TSTP Solution File: SCT058-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT058-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 22:13:15 EDT 2022
% Result : Unsatisfiable 40.75s 41.02s
% Output : Refutation 40.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 11 unt; 2 nHn; 19 RR)
% Number of literals : 27 ( 0 equ; 12 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 15 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(597,axiom,
( ~ hBOOL(c_in(c_Pair(u,v,w,x),y,tc_prod(w,x)))
| hBOOL(c_in(c_Pair(v,u,x,w),hAPP(c_Relation_Oconverse(w,x),y),tc_prod(x,w))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(599,axiom,
( ~ hBOOL(c_in(c_Pair(u,v,w,x),hAPP(c_Relation_Oconverse(x,w),y),tc_prod(w,x)))
| hBOOL(c_in(c_Pair(v,u,x,w),y,tc_prod(x,w))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(602,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(603,axiom,
( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(607,axiom,
equal(hAPP(c_Fun_Ocomp(u,v,w,x,y),z),hAPP(u,hAPP(v,z))),
file('SCT058-1.p',unknown),
[] ).
cnf(640,axiom,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(641,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT058-1.p',unknown),
[] ).
cnf(683,plain,
( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rew,[status(thm),theory(equality)],[607,640]),
[iquote('0:Rew:607.0,640.1')] ).
cnf(684,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rew,[status(thm),theory(equality)],[607,641]),
[iquote('0:Rew:607.0,641.1')] ).
cnf(64372,plain,
hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(s1)])],[683]),
[iquote('1:Spt:683.0')] ).
cnf(64373,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(mrr,[status(thm)],[684,64372]),
[iquote('1:MRR:684.0,64372.0')] ).
cnf(64399,plain,
hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[64372,602]),
[iquote('1:Res:64372.0,602.0')] ).
cnf(64415,plain,
~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[597,64373]),
[iquote('1:Res:597.1,64373.0')] ).
cnf(64416,plain,
$false,
inference(mrr,[status(thm)],[64415,64399]),
[iquote('1:MRR:64415.0,64399.0')] ).
cnf(64417,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(sa)])],[64416,64372]),
[iquote('1:Spt:64416.0,683.0,64372.0')] ).
cnf(64418,plain,
hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(s2)])],[683]),
[iquote('1:Spt:64416.0,683.1')] ).
cnf(64443,plain,
hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[64418,599]),
[iquote('1:Res:64418.0,599.0')] ).
cnf(64476,plain,
~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[603,64417]),
[iquote('1:Res:603.1,64417.0')] ).
cnf(64477,plain,
$false,
inference(mrr,[status(thm)],[64476,64443]),
[iquote('1:MRR:64476.0,64443.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT058-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : Fri Jul 1 23:01:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 40.75/41.02
% 40.75/41.02 SPASS V 3.9
% 40.75/41.02 SPASS beiseite: Proof found.
% 40.75/41.02 % SZS status Theorem
% 40.75/41.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.75/41.02 SPASS derived 49959 clauses, backtracked 3 clauses, performed 1 splits and kept 11498 clauses.
% 40.75/41.02 SPASS allocated 133021 KBytes.
% 40.75/41.02 SPASS spent 0:0:38.87 on the problem.
% 40.75/41.02 0:00:00.06 for the input.
% 40.75/41.02 0:00:00.00 for the FLOTTER CNF translation.
% 40.75/41.02 0:00:00.70 for inferences.
% 40.75/41.02 0:00:00.03 for the backtracking.
% 40.75/41.02 0:0:37.69 for the reduction.
% 40.75/41.02
% 40.75/41.02
% 40.75/41.02 Here is a proof with depth 2, length 19 :
% 40.75/41.02 % SZS output start Refutation
% See solution above
% 40.75/41.02 Formulae used in the proof : cls_converse__iff_1 cls_converseD_0 cls_iff_1 cls_iff_0 cls_o__apply_0 cls_conjecture_0 cls_conjecture_1
% 40.75/41.02
%------------------------------------------------------------------------------