TSTP Solution File: COM011-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM011-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 10.06s 10.26s
% Output : Refutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 7 unt; 3 nHn; 19 RR)
% Number of literals : 35 ( 0 equ; 16 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(9,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('COM011-1.p',unknown),
[] ).
cnf(12,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('COM011-1.p',unknown),
[] ).
cnf(13,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('COM011-1.p',unknown),
[] ).
cnf(14,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('COM011-1.p',unknown),
[] ).
cnf(15,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('COM011-1.p',unknown),
[] ).
cnf(16,axiom,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('COM011-1.p',unknown),
[] ).
cnf(17,axiom,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('COM011-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ c_in(u,c_minus(v,w,tc_set(x)),x)
| c_in(u,v,x) ),
file('COM011-1.p',unknown),
[] ).
cnf(324,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('COM011-1.p',unknown),
[] ).
cnf(325,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('COM011-1.p',unknown),
[] ).
cnf(1391,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)],[16,14]),
[iquote('0:Res:16.0,14.0')] ).
cnf(1398,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)],[13,17]),
[iquote('0:Res:13.1,17.0')] ).
cnf(1422,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)],[15,9]),
[iquote('0:Res:15.0,9.0')] ).
cnf(1695,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)],[324,175]),
[iquote('0:Res:324.1,175.0')] ).
cnf(5780,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)],[1422,12]),
[iquote('0:Res:1422.1,12.1')] ).
cnf(5786,plain,
~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a)),
inference(mrr,[status(thm)],[5780,1391,1398]),
[iquote('0:MRR:5780.1,5780.2,1391.1,1398.0')] ).
cnf(14862,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)],[1695,325]),
[iquote('0:Res:1695.1,325.0')] ).
cnf(14879,plain,
c_lessequals(c_minus(u,v,tc_set(w)),u,tc_set(w)),
inference(obv,[status(thm),theory(equality)],[14862]),
[iquote('0:Obv:14862.0')] ).
cnf(14880,plain,
$false,
inference(unc,[status(thm)],[14879,5786]),
[iquote('0:UnC:14879.0,5786.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM011-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 : Thu Jun 16 19:29:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.06/10.26
% 10.06/10.26 SPASS V 3.9
% 10.06/10.26 SPASS beiseite: Proof found.
% 10.06/10.26 % SZS status Theorem
% 10.06/10.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.06/10.26 SPASS derived 11050 clauses, backtracked 376 clauses, performed 5 splits and kept 6119 clauses.
% 10.06/10.26 SPASS allocated 95534 KBytes.
% 10.06/10.26 SPASS spent 0:00:09.60 on the problem.
% 10.06/10.26 0:00:00.09 for the input.
% 10.06/10.26 0:00:00.00 for the FLOTTER CNF translation.
% 10.06/10.26 0:00:00.37 for inferences.
% 10.06/10.26 0:00:00.02 for the backtracking.
% 10.06/10.26 0:00:08.79 for the reduction.
% 10.06/10.26
% 10.06/10.26
% 10.06/10.26 Here is a proof with depth 2, length 19 :
% 10.06/10.26 % SZS output start Refutation
% See solution above
% 10.06/10.26 Formulae used in the proof : 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 cls_Set_ODiffE_1 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1
% 10.06/10.26
%------------------------------------------------------------------------------