TSTP Solution File: SET830-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET830-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:29:00 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 9 unt; 5 nHn; 23 RR)
% Number of literals : 40 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 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,c_inter(v,w,x),x)
| c_in(u,w,x) ),
file('SET830-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_inter(v,w,x),x)
| c_in(u,v,x) ),
file('SET830-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,w)
| ~ c_in(u,x,w)
| c_in(u,c_inter(v,x,w),w) ),
file('SET830-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET830-2.p',unknown),
[] ).
cnf(5,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET830-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET830-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(v_x,v_Y,t_a),
file('SET830-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_x,v_Z,t_a),
file('SET830-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_in(v_x,v_X,t_a),
file('SET830-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ c_lessequals(u,v_Y,tc_set(t_a))
| ~ c_lessequals(u,v_Z,tc_set(t_a))
| c_lessequals(u,v_X,tc_set(t_a)) ),
file('SET830-2.p',unknown),
[] ).
cnf(11,plain,
( ~ c_in(v_x,u,t_a)
| c_in(v_x,c_inter(u,v_Z,t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[8,3]),
[iquote('0:Res:8.0,3.0')] ).
cnf(19,plain,
( ~ c_lessequals(u,v_X,tc_set(t_a))
| ~ c_in(v_x,u,t_a) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.2,9.0')] ).
cnf(23,plain,
c_in(v_x,c_inter(v_Y,v_Z,t_a),t_a),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.0,11.0')] ).
cnf(28,plain,
( c_lessequals(c_inter(u,v,w),x,tc_set(w))
| c_in(c_Main_OsubsetI__1(c_inter(u,v,w),x,w),u,w) ),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(32,plain,
( c_lessequals(c_inter(u,v,w),x,tc_set(w))
| c_in(c_Main_OsubsetI__1(c_inter(u,v,w),x,w),v,w) ),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.1,1.0')] ).
cnf(60,plain,
( c_lessequals(c_inter(u,v,w),u,tc_set(w))
| c_lessequals(c_inter(u,v,w),u,tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[28,6]),
[iquote('0:Res:28.1,6.0')] ).
cnf(63,plain,
c_lessequals(c_inter(u,v,w),u,tc_set(w)),
inference(obv,[status(thm),theory(equality)],[60]),
[iquote('0:Obv:60.0')] ).
cnf(65,plain,
( ~ c_lessequals(c_inter(v_Y,u,t_a),v_Z,tc_set(t_a))
| c_lessequals(c_inter(v_Y,u,t_a),v_X,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[63,10]),
[iquote('0:Res:63.0,10.0')] ).
cnf(67,plain,
( c_lessequals(c_inter(u,v,w),v,tc_set(w))
| c_lessequals(c_inter(u,v,w),v,tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[32,6]),
[iquote('0:Res:32.1,6.0')] ).
cnf(70,plain,
c_lessequals(c_inter(u,v,w),v,tc_set(w)),
inference(obv,[status(thm),theory(equality)],[67]),
[iquote('0:Obv:67.0')] ).
cnf(79,plain,
c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[70,65]),
[iquote('0:Res:70.0,65.0')] ).
cnf(82,plain,
~ c_in(v_x,c_inter(v_Y,v_Z,t_a),t_a),
inference(res,[status(thm),theory(equality)],[79,19]),
[iquote('0:Res:79.0,19.0')] ).
cnf(84,plain,
$false,
inference(mrr,[status(thm)],[82,23]),
[iquote('0:MRR:82.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET830-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 : Sun Jul 10 05:10:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 64 clauses, backtracked 0 clauses, performed 0 splits and kept 43 clauses.
% 0.18/0.40 SPASS allocated 63163 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 5, length 23 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.40 Formulae used in the proof : cls_Set_OIntE_0 cls_Set_OIntE_1 cls_Set_OIntI_0 cls_Set_OsubsetD_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.18/0.40
%------------------------------------------------------------------------------