%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT067-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:08:16 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.47s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 57 ( 21 unt; 24 nHn; 44 RR)
% Number of literals : 214 ( 66 equ; 86 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 85 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_CHAINED_0_06,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_06) ).
cnf(cls_A_I2_J_0,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I2_J_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_CHAINED_0_08,axiom,
v_a____ = v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_08) ).
cnf(cls_A_I5_J_1,axiom,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I5_J_1) ).
cnf(cls_A_I5_J_0,axiom,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I5_J_0) ).
cnf(cls_CHAINED_0_02,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
cnf(cls_CHAINED_2,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_2) ).
cnf(cls_A_I1_J_0,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A_I1_J_0) ).
cnf(cls_CHAINED_1_07,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1_07) ).
cnf(cls_CHAINED_1_05,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1_05) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ 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))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_3) ).
cnf(c_0_14,plain,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_0_06]) ).
cnf(c_0_15,plain,
v_a_H____ != v_b_H____,
inference(fof_simplification,[status(thm)],[cls_A_I2_J_0]) ).
cnf(c_0_16,plain,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_14 ).
cnf(c_0_17,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
cls_CHAINED_0_01 ).
cnf(c_0_18,negated_conjecture,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| 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)) ),
cls_conjecture_1 ).
cnf(c_0_19,axiom,
v_a____ = v_b_H____,
cls_CHAINED_0_08 ).
cnf(c_0_20,plain,
v_a_H____ != v_b_H____,
c_0_15 ).
cnf(c_0_21,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_A_I5_J_1]) ).
cnf(c_0_22,plain,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X2,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X2,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| X3 = X2
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( 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))
| c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
v_a_H____ != v_a____,
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_A_I5_J_0]) ).
cnf(c_0_26,plain,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_21 ).
cnf(c_0_27,negated_conjecture,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| 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))
| c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_a____ = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
cls_CHAINED_0_02 ).
cnf(c_0_29,plain,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_2]) ).
cnf(c_0_30,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_25 ).
cnf(c_0_31,plain,
( ~ c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(rw,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( c_in(c_Pair(v_a____,X1,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_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))
| c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X1
| X1 = v_a_H____ ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
v_a____ != v_b____,
inference(fof_simplification,[status(thm)],[cls_A_I1_J_0]) ).
cnf(c_0_34,plain,
v_b____ != v_a_H____,
inference(fof_simplification,[status(thm)],[cls_CHAINED_1_07]) ).
cnf(c_0_35,plain,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_1_05]) ).
cnf(c_0_36,plain,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X5,X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_29 ).
cnf(c_0_37,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(rw,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( c_in(c_Pair(v_a____,X1,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_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))
| c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_a____ = X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
v_a____ != v_b____,
c_0_33 ).
cnf(c_0_40,plain,
v_b____ != v_a_H____,
c_0_34 ).
cnf(c_0_41,plain,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_35 ).
cnf(c_0_42,plain,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X1
| X1 = v_a_H____ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17])]),c_0_24]) ).
cnf(c_0_43,negated_conjecture,
( 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))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ 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))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_45,plain,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X2,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(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P____,X3,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X4,v_P____,X3,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| X3 = X2
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_46,negated_conjecture,
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)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]),c_0_40]),c_0_39]),c_0_23]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ 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))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_44 ).
cnf(c_0_48,negated_conjecture,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X1 = v_a____ ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( ~ c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ 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)) ),
inference(rw,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_50,plain,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_3]) ).
cnf(c_0_51,negated_conjecture,
( c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,X1,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X1 = v_b____ ),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_52,negated_conjecture,
~ c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_46])]) ).
cnf(c_0_53,plain,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X1,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_50 ).
cnf(c_0_54,negated_conjecture,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_40]),c_0_24]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
~ c_in(c_Pair(v_a_H____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_28]),c_0_17]),c_0_46])]),c_0_24]),c_0_40]),c_0_39]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT067-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:30:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.47 % Version: 3.5.1
% 0.28/0.47 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.28/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.47 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.28/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.47 % Starting sh5l with 300s (1) cores
% 0.28/0.47 % new_bool_1 with pid 2002136 completed with status 0
% 0.28/0.47 % Result found by new_bool_1
% 0.28/0.47 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.28/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.47 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.28/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.47 % Search class: FGHSF-FFMS32-MFFFFFNN
% 0.28/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.47 % SubtermCWHack with pid 2002139 completed with status 0
% 0.28/0.47 % Result found by SubtermCWHack
% 0.28/0.47 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.28/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.47 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.28/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.47 % Search class: FGHSF-FFMS32-MFFFFFNN
% 0.28/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.47 % Preprocessing time : 0.002 s
% 0.28/0.47
% 0.28/0.47 % Proof found!
% 0.28/0.47 % SZS status Unsatisfiable
% 0.28/0.47 % SZS output start CNFRefutation
% See solution above
% 0.28/0.47 % Parsed axioms : 694
% 0.28/0.47 % Removed by relevancy pruning/SinE : 672
% 0.28/0.47 % Initial clauses : 22
% 0.28/0.47 % Removed in clause preprocessing : 0
% 0.28/0.47 % Initial clauses in saturation : 22
% 0.28/0.47 % Processed clauses : 46
% 0.28/0.47 % ...of these trivial : 2
% 0.28/0.47 % ...subsumed : 5
% 0.28/0.47 % ...remaining for further processing : 39
% 0.28/0.47 % Other redundant clauses eliminated : 0
% 0.28/0.47 % Clauses deleted for lack of memory : 0
% 0.28/0.47 % Backward-subsumed : 1
% 0.28/0.47 % Backward-rewritten : 13
% 0.28/0.47 % Generated clauses : 43
% 0.28/0.47 % ...of the previous two non-redundant : 26
% 0.28/0.47 % ...aggressively subsumed : 0
% 0.28/0.47 % Contextual simplify-reflections : 2
% 0.28/0.47 % Paramodulations : 39
% 0.28/0.47 % Factorizations : 2
% 0.28/0.47 % NegExts : 0
% 0.28/0.47 % Equation resolutions : 2
% 0.28/0.47 % Disequality decompositions : 0
% 0.28/0.47 % Total rewrite steps : 54
% 0.28/0.47 % ...of those cached : 49
% 0.28/0.47 % Propositional unsat checks : 0
% 0.28/0.47 % Propositional check models : 0
% 0.28/0.47 % Propositional check unsatisfiable : 0
% 0.28/0.47 % Propositional clauses : 0
% 0.28/0.47 % Propositional clauses after purity: 0
% 0.28/0.47 % Propositional unsat core size : 0
% 0.28/0.47 % Propositional preprocessing time : 0.000
% 0.28/0.47 % Propositional encoding time : 0.000
% 0.28/0.47 % Propositional solver time : 0.000
% 0.28/0.47 % Success case prop preproc time : 0.000
% 0.28/0.47 % Success case prop encoding time : 0.000
% 0.28/0.47 % Success case prop solver time : 0.000
% 0.28/0.47 % Current number of processed clauses : 25
% 0.28/0.47 % Positive orientable unit clauses : 5
% 0.28/0.47 % Positive unorientable unit clauses: 0
% 0.28/0.47 % Negative unit clauses : 5
% 0.28/0.47 % Non-unit-clauses : 15
% 0.28/0.47 % Current number of unprocessed clauses: 2
% 0.28/0.47 % ...number of literals in the above : 13
% 0.28/0.47 % Current number of archived formulas : 0
% 0.28/0.47 % Current number of archived clauses : 14
% 0.28/0.47 % Clause-clause subsumption calls (NU) : 438
% 0.28/0.47 % Rec. Clause-clause subsumption calls : 26
% 0.28/0.47 % Non-unit clause-clause subsumptions : 5
% 0.28/0.47 % Unit Clause-clause subsumption calls : 23
% 0.28/0.47 % Rewrite failures with RHS unbound : 0
% 0.28/0.47 % BW rewrite match attempts : 4
% 0.28/0.47 % BW rewrite match successes : 1
% 0.28/0.47 % Condensation attempts : 0
% 0.28/0.47 % Condensation successes : 0
% 0.28/0.47 % Termbank termtop insertions : 12067
% 0.28/0.47 % Search garbage collected termcells : 2778
% 0.28/0.47
% 0.28/0.47 % -------------------------------------------------
% 0.28/0.47 % User time : 0.011 s
% 0.28/0.47 % System time : 0.005 s
% 0.28/0.47 % Total time : 0.016 s
% 0.28/0.47 % Maximum resident set size: 4440 pages
% 0.28/0.47
% 0.28/0.47 % -------------------------------------------------
% 0.28/0.47 % User time : 0.031 s
% 0.28/0.47 % System time : 0.010 s
% 0.28/0.47 % Total time : 0.041 s
% 0.28/0.47 % Maximum resident set size: 5376 pages
% 0.28/0.47 % E exiting
%------------------------------------------------------------------------------