%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET837-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:29:06 EDT 2022
% Result : Unsatisfiable 0.45s 0.62s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of clauses : 75 ( 20 unt; 23 nHn; 75 RR)
% Number of literals : 157 ( 0 equ; 62 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SET837-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SET837-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_union(v,w,x),x)
| c_in(u,v,x)
| c_in(u,w,x) ),
file('SET837-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET837-2.p',unknown),
[] ).
cnf(5,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET837-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET837-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('SET837-2.p',unknown),
[] ).
cnf(8,axiom,
( equal(c_union(v_Y,v_Z,t_a),v_X)
| c_lessequals(v_Y,v_X,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(9,axiom,
( equal(c_union(v_Y,v_Z,t_a),v_X)
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(c_union(v_Y,v_Z,t_a),v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(c_union(v_Y,v_Z,t_a),v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(c_union(v_Y,v_Z,t_a),v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ c_lessequals(v_Y,u,tc_set(t_a))
| ~ c_lessequals(v_Z,u,tc_set(t_a))
| equal(c_union(v_Y,v_Z,t_a),v_X)
| c_lessequals(v_X,u,tc_set(t_a)) ),
file('SET837-2.p',unknown),
[] ).
cnf(14,plain,
equal(c_union(v_Y,v_Z,t_a),v_X),
inference(spt,[spt(split,[position(s1)])],[9]),
[iquote('1:Spt:9.0')] ).
cnf(15,plain,
( ~ equal(v_X,v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(rew,[status(thm),theory(equality)],[14,12]),
[iquote('1:Rew:14.0,12.0')] ).
cnf(16,plain,
( ~ equal(v_X,v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(rew,[status(thm),theory(equality)],[14,10]),
[iquote('1:Rew:14.0,10.0')] ).
cnf(17,plain,
( ~ equal(v_X,v_X)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(rew,[status(thm),theory(equality)],[14,11]),
[iquote('1:Rew:14.0,11.0')] ).
cnf(18,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('1:Obv:16.0')] ).
cnf(19,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(obv,[status(thm),theory(equality)],[17]),
[iquote('1:Obv:17.0')] ).
cnf(20,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('1:Obv:15.0')] ).
cnf(22,plain,
( ~ c_in(u,v_Y,t_a)
| c_in(u,v_X,t_a) ),
inference(spr,[status(thm),theory(equality)],[14,2]),
[iquote('1:SpR:14.0,2.1')] ).
cnf(23,plain,
( c_lessequals(v_Y,u,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_Y,u,t_a),v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[5,22]),
[iquote('1:Res:5.1,22.0')] ).
cnf(24,plain,
( ~ c_in(u,v_Z,t_a)
| c_in(u,v_X,t_a) ),
inference(spr,[status(thm),theory(equality)],[14,1]),
[iquote('1:SpR:14.0,1.1')] ).
cnf(25,plain,
( c_lessequals(v_Z,u,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_Z,u,t_a),v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('1:Res:5.1,24.0')] ).
cnf(27,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_union(v,w,x),x),v,x)
| c_lessequals(u,c_union(v,w,x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.1,6.0')] ).
cnf(28,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_union(v,w,x),x),w,x)
| c_lessequals(u,c_union(v,w,x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.1,6.0')] ).
cnf(29,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_X,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[23,6]),
[iquote('1:Res:23.1,6.0')] ).
cnf(30,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[25,6]),
[iquote('1:Res:25.1,6.0')] ).
cnf(32,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[29]),
[iquote('1:Obv:29.0')] ).
cnf(33,plain,
( ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(mrr,[status(thm)],[18,32]),
[iquote('1:MRR:18.0,32.0')] ).
cnf(34,plain,
( ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(mrr,[status(thm)],[19,32]),
[iquote('1:MRR:19.0,32.0')] ).
cnf(35,plain,
( ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(mrr,[status(thm)],[20,32]),
[iquote('1:MRR:20.0,32.0')] ).
cnf(36,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[30]),
[iquote('1:Obv:30.0')] ).
cnf(37,plain,
c_lessequals(v_Y,v_x,tc_set(t_a)),
inference(mrr,[status(thm)],[33,36]),
[iquote('1:MRR:33.0,36.0')] ).
cnf(38,plain,
c_lessequals(v_Z,v_x,tc_set(t_a)),
inference(mrr,[status(thm)],[34,36]),
[iquote('1:MRR:34.0,36.0')] ).
cnf(39,plain,
~ c_lessequals(v_X,v_x,tc_set(t_a)),
inference(mrr,[status(thm)],[35,36]),
[iquote('1:MRR:35.0,36.0')] ).
cnf(47,plain,
( ~ c_in(u,v_Y,t_a)
| c_in(u,v_x,t_a) ),
inference(res,[status(thm),theory(equality)],[37,4]),
[iquote('1:Res:37.0,4.1')] ).
cnf(49,plain,
( ~ c_in(u,v_Z,t_a)
| c_in(u,v_x,t_a) ),
inference(res,[status(thm),theory(equality)],[38,4]),
[iquote('1:Res:38.0,4.1')] ).
cnf(50,plain,
( ~ c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_Y,t_a)
| c_lessequals(u,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[47,6]),
[iquote('1:Res:47.1,6.0')] ).
cnf(51,plain,
( ~ c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_Z,t_a)
| c_lessequals(u,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[49,6]),
[iquote('1:Res:49.1,6.0')] ).
cnf(56,plain,
( ~ c_in(u,v_X,t_a)
| c_in(u,v_Y,t_a)
| c_in(u,v_Z,t_a) ),
inference(spl,[status(thm),theory(equality)],[14,3]),
[iquote('1:SpL:14.0,3.0')] ).
cnf(57,plain,
( c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_in(c_Main_OsubsetI__1(c_union(u,v,w),x,w),u,w)
| c_in(c_Main_OsubsetI__1(c_union(u,v,w),x,w),v,w) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.1,3.0')] ).
cnf(62,plain,
( ~ c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_X,t_a)
| c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_Y,t_a)
| c_lessequals(u,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[56,51]),
[iquote('1:Res:56.2,51.0')] ).
cnf(63,plain,
( ~ c_in(c_Main_OsubsetI__1(u,v_x,t_a),v_X,t_a)
| c_lessequals(u,v_x,tc_set(t_a)) ),
inference(mrr,[status(thm)],[62,50]),
[iquote('1:MRR:62.1,50.0')] ).
cnf(64,plain,
( c_lessequals(v_X,v_x,tc_set(t_a))
| c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[5,63]),
[iquote('1:Res:5.1,63.0')] ).
cnf(67,plain,
c_lessequals(v_X,v_x,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[64]),
[iquote('1:Obv:64.0')] ).
cnf(68,plain,
$false,
inference(mrr,[status(thm)],[67,39]),
[iquote('1:MRR:67.0,39.0')] ).
cnf(71,plain,
~ equal(c_union(v_Y,v_Z,t_a),v_X),
inference(spt,[spt(split,[position(sa)])],[68,14]),
[iquote('1:Spt:68.0,9.0,14.0')] ).
cnf(72,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(spt,[spt(split,[position(s2)])],[9]),
[iquote('1:Spt:68.0,9.1')] ).
cnf(73,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(mrr,[status(thm)],[8,71]),
[iquote('1:MRR:8.0,71.0')] ).
cnf(74,plain,
( ~ c_lessequals(v_Y,u,tc_set(t_a))
| ~ c_lessequals(v_Z,u,tc_set(t_a))
| c_lessequals(v_X,u,tc_set(t_a)) ),
inference(mrr,[status(thm)],[13,71]),
[iquote('1:MRR:13.2,71.0')] ).
cnf(76,plain,
( ~ c_in(u,v_Z,t_a)
| c_in(u,v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[72,4]),
[iquote('1:Res:72.0,4.1')] ).
cnf(78,plain,
( ~ c_in(u,v_Y,t_a)
| c_in(u,v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[73,4]),
[iquote('1:Res:73.0,4.1')] ).
cnf(83,plain,
( c_lessequals(u,c_union(u,v,w),tc_set(w))
| c_lessequals(u,c_union(u,v,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[5,27]),
[iquote('0:Res:5.1,27.0')] ).
cnf(86,plain,
c_lessequals(u,c_union(u,v,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[83]),
[iquote('0:Obv:83.0')] ).
cnf(89,plain,
( ~ c_lessequals(v_Y,c_union(v_Z,u,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(v_Z,u,t_a),tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[86,74]),
[iquote('1:Res:86.0,74.1')] ).
cnf(97,plain,
( c_lessequals(u,c_union(v,u,w),tc_set(w))
| c_lessequals(u,c_union(v,u,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[5,28]),
[iquote('0:Res:5.1,28.0')] ).
cnf(101,plain,
c_lessequals(u,c_union(v,u,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[97]),
[iquote('0:Obv:97.0')] ).
cnf(127,plain,
( c_lessequals(c_union(u,v_Y,t_a),v,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_union(u,v_Y,t_a),v,t_a),u,t_a)
| c_in(c_Main_OsubsetI__1(c_union(u,v_Y,t_a),v,t_a),v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[57,78]),
[iquote('1:Res:57.2,78.0')] ).
cnf(128,plain,
( c_lessequals(c_union(u,v,w),c_union(v,x,w),tc_set(w))
| c_in(c_Main_OsubsetI__1(c_union(u,v,w),c_union(v,x,w),w),u,w)
| c_lessequals(c_union(u,v,w),c_union(v,x,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[57,27]),
[iquote('0:Res:57.2,27.0')] ).
cnf(133,plain,
( c_in(c_Main_OsubsetI__1(c_union(u,v,w),c_union(v,x,w),w),u,w)
| c_lessequals(c_union(u,v,w),c_union(v,x,w),tc_set(w)) ),
inference(obv,[status(thm),theory(equality)],[128]),
[iquote('0:Obv:128.0')] ).
cnf(463,plain,
( c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w))
| c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[133,28]),
[iquote('0:Res:133.0,28.0')] ).
cnf(466,plain,
c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[463]),
[iquote('0:Obv:463.0')] ).
cnf(489,plain,
( ~ c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w))
| equal(c_union(v,u,w),c_union(u,v,w)) ),
inference(res,[status(thm),theory(equality)],[466,7]),
[iquote('0:Res:466.0,7.0')] ).
cnf(496,plain,
equal(c_union(u,v,w),c_union(v,u,w)),
inference(mrr,[status(thm)],[489,466]),
[iquote('0:MRR:489.0,466.0')] ).
cnf(691,plain,
c_lessequals(v_X,c_union(v_Z,v_Y,t_a),tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[101,89]),
[iquote('1:Res:101.0,89.0')] ).
cnf(693,plain,
c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(rew,[status(thm),theory(equality)],[496,691]),
[iquote('1:Rew:496.0,691.0')] ).
cnf(697,plain,
( ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| equal(c_union(v_Y,v_Z,t_a),v_X) ),
inference(res,[status(thm),theory(equality)],[693,7]),
[iquote('1:Res:693.0,7.0')] ).
cnf(699,plain,
~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(mrr,[status(thm)],[697,71]),
[iquote('1:MRR:697.1,71.0')] ).
cnf(1066,plain,
( c_lessequals(c_union(v_Z,v_Y,t_a),u,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_union(v_Z,v_Y,t_a),u,t_a),v_X,t_a)
| c_in(c_Main_OsubsetI__1(c_union(v_Z,v_Y,t_a),u,t_a),v_X,t_a) ),
inference(res,[status(thm),theory(equality)],[127,76]),
[iquote('1:Res:127.1,76.0')] ).
cnf(1086,plain,
( c_lessequals(c_union(v_Z,v_Y,t_a),u,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_union(v_Z,v_Y,t_a),u,t_a),v_X,t_a) ),
inference(obv,[status(thm),theory(equality)],[1066]),
[iquote('1:Obv:1066.1')] ).
cnf(1087,plain,
( c_lessequals(c_union(v_Y,v_Z,t_a),u,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),u,t_a),v_X,t_a) ),
inference(rew,[status(thm),theory(equality)],[496,1086]),
[iquote('1:Rew:496.0,1086.1,496.0,1086.0')] ).
cnf(1838,plain,
( c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[1087,6]),
[iquote('1:Res:1087.1,6.0')] ).
cnf(1845,plain,
c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[1838]),
[iquote('1:Obv:1838.0')] ).
cnf(1846,plain,
$false,
inference(mrr,[status(thm)],[1845,699]),
[iquote('1:MRR:1845.0,699.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET837-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 16:43:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.62
% 0.45/0.62 SPASS V 3.9
% 0.45/0.62 SPASS beiseite: Proof found.
% 0.45/0.62 % SZS status Theorem
% 0.45/0.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.62 SPASS derived 1370 clauses, backtracked 7 clauses, performed 1 splits and kept 477 clauses.
% 0.45/0.62 SPASS allocated 64731 KBytes.
% 0.45/0.62 SPASS spent 0:00:00.27 on the problem.
% 0.45/0.62 0:00:00.03 for the input.
% 0.45/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.62 0:00:00.03 for inferences.
% 0.45/0.62 0:00:00.01 for the backtracking.
% 0.45/0.62 0:00:00.18 for the reduction.
% 0.45/0.62
% 0.45/0.62
% 0.45/0.62 Here is a proof with depth 5, length 75 :
% 0.45/0.62 % SZS output start Refutation
% See solution above
% 0.45/0.62 Formulae used in the proof : cls_Set_OUnCI_0 cls_Set_OUnCI_1 cls_Set_OUnE_0 cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__antisym_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.46/0.63
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