TSTP Solution File: SCT023-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT023-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 : Mon Jul 18 22:13:04 EDT 2022
% Result : Unsatisfiable 18.22s 18.41s
% Output : Refutation 18.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 15 unt; 4 nHn; 26 RR)
% Number of literals : 42 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(299,axiom,
( ~ c_in(c_Pair(u,v,w,x),y,tc_prod(w,x))
| c_in(v,c_Relation_OImage(y,c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w),w,x),x) ),
file('SCT023-1.p',unknown),
[] ).
cnf(300,axiom,
( ~ c_in(u,c_Relation_OImage(v,c_Set_Oinsert(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),x),x,y),y)
| c_in(c_Pair(w,u,x,y),v,tc_prod(x,y)) ),
file('SCT023-1.p',unknown),
[] ).
cnf(573,axiom,
( ~ c_Relation_Otrans(u,v)
| ~ c_in(c_Pair(w,x,v,v),u,tc_prod(v,v))
| ~ c_in(c_Pair(x,y,v,v),u,tc_prod(v,v))
| c_in(c_Pair(w,y,v,v),u,tc_prod(v,v)) ),
file('SCT023-1.p',unknown),
[] ).
cnf(575,axiom,
( ~ hBOOL(hAPP(u,v))
| c_in(v,u,w) ),
file('SCT023-1.p',unknown),
[] ).
cnf(576,axiom,
( ~ c_in(u,v,w)
| hBOOL(hAPP(v,u)) ),
file('SCT023-1.p',unknown),
[] ).
cnf(599,axiom,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('SCT023-1.p',unknown),
[] ).
cnf(600,axiom,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
file('SCT023-1.p',unknown),
[] ).
cnf(601,axiom,
~ c_in(c_Pair(u,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('SCT023-1.p',unknown),
[] ).
cnf(602,axiom,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('SCT023-1.p',unknown),
[] ).
cnf(603,axiom,
( equal(u,v)
| c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,w),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,w),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('SCT023-1.p',unknown),
[] ).
cnf(605,axiom,
( ~ c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| equal(u,v)
| c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('SCT023-1.p',unknown),
[] ).
cnf(725,plain,
c_in(v_b,c_Relation_OImage(v_F(v_P),c_Set_Oinsert(v_a,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
inference(res,[status(thm),theory(equality)],[599,299]),
[iquote('0:Res:599.0,299.0')] ).
cnf(776,plain,
~ c_in(u,c_Relation_OImage(v_F(v_P),c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
inference(res,[status(thm),theory(equality)],[300,601]),
[iquote('0:Res:300.1,601.0')] ).
cnf(782,plain,
( ~ c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(res,[status(thm),theory(equality)],[573,601]),
[iquote('0:Res:573.3,601.0')] ).
cnf(811,plain,
( equal(v_b,v_a)
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(res,[status(thm),theory(equality)],[603,602]),
[iquote('0:Res:603.0,602.0')] ).
cnf(890,plain,
( ~ c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(mrr,[status(thm)],[782,600]),
[iquote('0:MRR:782.2,600.0')] ).
cnf(908,plain,
~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(res,[status(thm),theory(equality)],[599,890]),
[iquote('0:Res:599.0,890.0')] ).
cnf(938,plain,
equal(v_b,v_a),
inference(spt,[spt(split,[position(s1)])],[811]),
[iquote('1:Spt:811.0')] ).
cnf(948,plain,
c_in(v_a,c_Relation_OImage(v_F(v_P),c_Set_Oinsert(v_a,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
inference(rew,[status(thm),theory(equality)],[938,725]),
[iquote('1:Rew:938.0,725.0')] ).
cnf(959,plain,
$false,
inference(mrr,[status(thm)],[948,776]),
[iquote('1:MRR:948.0,776.0')] ).
cnf(961,plain,
~ equal(v_b,v_a),
inference(spt,[spt(split,[position(sa)])],[959,938]),
[iquote('1:Spt:959.0,811.0,938.0')] ).
cnf(962,plain,
c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(spt,[spt(split,[position(s2)])],[811]),
[iquote('1:Spt:959.0,811.1')] ).
cnf(1001,plain,
hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[962,576]),
[iquote('1:Res:962.0,576.0')] ).
cnf(1010,plain,
c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),u),
inference(res,[status(thm),theory(equality)],[1001,575]),
[iquote('1:Res:1001.0,575.0')] ).
cnf(35142,plain,
( equal(v_b,v_a)
| c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(res,[status(thm),theory(equality)],[1010,605]),
[iquote('1:Res:1010.0,605.0')] ).
cnf(35144,plain,
$false,
inference(mrr,[status(thm)],[35142,961,908]),
[iquote('1:MRR:35142.0,35142.1,961.0,908.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT023-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 21:27:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 18.22/18.41
% 18.22/18.41 SPASS V 3.9
% 18.22/18.41 SPASS beiseite: Proof found.
% 18.22/18.41 % SZS status Theorem
% 18.22/18.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.22/18.41 SPASS derived 28607 clauses, backtracked 20 clauses, performed 1 splits and kept 9224 clauses.
% 18.22/18.41 SPASS allocated 111389 KBytes.
% 18.22/18.41 SPASS spent 0:0:17.48 on the problem.
% 18.22/18.41 0:00:00.05 for the input.
% 18.22/18.41 0:00:00.00 for the FLOTTER CNF translation.
% 18.22/18.41 0:00:00.45 for inferences.
% 18.22/18.41 0:00:00.06 for the backtracking.
% 18.22/18.41 0:0:16.61 for the reduction.
% 18.22/18.41
% 18.22/18.41
% 18.22/18.41 Here is a proof with depth 5, length 26 :
% 18.22/18.41 % SZS output start Refutation
% See solution above
% 18.22/18.41 Formulae used in the proof : cls_Image__singleton__iff_1 cls_Image__singleton__iff_0 cls_trans__def_0 cls_mem__def_1 cls_mem__def_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_conjecture_6 cls_conjecture_8
% 18.22/18.41
%------------------------------------------------------------------------------