%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM011-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 : Fri Jul 15 01:44:16 EDT 2022
% Result : Unsatisfiable 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 8 unt; 4 nHn; 23 RR)
% Number of literals : 43 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,c_minus(v,w,tc_set(x)),x)
| c_in(u,v,x) ),
file('COM011-2.p',unknown),
[] ).
cnf(2,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('COM011-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('COM011-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_in(x,c_UNITY_Oconstrains(v,y,w),tc_UNITY_Oprogram(w))
| c_in(x,c_UNITY_Oconstrains(u,y,w),tc_UNITY_Oprogram(w)) ),
file('COM011-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,c_WFair_Otransient(c_minus(v,w,tc_set(x)),x),tc_UNITY_Oprogram(x))
| ~ c_in(u,c_UNITY_Oconstrains(c_minus(v,w,tc_set(x)),c_union(v,w,x),x),tc_UNITY_Oprogram(x))
| c_in(u,c_WFair_Oensures(v,w,x),tc_UNITY_Oprogram(x)) ),
file('COM011-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,c_WFair_Oensures(v,w,x),tc_UNITY_Oprogram(x))
| c_in(u,c_WFair_OleadsTo(v,w,x),tc_UNITY_Oprogram(x)) ),
file('COM011-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_in(x,c_WFair_Otransient(v,w),tc_UNITY_Oprogram(w))
| c_in(x,c_WFair_Otransient(u,w),tc_UNITY_Oprogram(w)) ),
file('COM011-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
file('COM011-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('COM011-2.p',unknown),
[] ).
cnf(10,axiom,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('COM011-2.p',unknown),
[] ).
cnf(11,plain,
( ~ c_lessequals(u,v_A,tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(u,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.0,7.0')] ).
cnf(13,plain,
~ c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.1,10.0')] ).
cnf(14,plain,
( ~ c_lessequals(u,v_A,tc_set(t_a))
| c_in(v_F,c_UNITY_Oconstrains(u,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(res,[status(thm),theory(equality)],[8,4]),
[iquote('0:Res:8.0,4.0')] ).
cnf(15,plain,
( c_lessequals(u,u,tc_set(v))
| c_lessequals(u,u,tc_set(v)) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.1,3.0')] ).
cnf(16,plain,
c_lessequals(u,u,tc_set(v)),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('0:Obv:15.0')] ).
cnf(17,plain,
( c_lessequals(c_minus(u,v,tc_set(w)),x,tc_set(w))
| c_in(c_Main_OsubsetI__1(c_minus(u,v,tc_set(w)),x,w),u,w) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.1,1.0')] ).
cnf(20,plain,
( c_lessequals(c_minus(u,v,tc_set(w)),u,tc_set(w))
| c_lessequals(c_minus(u,v,tc_set(w)),u,tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[17,3]),
[iquote('0:Res:17.1,3.0')] ).
cnf(22,plain,
c_lessequals(c_minus(u,v,tc_set(w)),u,tc_set(w)),
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('0:Obv:20.0')] ).
cnf(24,plain,
( ~ c_lessequals(u,v_A,tc_set(t_a))
| ~ c_lessequals(v,u,tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(v,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(res,[status(thm),theory(equality)],[11,7]),
[iquote('0:Res:11.1,7.1')] ).
cnf(32,plain,
( ~ c_lessequals(u,c_minus(v_A,v,tc_set(t_a)),tc_set(t_a))
| c_in(v_F,c_WFair_Otransient(u,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(res,[status(thm),theory(equality)],[22,24]),
[iquote('0:Res:22.0,24.0')] ).
cnf(33,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,u,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(res,[status(thm),theory(equality)],[16,32]),
[iquote('0:Res:16.0,32.0')] ).
cnf(37,plain,
( ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a))
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(res,[status(thm),theory(equality)],[14,5]),
[iquote('0:Res:14.1,5.1')] ).
cnf(40,plain,
$false,
inference(mrr,[status(thm)],[37,22,33,13]),
[iquote('0:MRR:37.0,37.1,37.2,22.0,33.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COM011-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 17:25:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.43
% 0.22/0.43 SPASS V 3.9
% 0.22/0.43 SPASS beiseite: Proof found.
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.43 SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.22/0.43 SPASS allocated 63171 KBytes.
% 0.22/0.43 SPASS spent 0:00:00.06 on the problem.
% 0.22/0.43 0:00:00.03 for the input.
% 0.22/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.43 0:00:00.00 for inferences.
% 0.22/0.43 0:00:00.00 for the backtracking.
% 0.22/0.43 0:00:00.00 for the reduction.
% 0.22/0.43
% 0.22/0.43
% 0.22/0.43 Here is a proof with depth 4, length 23 :
% 0.22/0.43 % SZS output start Refutation
% See solution above
% 0.22/0.43 Formulae used in the proof : cls_Set_ODiffE_1 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_UNITY_Oconstrains__weaken__L_0 cls_WFair_OensuresI_0 cls_WFair_OleadsTo__Basis_0 cls_WFair_Otransient__strengthen_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.22/0.43
%------------------------------------------------------------------------------