%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT058-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 02:07:39 PM UTC 2026
% Result : Unsatisfiable 0.19s 5.83s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 10 unt; 5 nHn; 29 RR)
% Number of literals : 74 ( 5 equ; 32 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-5 aty)
% Number of variables : 94 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_conjecture_0,negated_conjecture,
( 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)))
| 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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_insert__absorb_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_iff_1,axiom,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,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)))
| hBOOL(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/sandbox/benchmark/theBenchmark.p',cls_iff_1) ).
cnf(cls_converseD_0,axiom,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
cnf(cls_o__eq__dest__lhs_0,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 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)))
| ~ 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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_iff_0,axiom,
( ~ hBOOL(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)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,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/sandbox/benchmark/theBenchmark.p',cls_iff_0) ).
cnf(cls_converse__iff_1,axiom,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
cnf(c_0_11,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_0]) ).
cnf(c_0_12,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_13,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
c_0_11 ).
cnf(c_0_14,negated_conjecture,
( 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)))
| 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))) ),
cls_conjecture_0 ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_12 ).
cnf(c_0_16,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1 ).
cnf(c_0_17,plain,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[cls_insert__absorb_0]) ).
cnf(c_0_18,negated_conjecture,
( 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(hAPP(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),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) = X2 ),
c_0_17 ).
cnf(c_0_21,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,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)))
| hBOOL(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_iff_1]) ).
cnf(c_0_22,plain,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
inference(fof_simplification,[status(thm)],[cls_converseD_0]) ).
cnf(c_0_23,negated_conjecture,
( 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),X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_24,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
cls_o__eq__dest__lhs_0 ).
cnf(c_0_25,plain,
( ~ hBOOL(c_in(X1,X2,X4))
| hBOOL(c_in(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,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)))
| hBOOL(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,
( ~ 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)))
| ~ 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(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_28,plain,
( ~ hBOOL(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)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,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_iff_0]) ).
cnf(c_0_29,plain,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
c_0_22 ).
cnf(c_0_30,negated_conjecture,
( 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)),X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,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)))
| hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( ~ 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)))
| ~ 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))) ),
c_0_27 ).
cnf(c_0_33,plain,
( ~ hBOOL(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)))
| hBOOL(c_in(c_Pair(v_b____,v_c____,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_28 ).
cnf(c_0_34,negated_conjecture,
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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ 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(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_36,negated_conjecture,
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(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4))) ),
inference(fof_simplification,[status(thm)],[cls_converse__iff_1]) ).
cnf(c_0_38,negated_conjecture,
~ 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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_39,plain,
( ~ hBOOL(c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4))) ),
c_0_37 ).
cnf(c_0_40,negated_conjecture,
hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),X1)),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT058-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 % Computer : n014.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 04:28:55 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.49 Running first-order theorem proving
% 0.13/5.49 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.19/5.83 % Version: 3.5.1
% 0.19/5.83 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.19/5.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.83 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.19/5.83 % Starting new_bool_3 with 600s (2) cores
% 0.19/5.83 % Starting new_bool_1 with 300s (1) cores
% 0.19/5.83 % Starting sh5l with 300s (1) cores
% 0.19/5.83 % new_bool_3 with pid 3135789 completed with status 0
% 0.19/5.83 % Result found by new_bool_3
% 0.19/5.83 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.19/5.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.83 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.19/5.83 % Starting new_bool_3 with 600s (2) cores
% 0.19/5.83 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/5.83 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/5.83 % Search class: FGHSM-FSLS32-DFFFFFNN
% 0.19/5.83 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.19/5.83 % Starting SubtermCWHack with 61s (1) cores
% 0.19/5.83 % Starting SAT001_MinMin_p005000_rr_RG with 200s (1) cores
% 0.19/5.83 % SAT001_MinMin_p005000_rr_RG with pid 3135794 completed with status 0
% 0.19/5.83 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/5.83 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.19/5.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.83 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.19/5.83 % Starting new_bool_3 with 600s (2) cores
% 0.19/5.83 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/5.83 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/5.83 % Search class: FGHSM-FSLS32-DFFFFFNN
% 0.19/5.83 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.19/5.83 % Starting SubtermCWHack with 61s (1) cores
% 0.19/5.83 % Starting SAT001_MinMin_p005000_rr_RG with 200s (1) cores
% 0.19/5.83 % Preprocessing time : 0.009 s
% 0.19/5.83 % Presaturation interreduction done
% 0.19/5.83
% 0.19/5.83 % Proof found!
% 0.19/5.83 % SZS status Unsatisfiable
% 0.19/5.83 % SZS output start CNFRefutation
% See solution above
% 0.19/5.84 % Parsed axioms : 641
% 0.19/5.84 % Removed by relevancy pruning/SinE : 284
% 0.19/5.84 % Initial clauses : 357
% 0.19/5.84 % Removed in clause preprocessing : 0
% 0.19/5.84 % Initial clauses in saturation : 357
% 0.19/5.84 % Processed clauses : 1766
% 0.19/5.84 % ...of these trivial : 65
% 0.19/5.84 % ...subsumed : 842
% 0.19/5.84 % ...remaining for further processing : 859
% 0.19/5.84 % Other redundant clauses eliminated : 45
% 0.19/5.84 % Clauses deleted for lack of memory : 0
% 0.19/5.84 % Backward-subsumed : 26
% 0.19/5.84 % Backward-rewritten : 75
% 0.19/5.84 % Generated clauses : 5658
% 0.19/5.84 % ...of the previous two non-redundant : 4653
% 0.19/5.84 % ...aggressively subsumed : 0
% 0.19/5.84 % Contextual simplify-reflections : 1
% 0.19/5.84 % Paramodulations : 5607
% 0.19/5.84 % Factorizations : 0
% 0.19/5.84 % NegExts : 0
% 0.19/5.84 % Equation resolutions : 51
% 0.19/5.84 % Disequality decompositions : 0
% 0.19/5.84 % Total rewrite steps : 1900
% 0.19/5.84 % ...of those cached : 1177
% 0.19/5.84 % Propositional unsat checks : 0
% 0.19/5.84 % Propositional check models : 0
% 0.19/5.84 % Propositional check unsatisfiable : 0
% 0.19/5.84 % Propositional clauses : 0
% 0.19/5.84 % Propositional clauses after purity: 0
% 0.19/5.84 % Propositional unsat core size : 0
% 0.19/5.84 % Propositional preprocessing time : 0.000
% 0.19/5.84 % Propositional encoding time : 0.000
% 0.19/5.84 % Propositional solver time : 0.000
% 0.19/5.84 % Success case prop preproc time : 0.000
% 0.19/5.84 % Success case prop encoding time : 0.000
% 0.19/5.84 % Success case prop solver time : 0.000
% 0.19/5.84 % Current number of processed clauses : 474
% 0.19/5.84 % Positive orientable unit clauses : 129
% 0.19/5.84 % Positive unorientable unit clauses: 11
% 0.19/5.84 % Negative unit clauses : 74
% 0.19/5.84 % Non-unit-clauses : 260
% 0.19/5.84 % Current number of unprocessed clauses: 3430
% 0.19/5.84 % ...number of literals in the above : 6480
% 0.19/5.84 % Current number of archived formulas : 0
% 0.19/5.84 % Current number of archived clauses : 385
% 0.19/5.84 % Clause-clause subsumption calls (NU) : 22195
% 0.19/5.84 % Rec. Clause-clause subsumption calls : 18757
% 0.19/5.84 % Non-unit clause-clause subsumptions : 430
% 0.19/5.84 % Unit Clause-clause subsumption calls : 4353
% 0.19/5.84 % Rewrite failures with RHS unbound : 0
% 0.19/5.84 % BW rewrite match attempts : 603
% 0.19/5.84 % BW rewrite match successes : 92
% 0.19/5.84 % Condensation attempts : 0
% 0.19/5.84 % Condensation successes : 0
% 0.19/5.84 % Termbank termtop insertions : 105382
% 0.19/5.84 % Search garbage collected termcells : 2085
% 0.19/5.84
% 0.19/5.84 % -------------------------------------------------
% 0.19/5.84 % User time : 0.277 s
% 0.19/5.84 % System time : 0.017 s
% 0.19/5.84 % Total time : 0.294 s
% 0.19/5.84 % Maximum resident set size: 4692 pages
% 0.19/5.84
% 0.19/5.84 % -------------------------------------------------
% 0.19/5.84 % User time : 0.561 s
% 0.19/5.84 % System time : 0.036 s
% 0.19/5.84 % Total time : 0.597 s
% 0.19/5.84 % Maximum resident set size: 5376 pages
% 0.19/5.84 % E exiting
%------------------------------------------------------------------------------