%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU427+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Tue Jul 19 14:37:20 EDT 2022
% Result : Theorem 231.28s 231.48s
% Output : Refutation 231.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 48 ( 21 unt; 0 nHn; 48 RR)
% Number of literals : 88 ( 0 equ; 52 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
m1_subset_1(skc10,k1_zfmisc_1(skc8)),
file('SEU427+1.p',unknown),
[] ).
cnf(15,axiom,
m1_subset_1(skc9,k1_zfmisc_1(skc8)),
file('SEU427+1.p',unknown),
[] ).
cnf(27,axiom,
equal(k2_xboole_0(u,k1_xboole_0),u),
file('SEU427+1.p',unknown),
[] ).
cnf(28,axiom,
m1_subset_1(skc12,k1_zfmisc_1(k2_zfmisc_1(skc8,skc11))),
file('SEU427+1.p',unknown),
[] ).
cnf(34,axiom,
equal(k2_xboole_0(u,v),k2_xboole_0(v,u)),
file('SEU427+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ v1_relat_1(u)
| v1_relat_1(k5_relset_2(v,u)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ v1_relat_1(u)
| v1_funct_1(k5_relset_2(v,u)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('SEU427+1.p',unknown),
[] ).
cnf(50,axiom,
equal(k2_xboole_0(k3_pua2mss1(u),k3_pua2mss1(v)),k3_pua2mss1(k2_xboole_0(u,v))),
file('SEU427+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('SEU427+1.p',unknown),
[] ).
cnf(53,axiom,
equal(k4_relset_2(k1_zfmisc_1(skc8),skc11,k6_relset_2(skc11,skc8,skc12),k3_pua2mss1(skc9)),k1_xboole_0),
file('SEU427+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(k8_relset_2(skc8,skc11,k4_subset_1(skc8,skc9,skc10),skc12),k8_relset_2(skc8,skc11,skc10,skc12)),
file('SEU427+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| equal(k6_relset_2(w,v,u),k5_relset_2(v,u)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| m2_relset_1(k6_relset_2(w,v,u),k1_zfmisc_1(v),k1_zfmisc_1(w)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ v1_relat_1(u)
| equal(k9_relat_1(u,k2_xboole_0(v,w)),k2_xboole_0(k9_relat_1(u,v),k9_relat_1(u,w))) ),
file('SEU427+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| m1_subset_1(k4_subset_1(v,w,u),k1_zfmisc_1(v)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,k1_zfmisc_1(w))))
| equal(k4_relset_2(v,w,u,x),k9_relat_1(u,x)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(v))
| equal(k4_subset_1(v,w,u),k2_xboole_0(w,u)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| ~ m1_subset_1(x,k1_zfmisc_1(v))
| equal(k7_relset_2(v,w,x,u),k8_relset_2(v,w,x,u)) ),
file('SEU427+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| ~ m1_subset_1(x,k1_zfmisc_1(v))
| equal(k7_relset_2(v,w,x,u),k8_setfam_1(w,k4_relset_2(k1_zfmisc_1(v),w,k6_relset_2(w,v,u),k3_pua2mss1(x)))) ),
file('SEU427+1.p',unknown),
[] ).
cnf(72,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| m2_relset_1(k5_relset_2(v,u),k1_zfmisc_1(v),k1_zfmisc_1(w)) ),
inference(rew,[status(thm),theory(equality)],[59,61]),
[iquote('0:Rew:59.1,61.1')] ).
cnf(75,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(v))
| ~ m1_subset_1(w,k1_zfmisc_1(k2_zfmisc_1(v,x)))
| equal(k8_relset_2(v,x,u,w),k8_setfam_1(x,k4_relset_2(k1_zfmisc_1(v),x,k5_relset_2(v,w),k3_pua2mss1(u)))) ),
inference(rew,[status(thm),theory(equality)],[69,70,59]),
[iquote('0:Rew:69.2,70.2,59.1,70.2')] ).
cnf(81,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(skc8))
| m1_subset_1(k4_subset_1(skc8,skc9,u),k1_zfmisc_1(skc8)) ),
inference(res,[status(thm),theory(equality)],[15,64]),
[iquote('0:Res:15.0,64.0')] ).
cnf(114,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(skc8))
| equal(k8_relset_2(skc8,skc11,u,skc12),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(u)))) ),
inference(res,[status(thm),theory(equality)],[28,75]),
[iquote('0:Res:28.0,75.0')] ).
cnf(116,plain,
m2_relset_1(k5_relset_2(skc8,skc12),k1_zfmisc_1(skc8),k1_zfmisc_1(skc11)),
inference(res,[status(thm),theory(equality)],[28,72]),
[iquote('0:Res:28.0,72.0')] ).
cnf(118,plain,
equal(k6_relset_2(skc11,skc8,skc12),k5_relset_2(skc8,skc12)),
inference(res,[status(thm),theory(equality)],[28,59]),
[iquote('0:Res:28.0,59.0')] ).
cnf(119,plain,
v1_relat_1(skc12),
inference(res,[status(thm),theory(equality)],[28,42]),
[iquote('0:Res:28.0,42.0')] ).
cnf(132,plain,
equal(k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc9)),k1_xboole_0),
inference(rew,[status(thm),theory(equality)],[118,53]),
[iquote('0:Rew:118.0,53.0')] ).
cnf(135,plain,
equal(k8_relset_2(skc8,skc11,skc10,skc12),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))),
inference(res,[status(thm),theory(equality)],[14,114]),
[iquote('0:Res:14.0,114.0')] ).
cnf(146,plain,
m1_subset_1(k4_subset_1(skc8,skc9,skc10),k1_zfmisc_1(skc8)),
inference(res,[status(thm),theory(equality)],[14,81]),
[iquote('0:Res:14.0,81.0')] ).
cnf(174,plain,
~ equal(k8_relset_2(skc8,skc11,k4_subset_1(skc8,skc9,skc10),skc12),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))),
inference(rew,[status(thm),theory(equality)],[135,58]),
[iquote('0:Rew:135.0,58.0')] ).
cnf(194,plain,
equal(k2_xboole_0(k1_xboole_0,u),u),
inference(spr,[status(thm),theory(equality)],[34,27]),
[iquote('0:SpR:34.0,27.0')] ).
cnf(638,plain,
m1_subset_1(k5_relset_2(skc8,skc12),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(skc8),k1_zfmisc_1(skc11)))),
inference(res,[status(thm),theory(equality)],[116,51]),
[iquote('0:Res:116.0,51.0')] ).
cnf(729,plain,
( ~ v1_relat_1(u)
| equal(k9_relat_1(u,k3_pua2mss1(k2_xboole_0(v,w))),k2_xboole_0(k9_relat_1(u,k3_pua2mss1(v)),k9_relat_1(u,k3_pua2mss1(w)))) ),
inference(spr,[status(thm),theory(equality)],[50,62]),
[iquote('0:SpR:50.0,62.1')] ).
cnf(853,plain,
( ~ m1_subset_1(k5_relset_2(skc8,skc12),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(skc8),k1_zfmisc_1(skc11))))
| equal(k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc9)),k1_xboole_0) ),
inference(spr,[status(thm),theory(equality)],[65,132]),
[iquote('0:SpR:65.1,132.0')] ).
cnf(856,plain,
equal(k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc9)),k1_xboole_0),
inference(mrr,[status(thm)],[853,638]),
[iquote('0:MRR:853.0,638.0')] ).
cnf(3694,plain,
( ~ v1_relat_1(u)
| ~ m1_subset_1(v,k1_zfmisc_1(w))
| ~ m1_subset_1(x,k1_zfmisc_1(w))
| equal(k9_relat_1(u,k3_pua2mss1(k4_subset_1(w,x,v))),k2_xboole_0(k9_relat_1(u,k3_pua2mss1(x)),k9_relat_1(u,k3_pua2mss1(v)))) ),
inference(spr,[status(thm),theory(equality)],[66,729]),
[iquote('0:SpR:66.2,729.1')] ).
cnf(9791,plain,
( ~ m1_subset_1(k4_subset_1(skc8,skc9,skc10),k1_zfmisc_1(skc8))
| ~ m1_subset_1(skc12,k1_zfmisc_1(k2_zfmisc_1(skc8,skc11)))
| ~ equal(k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10)))),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))) ),
inference(spl,[status(thm),theory(equality)],[75,174]),
[iquote('0:SpL:75.2,174.0')] ).
cnf(9794,plain,
( ~ m1_subset_1(k4_subset_1(skc8,skc9,skc10),k1_zfmisc_1(skc8))
| ~ equal(k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10)))),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))) ),
inference(mrr,[status(thm)],[9791,28]),
[iquote('0:MRR:9791.1,28.0')] ).
cnf(9795,plain,
~ equal(k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10)))),k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))),
inference(mrr,[status(thm)],[9794,146]),
[iquote('0:MRR:9794.0,146.0')] ).
cnf(105378,plain,
( ~ m1_subset_1(k5_relset_2(skc8,skc12),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(skc8),k1_zfmisc_1(skc11))))
| ~ equal(k8_setfam_1(skc11,k4_relset_2(k1_zfmisc_1(skc8),skc11,k5_relset_2(skc8,skc12),k3_pua2mss1(skc10))),k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10))))) ),
inference(spl,[status(thm),theory(equality)],[65,9795]),
[iquote('0:SpL:65.1,9795.0')] ).
cnf(105384,plain,
( ~ m1_subset_1(k5_relset_2(skc8,skc12),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(skc8),k1_zfmisc_1(skc11))))
| ~ equal(k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10)))),k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))) ),
inference(rew,[status(thm),theory(equality)],[65,105378]),
[iquote('0:Rew:65.1,105378.1')] ).
cnf(105385,plain,
~ equal(k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(k4_subset_1(skc8,skc9,skc10)))),k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))),
inference(mrr,[status(thm)],[105384,638]),
[iquote('0:MRR:105384.0,638.0')] ).
cnf(108630,plain,
( ~ v1_relat_1(k5_relset_2(skc8,skc12))
| ~ m1_subset_1(skc10,k1_zfmisc_1(skc8))
| ~ m1_subset_1(skc9,k1_zfmisc_1(skc8))
| ~ equal(k8_setfam_1(skc11,k2_xboole_0(k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc9)),k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))),k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))) ),
inference(spl,[status(thm),theory(equality)],[3694,105385]),
[iquote('0:SpL:3694.3,105385.0')] ).
cnf(108656,plain,
( ~ v1_relat_1(k5_relset_2(skc8,skc12))
| ~ m1_subset_1(skc10,k1_zfmisc_1(skc8))
| ~ m1_subset_1(skc9,k1_zfmisc_1(skc8))
| ~ equal(k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10))),k8_setfam_1(skc11,k9_relat_1(k5_relset_2(skc8,skc12),k3_pua2mss1(skc10)))) ),
inference(rew,[status(thm),theory(equality)],[194,108630,856]),
[iquote('0:Rew:194.0,108630.3,856.0,108630.3')] ).
cnf(108657,plain,
( ~ v1_relat_1(k5_relset_2(skc8,skc12))
| ~ m1_subset_1(skc10,k1_zfmisc_1(skc8))
| ~ m1_subset_1(skc9,k1_zfmisc_1(skc8)) ),
inference(obv,[status(thm),theory(equality)],[108656]),
[iquote('0:Obv:108656.3')] ).
cnf(108658,plain,
( ~ m1_subset_1(skc10,k1_zfmisc_1(skc8))
| ~ m1_subset_1(skc9,k1_zfmisc_1(skc8)) ),
inference(ssi,[status(thm)],[108657,36,119,35]),
[iquote('0:SSi:108657.0,36.0,119.1,35.0,119.1')] ).
cnf(108659,plain,
$false,
inference(mrr,[status(thm)],[108658,14,15]),
[iquote('0:MRR:108658.0,108658.1,14.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU427+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : Mon Jun 20 08:32:52 EDT 2022
% 0.18/0.33 % CPUTime :
% 231.28/231.48
% 231.28/231.48 SPASS V 3.9
% 231.28/231.48 SPASS beiseite: Proof found.
% 231.28/231.48 % SZS status Theorem
% 231.28/231.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 231.28/231.48 SPASS derived 85197 clauses, backtracked 10880 clauses, performed 65 splits and kept 37700 clauses.
% 231.28/231.48 SPASS allocated 191150 KBytes.
% 231.28/231.48 SPASS spent 0:3:38.68 on the problem.
% 231.28/231.48 0:00:00.04 for the input.
% 231.28/231.48 0:00:00.03 for the FLOTTER CNF translation.
% 231.28/231.48 0:00:01.19 for inferences.
% 231.28/231.48 0:00:07.47 for the backtracking.
% 231.28/231.48 0:3:28.51 for the reduction.
% 231.28/231.48
% 231.28/231.48
% 231.28/231.48 Here is a proof with depth 3, length 48 :
% 231.28/231.48 % SZS output start Refutation
% See solution above
% 231.28/231.48 Formulae used in the proof : t26_relset_2 t1_boole commutativity_k2_xboole_0 dt_k5_relset_2 cc1_relset_1 t3_relset_2 dt_m2_relset_1 redefinition_k6_relset_2 dt_k6_relset_2 t153_relat_1 dt_k4_subset_1 redefinition_k4_relset_2 redefinition_k4_subset_1 redefinition_k8_relset_2 d4_relset_2
% 231.28/231.48
%------------------------------------------------------------------------------