%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT055-1 : 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 22:13:14 EDT 2022
% Result : Unsatisfiable 182.51s 182.66s
% Output : Refutation 182.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 10 unt; 1 nHn; 16 RR)
% Number of literals : 22 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(632,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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('SCT055-1.p',unknown),
[] ).
cnf(633,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_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P_H____(u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT055-1.p',unknown),
[] ).
cnf(638,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_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,u)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT055-1.p',unknown),
[] ).
cnf(639,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,u)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),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('SCT055-1.p',unknown),
[] ).
cnf(662,axiom,
( hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,v_x)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT055-1.p',unknown),
[] ).
cnf(663,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,v_x)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('SCT055-1.p',unknown),
[] ).
cnf(121647,plain,
hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P_H____(v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(s1)])],[662]),
[iquote('1:Spt:662.0')] ).
cnf(121648,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,v_x)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(mrr,[status(thm)],[663,121647]),
[iquote('1:MRR:663.0,121647.0')] ).
cnf(122473,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)],[638,121648]),
[iquote('1:Res:638.1,121648.0')] ).
cnf(123809,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P_H____(v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[632,122473]),
[iquote('1:Res:632.1,122473.0')] ).
cnf(123810,plain,
$false,
inference(mrr,[status(thm)],[123809,121647]),
[iquote('1:MRR:123809.0,121647.0')] ).
cnf(123811,plain,
~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P_H____(v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(sa)])],[123810,121647]),
[iquote('1:Spt:123810.0,662.0,121647.0')] ).
cnf(123812,plain,
hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,v_x)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spt,[spt(split,[position(s2)])],[662]),
[iquote('1:Spt:123810.0,662.1')] ).
cnf(123847,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)],[123812,639]),
[iquote('1:Res:123812.0,639.0')] ).
cnf(123947,plain,
hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P_H____(v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(res,[status(thm),theory(equality)],[123847,633]),
[iquote('1:Res:123847.0,633.0')] ).
cnf(123950,plain,
$false,
inference(mrr,[status(thm)],[123947,123811]),
[iquote('1:MRR:123947.0,123811.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT055-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.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 : Sat Jul 2 02:56:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 182.51/182.66
% 182.51/182.66 SPASS V 3.9
% 182.51/182.66 SPASS beiseite: Proof found.
% 182.51/182.66 % SZS status Theorem
% 182.51/182.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 182.51/182.66 SPASS derived 99190 clauses, backtracked 3 clauses, performed 1 splits and kept 22130 clauses.
% 182.51/182.66 SPASS allocated 179167 KBytes.
% 182.51/182.66 SPASS spent 0:2:55.34 on the problem.
% 182.51/182.66 0:00:00.06 for the input.
% 182.51/182.66 0:00:00.00 for the FLOTTER CNF translation.
% 182.51/182.66 0:00:01.79 for inferences.
% 182.51/182.66 0:00:00.21 for the backtracking.
% 182.51/182.66 0:2:52.05 for the reduction.
% 182.51/182.66
% 182.51/182.66
% 182.51/182.66 Here is a proof with depth 3, length 16 :
% 182.51/182.66 % SZS output start Refutation
% See solution above
% 182.51/182.66 Formulae used in the proof : cls_iff_1 cls_iff_0 cls_CHAINED_1_01 cls_CHAINED_0_02 cls_conjecture_0 cls_conjecture_1
% 182.51/182.66
%------------------------------------------------------------------------------