%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SCT028-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 : Fri Sep 25 02:39:51 PM UTC 2026
% Result : Unsatisfiable 36.26s 5.10s
% Output : Proof 36.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 35
% Syntax : Number of formulae : 190 ( 130 unt; 0 def)
% Number of atoms : 286 ( 106 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 270 ( 174 ~; 96 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 8 con; 0-4 aty)
% Number of variables : 419 ( 54 sgn 166 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f511,negated_conjecture,
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f511_nnf,plain,
! [V_x] :
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(nnf_transformation,[status(thm)],[f511]) ).
fof(f511_sk,plain,
! [V_x] :
( ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemisation,[status(esa)],[f511_nnf]) ).
cnf(c511,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(esa)],[f511_sk]) ).
cnf(t120,plain,
ifeq(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),true,ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c511]) ).
cnf(t496,plain,
ifeq(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),true,ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,false,true),true) = true,
inference(orient,[status(thm)],[t120]) ).
cnf(f359,axiom,
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
fof(f359_nnf,plain,
! [V_a,V_b,T_a,T_b,V_r] :
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
inference(nnf_transformation,[status(thm)],[f359]) ).
fof(f359_sk,plain,
! [V_a,V_b,T_a,T_b,V_r] :
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
inference(skolemisation,[status(esa)],[f359_nnf]) ).
cnf(c359,plain,
( ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
| c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f359_sk]) ).
cnf(hi348,axiom,
ifeq(c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),true,c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c359]) ).
cnf(f81,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
fof(f81_nnf,plain,
! [V_x,V_A,T_a] : c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f81]) ).
fof(f81_sk,plain,
! [V_x,V_A,T_a] : c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
inference(skolemisation,[status(esa)],[f81_nnf]) ).
cnf(c81,plain,
c_in(X0,c_Set_Oinsert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(hi75,axiom,
c_in(X0,c_Set_Oinsert(X0,X1,X2),X2) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t101,plain,
c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)),X4,X3),tc_prod(X3,X4)) = true,
inference(hyper_resolution,[status(thm)],[hi348,hi75]) ).
cnf(t212,plain,
c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)),X4,X3),tc_prod(X3,X4)) = true,
inference(orient,[status(thm)],[t101]) ).
cnf(f172,axiom,
( ~ c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f172_nnf,plain,
! [V_a,V_B,T_a,V_C] :
( ~ c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
inference(nnf_transformation,[status(thm)],[f172]) ).
fof(f172_sk,plain,
! [V_a,V_B,T_a,V_C] :
( ~ c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
inference(skolemisation,[status(esa)],[f172_nnf]) ).
cnf(c172,plain,
( ~ c_in(X0,X3,X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(cnf_transformation,[status(esa)],[f172_sk]) ).
cnf(t138,plain,
ifeq(c_in(X1,X2,X3),true,c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3),
inference(equality_encoding,[status(esa)],[c172]) ).
cnf(t908,plain,
ifeq(c_in(X1,X2,X3),true,c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3),
inference(orient,[status(thm)],[t138]) ).
cnf(f136,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f136_nnf,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
inference(nnf_transformation,[status(thm)],[f136]) ).
fof(f136_sk,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
inference(skolemisation,[status(esa)],[f136_nnf]) ).
cnf(c136,plain,
( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)) = X1 ),
inference(cnf_transformation,[status(esa)],[f136_sk]) ).
cnf(t66,plain,
ifeq(c_lessequals(X1,X2,tc_fun(X3,tc_bool)),true,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X1) = X1,
inference(equality_encoding,[status(esa)],[c136]) ).
cnf(t185,plain,
ifeq(c_lessequals(X1,X2,tc_fun(X3,tc_bool)),true,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X1) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(f154,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f154_nnf,plain,
! [V_B,V_a,T_a] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
inference(nnf_transformation,[status(thm)],[f154]) ).
fof(f154_sk,plain,
! [V_B,V_a,T_a] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
inference(skolemisation,[status(esa)],[f154_nnf]) ).
cnf(c154,plain,
c_lessequals(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(esa)],[f154_sk]) ).
cnf(t33,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)) = true,
inference(equality_encoding,[status(esa)],[c154]) ).
cnf(t221,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t222,plain,
X1 = ifeq(true,true,c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X1,X3),X1,tc_fun(X3,tc_bool)),X1),
inference(cp,[status(thm)],[t185,t221]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t183,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t2139,plain,
X1 = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X1,X3),X1,tc_fun(X3,tc_bool)),
inference(step,[status(thm)],[t222,t183]) ).
cnf(t1256,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X2,tc_fun(X3,tc_bool)) = X2,
inference(orient,[status(thm)],[t2139]) ).
cnf(t1265,plain,
c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X3,tc_bool)),X3) = ifeq(c_in(X1,X2,X3),true,X2,c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X3,tc_bool)),X3)),
inference(cp,[status(thm)],[t908,t1256]) ).
cnf(f195,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f195_nnf,plain,
! [V_A,T_a] : c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
! [V_A,T_a] : c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_bool)) = X0,
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(t13,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t180,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t2166,plain,
c_Set_Oinsert(X1,X2,X3) = ifeq(c_in(X1,X2,X3),true,X2,c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X3,tc_bool)),X3)),
inference(step,[status(thm)],[t1265,t180]) ).
cnf(t2167,plain,
c_Set_Oinsert(X1,X2,X3) = ifeq(c_in(X1,X2,X3),true,X2,c_Set_Oinsert(X1,X2,X3)),
inference(step,[status(thm)],[t2166,t180]) ).
cnf(t1530,plain,
ifeq(c_in(X1,X2,X3),true,X2,c_Set_Oinsert(X1,X2,X3)) = c_Set_Oinsert(X1,X2,X3),
inference(orient,[status(thm)],[t2167]) ).
cnf(f506,axiom,
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| V_x = V_y
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
fof(f506_nnf,plain,
! [V_y,V_x,V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| V_x = V_y
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(nnf_transformation,[status(thm)],[f506]) ).
fof(f506_sk,plain,
! [V_y,V_x,V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| V_x = V_y
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemisation,[status(esa)],[f506_nnf]) ).
cnf(c506,plain,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X0
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(esa)],[f506_sk]) ).
cnf(t148,plain,
ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,or(c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),or(c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),eq(X3,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c506]) ).
cnf(t461,plain,
ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,or(c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),or(c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),eq(X3,X2))),true) = true,
inference(orient,[status(thm)],[t148]) ).
cnf(t20,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t1168,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t20]) ).
cnf(t100,plain,
or(not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),not(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) = true,
inference(equality_encoding,[status(esa)],[c511]) ).
cnf(t386,plain,
or(not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),not(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(f447,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).
fof(f447_nnf,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(nnf_transformation,[status(thm)],[f447]) ).
cnf(c447,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(cnf_transformation,[status(esa)],[f447_nnf]) ).
cnf(t32,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = true,
inference(equality_encoding,[status(esa)],[c447]) ).
cnf(t217,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t394,plain,
true = or(not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),not(true)),
inference(cp,[status(thm)],[t386,t217]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t1217,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t2180,plain,
true = or(not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),false),
inference(step,[status(thm)],[t394,t1217]) ).
cnf(t4,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t181,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t2181,plain,
true = not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(step,[status(thm)],[t2180,t181]) ).
cnf(t1771,plain,
not(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) = true,
inference(orient,[status(thm)],[t2181]) ).
cnf(t1772,plain,
false = ifeq(true,true,c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),false),
inference(cp,[status(thm)],[t1168,t1771]) ).
cnf(t2182,plain,
false = c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(step,[status(thm)],[t1772,t183]) ).
cnf(t1773,plain,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = false,
inference(orient,[status(thm)],[t2182]) ).
cnf(t1786,plain,
true = ifeq(c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,or(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),or(false,eq(v_a,v_b))),true),
inference(cp,[status(thm)],[t461,t1773]) ).
cnf(t2183,plain,
true = ifeq(true,true,or(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),or(false,eq(v_a,v_b))),true),
inference(step,[status(thm)],[t1786,t217]) ).
cnf(t2184,plain,
true = or(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),or(false,eq(v_a,v_b))),
inference(step,[status(thm)],[t2183,t183]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t182,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t2185,plain,
true = or(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),eq(v_a,v_b)),
inference(step,[status(thm)],[t2184,t182]) ).
cnf(f504,axiom,
v_a != v_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
fof(f504_nnf,plain,
v_a != v_b,
inference(nnf_transformation,[status(thm)],[f504]) ).
fof(f504_sk,plain,
v_a != v_b,
inference(skolemisation,[status(esa)],[f504_nnf]) ).
cnf(c504,plain,
v_a != v_b,
inference(cnf_transformation,[status(esa)],[f504_sk]) ).
cnf(t3,plain,
eq(v_a,v_b) = false,
inference(equality_encoding,[status(esa)],[c504]) ).
cnf(t1225,plain,
eq(v_a,v_b) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t2186,plain,
true = or(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),false),
inference(step,[status(thm)],[t2185,t1225]) ).
cnf(t2187,plain,
true = c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(step,[status(thm)],[t2186,t181]) ).
cnf(t1791,plain,
c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = true,
inference(orient,[status(thm)],[t2187]) ).
cnf(t1792,plain,
c_Set_Oinsert(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = ifeq(true,true,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Set_Oinsert(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(cp,[status(thm)],[t1530,t1791]) ).
cnf(t2192,plain,
c_Set_Oinsert(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,
inference(step,[status(thm)],[t1792,t183]) ).
cnf(t1804,plain,
c_Set_Oinsert(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,
inference(orient,[status(thm)],[t2192]) ).
cnf(t1826,plain,
true = c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cp,[status(thm)],[t212,t1804]) ).
cnf(t2045,plain,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = true,
inference(orient,[status(thm)],[t1826]) ).
cnf(t2052,plain,
true = ifeq(true,true,ifeq(c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,false,true),true),
inference(cp,[status(thm)],[t496,t2045]) ).
cnf(t2200,plain,
true = ifeq(c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,false,true),
inference(step,[status(thm)],[t2052,t183]) ).
cnf(f449,axiom,
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
fof(f449_nnf,plain,
! [V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(nnf_transformation,[status(thm)],[f449]) ).
fof(f449_sk,plain,
! [V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(skolemisation,[status(esa)],[f449_nnf]) ).
cnf(c449,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(cnf_transformation,[status(esa)],[f449_sk]) ).
cnf(t103,plain,
ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true) = true,
inference(equality_encoding,[status(esa)],[c449]) ).
cnf(t457,plain,
ifeq(c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true,c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true) = true,
inference(orient,[status(thm)],[t103]) ).
cnf(t458,plain,
true = ifeq(true,true,c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),true),
inference(cp,[status(thm)],[t457,t217]) ).
cnf(t2147,plain,
true = c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(step,[status(thm)],[t458,t183]) ).
cnf(t1326,plain,
c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = true,
inference(orient,[status(thm)],[t2147]) ).
cnf(t2201,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t2200,t1326]) ).
cnf(t2202,plain,
true = false,
inference(step,[status(thm)],[t2201,t183]) ).
cnf(t2066,plain,
false = true,
inference(orient,[status(thm)],[t2202]) ).
cnf(f1,axiom,
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
fof(f1_nnf,plain,
! [V_P,V_x,T_a] :
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_P,V_x,T_a] :
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f2,axiom,
~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f2_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f3,axiom,
~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f3_nnf,plain,
! [V_c,T_a] : ~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_c,T_a] : ~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f5,axiom,
~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f5_nnf,plain,
! [V_x,T_a] : ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_x,T_a] : ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f29,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f29_nnf,plain,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f37,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f37_nnf,plain,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(f39,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_x,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f39_nnf,plain,
! [V_x,V_B,T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_x,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [V_x,V_B,T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_x,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(f48,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f48_nnf,plain,
! [T_a,V_a,V_A] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [T_a,V_a,V_A] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(f96,axiom,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f96_nnf,plain,
! [V_x,V_y,T_a,V_r] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f96]) ).
fof(f96_sk,plain,
! [V_x,V_y,T_a,V_r] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f96_nnf]) ).
cnf(c96,plain,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)),X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f96_sk]) ).
cnf(f100,axiom,
( ~ c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
fof(f100_nnf,plain,
! [V_r,T_a,V_x] :
( ~ c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(nnf_transformation,[status(thm)],[f100]) ).
fof(f100_sk,plain,
! [V_r,T_a,V_x] :
( ~ c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(skolemisation,[status(esa)],[f100_nnf]) ).
cnf(c100,plain,
( ~ c_in(c_Pair(X2,X2,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X0,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_fun(tc_prod(X1,X1),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(cnf_transformation,[status(esa)],[f100_sk]) ).
cnf(f332,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(V_xa,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f332_nnf,plain,
! [V_y,V_Q,T_a,V_r,V_xa] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(V_xa,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
inference(nnf_transformation,[status(thm)],[f332]) ).
fof(f332_sk,plain,
! [V_y,V_Q,T_a,V_r,V_xa] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(V_xa,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(V_Q,V_r,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
inference(skolemisation,[status(esa)],[f332_nnf]) ).
cnf(c332,plain,
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X4,X1,X2)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f332_sk]) ).
cnf(f333,axiom,
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(V_x,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q,V_R,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f333_nnf,plain,
! [V_y,V_Q,T_a,V_R,V_x] :
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(V_x,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q,V_R,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
inference(nnf_transformation,[status(thm)],[f333]) ).
fof(f333_sk,plain,
! [V_y,V_Q,T_a,V_R,V_x] :
( ~ c_Wellfounded_Owf(V_R,T_a)
| ~ c_in(V_x,V_Q,T_a)
| ~ c_in(c_Pair(V_y,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(V_Q,V_R,T_a),T_a,T_a),V_R,tc_prod(T_a,T_a))
| ~ c_in(V_y,V_Q,T_a) ),
inference(skolemisation,[status(esa)],[f333_nnf]) ).
cnf(c333,plain,
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(X4,X1,X2)
| ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f333_sk]) ).
cnf(f353,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f353_nnf,plain,
! [V_x,V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f353]) ).
fof(f353_sk,plain,
! [V_x,V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f353_nnf]) ).
cnf(c353,plain,
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f353_sk]) ).
cnf(f416,axiom,
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f416_nnf,plain,
! [V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f416]) ).
fof(f416_sk,plain,
! [V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f416_nnf]) ).
cnf(c416,plain,
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(esa)],[f416_sk]) ).
cnf(f434,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
fof(f434_nnf,plain,
! [V_x,V_L] : ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(nnf_transformation,[status(thm)],[f434]) ).
fof(f434_sk,plain,
! [V_x,V_L] : ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(skolemisation,[status(esa)],[f434_nnf]) ).
cnf(c434,plain,
~ c_in(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X1,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[status(esa)],[f434_sk]) ).
cnf(f435,axiom,
~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f435_nnf,plain,
! [V_x,V_y,V_L] : ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(nnf_transformation,[status(thm)],[f435]) ).
fof(f435_sk,plain,
! [V_x,V_y,V_L] : ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(skolemisation,[status(esa)],[f435_nnf]) ).
cnf(c435,plain,
~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[status(esa)],[f435_sk]) ).
cnf(f438,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
fof(f438_nnf,plain,
! [V_x,V_L] : ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(nnf_transformation,[status(thm)],[f438]) ).
fof(f438_sk,plain,
! [V_x,V_L] : ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(skolemisation,[status(esa)],[f438_nnf]) ).
cnf(c438,plain,
~ c_in(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[status(esa)],[f438_sk]) ).
cnf(f439,axiom,
~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f439_nnf,plain,
! [V_xa,V_x,V_L] : ~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(nnf_transformation,[status(thm)],[f439]) ).
fof(f439_sk,plain,
! [V_xa,V_x,V_L] : ~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(skolemisation,[status(esa)],[f439_nnf]) ).
cnf(c439,plain,
~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnf_transformation,[status(esa)],[f439_sk]) ).
cnf(f509,axiom,
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
fof(f509_nnf,plain,
! [V_b,V_a,V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(nnf_transformation,[status(thm)],[f509]) ).
fof(f509_sk,plain,
! [V_b,V_a,V_L] :
( ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemisation,[status(esa)],[f509_nnf]) ).
cnf(c509,plain,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(esa)],[f509_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c2,c3,c5,c29,c37,c39,c48,c96,c100,c332,c333,c353,c416,c434,c435,c438,c439,c504,c509,c511]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2066]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT028-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 08:35:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.26/5.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.26/5.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------