TSTP Solution File: SET834-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET834-2 : 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 05:29:03 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 8 unt; 4 nHn; 23 RR)
% Number of literals : 42 ( 0 equ; 17 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,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SET834-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SET834-2.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('SET834-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET834-2.p',unknown),
[] ).
cnf(5,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SET834-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SET834-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(v_x,v_X,t_a),
file('SET834-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_in(v_x,v_Z,t_a),
file('SET834-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_in(v_x,v_Y,t_a),
file('SET834-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ 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)) ),
file('SET834-2.p',unknown),
[] ).
cnf(11,plain,
( ~ c_lessequals(v_X,u,tc_set(t_a))
| c_in(v_x,u,t_a) ),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('0:Res:7.0,4.0')] ).
cnf(19,plain,
( ~ c_in(v_x,c_union(v_Z,u,t_a),t_a)
| c_in(v_x,u,t_a) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.2,8.0')] ).
cnf(35,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(36,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(51,plain,
( ~ c_lessequals(v_Y,u,tc_set(t_a))
| ~ c_lessequals(v_Z,u,tc_set(t_a))
| c_in(v_x,u,t_a) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.2,11.0')] ).
cnf(57,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)],[5,35]),
[iquote('0:Res:5.1,35.0')] ).
cnf(60,plain,
c_lessequals(u,c_union(u,v,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[57]),
[iquote('0:Obv:57.0')] ).
cnf(64,plain,
( ~ c_lessequals(v_Y,c_union(v_Z,u,t_a),tc_set(t_a))
| c_in(v_x,c_union(v_Z,u,t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[60,51]),
[iquote('0:Res:60.0,51.1')] ).
cnf(65,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)],[5,36]),
[iquote('0:Res:5.1,36.0')] ).
cnf(68,plain,
c_lessequals(u,c_union(v,u,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[65]),
[iquote('0:Obv:65.0')] ).
cnf(74,plain,
c_in(v_x,c_union(v_Z,v_Y,t_a),t_a),
inference(res,[status(thm),theory(equality)],[68,64]),
[iquote('0:Res:68.0,64.0')] ).
cnf(76,plain,
c_in(v_x,v_Y,t_a),
inference(res,[status(thm),theory(equality)],[74,19]),
[iquote('0:Res:74.0,19.0')] ).
cnf(79,plain,
$false,
inference(mrr,[status(thm)],[76,9]),
[iquote('0:MRR:76.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET834-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 03:51:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 61 clauses, backtracked 0 clauses, performed 0 splits and kept 43 clauses.
% 0.12/0.41 SPASS allocated 63153 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 5, length 23 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 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_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.12/0.41
%------------------------------------------------------------------------------