%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET964+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:30:06 EDT 2022
% Result : Theorem 0.61s 0.82s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of clauses : 74 ( 20 unt; 13 nHn; 74 RR)
% Number of literals : 156 ( 0 equ; 86 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
subset(u,u),
file('SET964+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(skc7,empty_set),
file('SET964+1.p',unknown),
[] ).
cnf(6,axiom,
~ subset(skc5,skc6),
file('SET964+1.p',unknown),
[] ).
cnf(9,axiom,
( equal(u,empty_set)
| in(skf5(u),u) ),
file('SET964+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SET964+1.p',unknown),
[] ).
cnf(12,axiom,
( subset(u,v)
| in(skf9(v,u),u) ),
file('SET964+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(skf9(u,v),u)
| subset(w,u) ),
file('SET964+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ skP0(u,v,w)
| in(skf8(w,x,y),w) ),
file('SET964+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ skP0(u,v,w)
| in(skf7(v,x,y),v) ),
file('SET964+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SET964+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(u,w) ),
file('SET964+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SET964+1.p',unknown),
[] ).
cnf(20,axiom,
( subset(cartesian_product2(skc7,skc5),cartesian_product2(skc7,skc6))
| subset(cartesian_product2(skc5,skc7),cartesian_product2(skc6,skc7)) ),
file('SET964+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ in(u,v)
| ~ equal(v,cartesian_product2(w,x))
| skP0(u,x,w) ),
file('SET964+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ equal(u,cartesian_product2(v,w))
| ~ skP0(x,w,v)
| in(x,u) ),
file('SET964+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(u,v)
| ~ in(w,x)
| in(ordered_pair(u,w),cartesian_product2(v,x)) ),
file('SET964+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ skP0(u,v,w)
| equal(ordered_pair(skf8(w,v,u),skf7(v,u,w)),u) ),
file('SET964+1.p',unknown),
[] ).
cnf(25,axiom,
( equal(u,cartesian_product2(v,w))
| in(skf6(v,w,u),u)
| skP0(skf6(v,w,u),w,v) ),
file('SET964+1.p',unknown),
[] ).
cnf(29,plain,
in(skf9(skc6,skc5),skc5),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.1,6.0')] ).
cnf(30,plain,
~ in(skf9(skc6,u),skc6),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.1,6.0')] ).
cnf(31,plain,
in(skf5(skc7),skc7),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.1,5.0')] ).
cnf(63,plain,
( ~ subset(u,v)
| equal(u,empty_set)
| in(skf5(u),v) ),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.1,17.0')] ).
cnf(64,plain,
( ~ subset(skc5,u)
| in(skf9(skc6,skc5),u) ),
inference(res,[status(thm),theory(equality)],[29,17]),
[iquote('0:Res:29.0,17.0')] ).
cnf(133,plain,
( ~ in(u,cartesian_product2(v,w))
| skP0(u,w,v) ),
inference(eqr,[status(thm),theory(equality)],[21]),
[iquote('0:EqR:21.1')] ).
cnf(134,plain,
( equal(cartesian_product2(u,v),empty_set)
| skP0(skf5(cartesian_product2(u,v)),v,u) ),
inference(res,[status(thm),theory(equality)],[9,133]),
[iquote('0:Res:9.1,133.0')] ).
cnf(144,plain,
( equal(cartesian_product2(u,v),empty_set)
| in(skf8(u,w,x),u) ),
inference(res,[status(thm),theory(equality)],[134,15]),
[iquote('0:Res:134.1,15.0')] ).
cnf(145,plain,
( equal(cartesian_product2(u,v),empty_set)
| in(skf7(v,w,x),v) ),
inference(res,[status(thm),theory(equality)],[134,16]),
[iquote('0:Res:134.1,16.0')] ).
cnf(150,plain,
( ~ skP0(u,v,w)
| in(u,cartesian_product2(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[22]),
[iquote('0:EqR:22.0')] ).
cnf(169,plain,
( ~ in(u,v)
| ~ in(w,x)
| ~ subset(cartesian_product2(v,x),y)
| in(ordered_pair(u,w),y) ),
inference(res,[status(thm),theory(equality)],[23,17]),
[iquote('0:Res:23.2,17.0')] ).
cnf(171,plain,
( ~ in(u,v)
| ~ in(w,x)
| ~ equal(cartesian_product2(v,x),empty_set) ),
inference(res,[status(thm),theory(equality)],[23,11]),
[iquote('0:Res:23.2,11.0')] ).
cnf(213,plain,
( ~ equal(u,empty_set)
| equal(cartesian_product2(u,v),empty_set) ),
inference(res,[status(thm),theory(equality)],[144,11]),
[iquote('0:Res:144.1,11.0')] ).
cnf(226,plain,
( ~ equal(u,empty_set)
| ~ skP0(v,w,u)
| in(v,empty_set) ),
inference(spr,[status(thm),theory(equality)],[213,150]),
[iquote('0:SpR:213.1,150.1')] ).
cnf(227,plain,
( ~ equal(u,empty_set)
| ~ in(ordered_pair(v,w),empty_set)
| in(v,u) ),
inference(spl,[status(thm),theory(equality)],[213,18]),
[iquote('0:SpL:213.1,18.0')] ).
cnf(230,plain,
( ~ equal(u,empty_set)
| ~ in(v,empty_set)
| skP0(v,w,u) ),
inference(spl,[status(thm),theory(equality)],[213,133]),
[iquote('0:SpL:213.1,133.0')] ).
cnf(236,plain,
( ~ equal(u,empty_set)
| ~ in(ordered_pair(v,w),empty_set) ),
inference(mrr,[status(thm)],[227,11]),
[iquote('0:MRR:227.2,11.0')] ).
cnf(241,plain,
( ~ skP0(u,v,w)
| ~ equal(x,empty_set)
| ~ in(u,empty_set) ),
inference(spl,[status(thm),theory(equality)],[24,236]),
[iquote('0:SpL:24.1,236.1')] ).
cnf(242,plain,
( ~ skP0(u,v,w)
| ~ in(u,empty_set) ),
inference(aed,[status(thm),theory(equality)],[5,241]),
[iquote('0:AED:5.0,241.1')] ).
cnf(243,plain,
( ~ equal(u,empty_set)
| ~ in(v,empty_set) ),
inference(mrr,[status(thm)],[230,242]),
[iquote('0:MRR:230.2,242.0')] ).
cnf(244,plain,
( ~ equal(u,empty_set)
| ~ skP0(v,w,u) ),
inference(mrr,[status(thm)],[226,242]),
[iquote('0:MRR:226.2,242.1')] ).
cnf(245,plain,
~ in(u,empty_set),
inference(aed,[status(thm),theory(equality)],[5,243]),
[iquote('0:AED:5.0,243.0')] ).
cnf(259,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[63,245]),
[iquote('0:Res:63.2,245.0')] ).
cnf(300,plain,
( ~ equal(u,empty_set)
| equal(v,cartesian_product2(u,w))
| in(skf6(u,w,v),v) ),
inference(res,[status(thm),theory(equality)],[25,244]),
[iquote('0:Res:25.2,244.1')] ).
cnf(303,plain,
( ~ equal(u,empty_set)
| equal(v,empty_set)
| in(skf6(u,w,v),v) ),
inference(rew,[status(thm),theory(equality)],[213,300]),
[iquote('0:Rew:213.1,300.1')] ).
cnf(338,plain,
( ~ equal(u,empty_set)
| equal(cartesian_product2(v,u),empty_set) ),
inference(res,[status(thm),theory(equality)],[145,11]),
[iquote('0:Res:145.1,11.0')] ).
cnf(370,plain,
( ~ in(u,v)
| ~ in(w,x)
| ~ equal(empty_set,empty_set)
| in(skf8(v,y,z),v) ),
inference(spl,[status(thm),theory(equality)],[144,171]),
[iquote('0:SpL:144.0,171.2')] ).
cnf(381,plain,
( ~ in(u,v)
| ~ in(w,x)
| in(skf8(v,y,z),v) ),
inference(obv,[status(thm),theory(equality)],[370]),
[iquote('0:Obv:370.2')] ).
cnf(382,plain,
( ~ in(u,v)
| in(skf8(v,w,x),v) ),
inference(con,[status(thm)],[381]),
[iquote('0:Con:381.1')] ).
cnf(383,plain,
( ~ equal(skc6,empty_set)
| subset(cartesian_product2(skc7,skc5),empty_set)
| subset(cartesian_product2(skc5,skc7),cartesian_product2(skc6,skc7)) ),
inference(spr,[status(thm),theory(equality)],[338,20]),
[iquote('0:SpR:338.1,20.0')] ).
cnf(407,plain,
( ~ equal(skc6,empty_set)
| subset(cartesian_product2(skc7,skc5),empty_set)
| subset(cartesian_product2(skc5,skc7),empty_set) ),
inference(rew,[status(thm),theory(equality)],[213,383]),
[iquote('0:Rew:213.1,383.2')] ).
cnf(612,plain,
in(skf8(skc7,u,v),skc7),
inference(res,[status(thm),theory(equality)],[31,382]),
[iquote('0:Res:31.0,382.0')] ).
cnf(615,plain,
in(skf8(skc5,u,v),skc5),
inference(res,[status(thm),theory(equality)],[29,382]),
[iquote('0:Res:29.0,382.0')] ).
cnf(1971,plain,
( ~ equal(skc6,empty_set)
| subset(cartesian_product2(skc5,skc7),empty_set)
| equal(cartesian_product2(skc7,skc5),empty_set) ),
inference(res,[status(thm),theory(equality)],[407,259]),
[iquote('0:Res:407.1,259.0')] ).
cnf(2004,plain,
equal(cartesian_product2(skc7,skc5),empty_set),
inference(spt,[spt(split,[position(s1)])],[1971]),
[iquote('1:Spt:1971.2')] ).
cnf(2024,plain,
( ~ in(u,skc7)
| ~ in(v,skc5)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[2004,171]),
[iquote('1:SpL:2004.0,171.2')] ).
cnf(2042,plain,
( ~ in(u,skc7)
| ~ in(v,skc5) ),
inference(obv,[status(thm),theory(equality)],[2024]),
[iquote('1:Obv:2024.2')] ).
cnf(2096,plain,
( ~ equal(u,empty_set)
| ~ in(v,skc5)
| equal(skc7,empty_set) ),
inference(res,[status(thm),theory(equality)],[303,2042]),
[iquote('1:Res:303.2,2042.0')] ).
cnf(2128,plain,
( ~ in(u,skc5)
| equal(skc7,empty_set) ),
inference(aed,[status(thm),theory(equality)],[5,2096]),
[iquote('1:AED:5.0,2096.0')] ).
cnf(2129,plain,
~ in(u,skc5),
inference(mrr,[status(thm)],[2128,5]),
[iquote('1:MRR:2128.1,5.0')] ).
cnf(2130,plain,
$false,
inference(unc,[status(thm)],[2129,615]),
[iquote('1:UnC:2129.0,615.0')] ).
cnf(2133,plain,
~ equal(cartesian_product2(skc7,skc5),empty_set),
inference(spt,[spt(split,[position(sa)])],[2130,2004]),
[iquote('1:Spt:2130.0,1971.2,2004.0')] ).
cnf(2134,plain,
( ~ equal(skc6,empty_set)
| subset(cartesian_product2(skc5,skc7),empty_set) ),
inference(spt,[spt(split,[position(s2)])],[1971]),
[iquote('1:Spt:2130.0,1971.0,1971.1')] ).
cnf(2168,plain,
subset(cartesian_product2(skc7,skc5),cartesian_product2(skc7,skc6)),
inference(spt,[spt(split,[position(s2s1)])],[20]),
[iquote('2:Spt:20.0')] ).
cnf(2183,plain,
( ~ in(u,skc7)
| ~ in(v,skc5)
| in(ordered_pair(u,v),cartesian_product2(skc7,skc6)) ),
inference(res,[status(thm),theory(equality)],[2168,169]),
[iquote('2:Res:2168.0,169.2')] ).
cnf(2234,plain,
( ~ in(u,skc7)
| ~ in(v,skc5)
| in(v,skc6) ),
inference(res,[status(thm),theory(equality)],[2183,19]),
[iquote('2:Res:2183.2,19.0')] ).
cnf(2527,plain,
( ~ in(u,skc5)
| in(u,skc6) ),
inference(res,[status(thm),theory(equality)],[31,2234]),
[iquote('2:Res:31.0,2234.0')] ).
cnf(2570,plain,
~ in(skf9(skc6,u),skc5),
inference(res,[status(thm),theory(equality)],[2527,30]),
[iquote('2:Res:2527.1,30.0')] ).
cnf(2581,plain,
$false,
inference(unc,[status(thm)],[2570,29]),
[iquote('2:UnC:2570.0,29.0')] ).
cnf(2582,plain,
~ subset(cartesian_product2(skc7,skc5),cartesian_product2(skc7,skc6)),
inference(spt,[spt(split,[position(s2sa)])],[2581,2168]),
[iquote('2:Spt:2581.0,20.0,2168.0')] ).
cnf(2583,plain,
subset(cartesian_product2(skc5,skc7),cartesian_product2(skc6,skc7)),
inference(spt,[spt(split,[position(s2s2)])],[20]),
[iquote('2:Spt:2581.0,20.1')] ).
cnf(2599,plain,
( ~ in(u,skc5)
| ~ in(v,skc7)
| in(ordered_pair(u,v),cartesian_product2(skc6,skc7)) ),
inference(res,[status(thm),theory(equality)],[2583,169]),
[iquote('2:Res:2583.0,169.2')] ).
cnf(2623,plain,
( ~ in(u,skc5)
| ~ in(v,skc7)
| in(u,skc6) ),
inference(res,[status(thm),theory(equality)],[2599,18]),
[iquote('2:Res:2599.2,18.0')] ).
cnf(2766,plain,
( ~ subset(skc5,skc5)
| ~ in(u,skc7)
| in(skf9(skc6,skc5),skc6) ),
inference(res,[status(thm),theory(equality)],[64,2623]),
[iquote('2:Res:64.1,2623.0')] ).
cnf(2802,plain,
~ in(u,skc7),
inference(mrr,[status(thm)],[2766,4,30]),
[iquote('2:MRR:2766.0,2766.2,4.0,30.0')] ).
cnf(2803,plain,
$false,
inference(unc,[status(thm)],[2802,612]),
[iquote('2:UnC:2802.0,612.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET964+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 08:47:56 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.61/0.82
% 0.61/0.82 SPASS V 3.9
% 0.61/0.82 SPASS beiseite: Proof found.
% 0.61/0.82 % SZS status Theorem
% 0.61/0.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.82 SPASS derived 2194 clauses, backtracked 26 clauses, performed 2 splits and kept 793 clauses.
% 0.61/0.82 SPASS allocated 87199 KBytes.
% 0.61/0.82 SPASS spent 0:00:00.45 on the problem.
% 0.61/0.82 0:00:00.03 for the input.
% 0.61/0.82 0:00:00.04 for the FLOTTER CNF translation.
% 0.61/0.82 0:00:00.03 for inferences.
% 0.61/0.82 0:00:00.00 for the backtracking.
% 0.61/0.82 0:00:00.31 for the reduction.
% 0.61/0.82
% 0.61/0.82
% 0.61/0.82 Here is a proof with depth 10, length 74 :
% 0.61/0.82 % SZS output start Refutation
% See solution above
% 0.61/0.83 Formulae used in the proof : reflexivity_r1_tarski t117_zfmisc_1 d1_xboole_0 d3_tarski d2_zfmisc_1 l55_zfmisc_1
% 0.61/0.83
%------------------------------------------------------------------------------