1_struct_0(skc14))
| r2_hidden(skc17,k1_xboole_0) ),
inference(spr,[status(thm),theory(equality)],[669,71]),
[iquote('0:SpR:669.1,71.0')] ).
cnf(723,plain,
( r2_hidden(skc16,u1_struct_0(skc14))
| r2_hidden(skc17,k1_xboole_0) ),
inference(ssi,[status(thm)],[716,1,132]),
[iquote('0:SSi:716.0,1.0,132.0')] ).
cnf(724,plain,
$false,
inference(mrr,[status(thm)],[723,624,448]),
[iquote('0:MRR:723.0,723.1,624.0,448.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT359+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Tue Jun 28 20:02:14 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.16/0.49
% 0.16/0.49 SPASS V 3.9
% 0.16/0.49 SPASS beiseite: Proof found.
% 0.16/0.49 % SZS status Theorem
% 0.16/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.49 SPASS derived 524 clauses, backtracked 0 clauses, performed 0 splits and kept 421 clauses.
% 0.16/0.49 SPASS allocated 98282 KBytes.
% 0.16/0.49 SPASS spent 0:00:00.17 on the problem.
% 0.16/0.49 0:00:00.04 for the input.
% 0.16/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.16/0.49 0:00:00.01 for inferences.
% 0.16/0.49 0:00:00.00 for the backtracking.
% 0.16/0.49 0:00:00.05 for the reduction.
% 0.16/0.49
% 0.16/0.49
% 0.16/0.49 Here is a proof with depth 4, length 61 :
% 0.16/0.49 % SZS output start Refutation
% See solution above
% 0.16/0.49 Formulae used in the proof : t12_waybel34 fc6_membered rc2_funct_1 existence_m1_subset_1 cc1_funct_1 dt_l2_altcat_1 dt_m1_pboole t6_boole t1_subset t7_boole t2_subset dt_u1_altcat_1 t106_zfmisc_1 d3_pboole d1_binop_1 d4_funct_1 d2_altcat_1
% 0.16/0.49
%------------------------------------------------------------------------------