%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SCT027-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 23.82s 3.45s
% Output : Proof 23.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 154 ( 70 unt; 0 def)
% Number of atoms : 282 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 391 ( 263 ~; 128 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 368 ( 48 sgn 180 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f662,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f662_nnf,plain,
! [V_R] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
inference(nnf_transformation,[status(thm)],[f662]) ).
fof(f662_sk,plain,
! [V_R] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_R),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
inference(skolemisation,[status(esa)],[f662_nnf]) ).
cnf(c662,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| v_thesis____ ),
inference(cnf_transformation,[status(esa)],[f662_sk]) ).
cnf(t74,plain,
ifeq(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),true,v_thesis____,true) = true,
inference(equality_encoding,[status(esa)],[c662]) ).
cnf(t372,plain,
ifeq(hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),true,v_thesis____,true) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(f658,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).
fof(f658_nnf,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
inference(nnf_transformation,[status(thm)],[f658]) ).
cnf(c658,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[status(esa)],[f658_nnf]) ).
cnf(t41,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) = true,
inference(equality_encoding,[status(esa)],[c658]) ).
cnf(t601,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t661,plain,
true = ifeq(true,true,v_thesis____,true),
inference(cp,[status(thm)],[t372,t601]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t223,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t3168,plain,
true = v_thesis____,
inference(step,[status(thm)],[t661,t223]) ).
cnf(t2994,plain,
true = v_thesis____,
inference(orient,[status(thm)],[t3168]) ).
cnf(f666,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f666_nnf,plain,
~ v_thesis____,
inference(nnf_transformation,[status(thm)],[f666]) ).
fof(f666_sk,plain,
~ v_thesis____,
inference(skolemisation,[status(esa)],[f666_nnf]) ).
cnf(c666,plain,
~ v_thesis____,
inference(cnf_transformation,[status(esa)],[f666_sk]) ).
cnf(t0,plain,
v_thesis____ = false,
inference(equality_encoding,[status(esa)],[c666]) ).
cnf(t2972,plain,
false = v_thesis____,
inference(orient,[status(thm)],[t0]) ).
cnf(f187,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
fof(f187_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f187]) ).
fof(f187_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f187_nnf]) ).
cnf(c187,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ c_lessequals(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f187_sk]) ).
cnf(f189,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f189_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f189]) ).
fof(f189_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f189_nnf]) ).
cnf(c189,plain,
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f189_sk]) ).
cnf(f191,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f191_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f191]) ).
fof(f191_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f191_nnf]) ).
cnf(c191,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f191_sk]) ).
cnf(f193,axiom,
( ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
fof(f193_nnf,plain,
! [T_b,V_g,V_f,T_a] :
( ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
inference(nnf_transformation,[status(thm)],[f193]) ).
fof(f193_sk,plain,
! [T_b,V_g,V_f,T_a] :
( ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
inference(skolemisation,[status(esa)],[f193_nnf]) ).
cnf(c193,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_fun(X3,X0))
| ~ c_lessequals(X1,X2,tc_fun(X3,X0))
| ~ class_HOL_Oord(X0) ),
inference(cnf_transformation,[status(esa)],[f193_sk]) ).
cnf(f194,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f194_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(f312,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f312_nnf,plain,
! [V_xa,V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(nnf_transformation,[status(thm)],[f312]) ).
fof(f312_sk,plain,
! [V_xa,V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(skolemisation,[status(esa)],[f312_nnf]) ).
cnf(c312,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X2,X1))),
inference(cnf_transformation,[status(esa)],[f312_sk]) ).
cnf(f313,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
fof(f313_nnf,plain,
! [V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(nnf_transformation,[status(thm)],[f313]) ).
fof(f313_sk,plain,
! [V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(skolemisation,[status(esa)],[f313_nnf]) ).
cnf(c313,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(X1,X0))),
inference(cnf_transformation,[status(esa)],[f313_sk]) ).
cnf(f329,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(f329_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)],[f329]) ).
fof(f329_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)],[f329_nnf]) ).
cnf(c329,plain,
c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(esa)],[f329_sk]) ).
cnf(f388,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
fof(f388_nnf,plain,
! [T_b,V_f,V_a,V_A,T_a] :
( ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b))) ),
inference(nnf_transformation,[status(thm)],[f388]) ).
fof(f388_sk,plain,
! [T_b,V_f,V_a,V_A,T_a] :
( ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b))) ),
inference(skolemisation,[status(esa)],[f388_nnf]) ).
cnf(c388,plain,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X0))) ),
inference(cnf_transformation,[status(esa)],[f388_sk]) ).
cnf(f451,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f451_nnf,plain,
! [T_a,V_x] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(nnf_transformation,[status(thm)],[f451]) ).
fof(f451_sk,plain,
! [T_a,V_x] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(skolemisation,[status(esa)],[f451_nnf]) ).
cnf(c451,plain,
~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
inference(cnf_transformation,[status(esa)],[f451_sk]) ).
cnf(f453,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f453_nnf,plain,
! [T_a,V_c] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(nnf_transformation,[status(thm)],[f453]) ).
fof(f453_sk,plain,
! [T_a,V_c] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(skolemisation,[status(esa)],[f453_nnf]) ).
cnf(c453,plain,
~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
inference(cnf_transformation,[status(esa)],[f453_sk]) ).
cnf(f454,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f454_nnf,plain,
! [T_a,V_a] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(nnf_transformation,[status(thm)],[f454]) ).
fof(f454_sk,plain,
! [T_a,V_a] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
inference(skolemisation,[status(esa)],[f454_nnf]) ).
cnf(c454,plain,
~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
inference(cnf_transformation,[status(esa)],[f454_sk]) ).
cnf(f460,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f460_nnf,plain,
! [T_a,V_c,V_B,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
inference(nnf_transformation,[status(thm)],[f460]) ).
fof(f460_sk,plain,
! [T_a,V_c,V_B,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
inference(skolemisation,[status(esa)],[f460_nnf]) ).
cnf(c460,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X0,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f460_sk]) ).
cnf(f470,axiom,
~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
fof(f470_nnf,plain,
! [V_A,T_a] : ~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
inference(nnf_transformation,[status(thm)],[f470]) ).
fof(f470_sk,plain,
! [V_A,T_a] : ~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
inference(skolemisation,[status(esa)],[f470_nnf]) ).
cnf(c470,plain,
~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(cnf_transformation,[status(esa)],[f470_sk]) ).
cnf(f483,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(f483_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)],[f483]) ).
fof(f483_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)],[f483_nnf]) ).
cnf(c483,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(esa)],[f483_sk]) ).
cnf(f489,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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f489_nnf,plain,
! [T_a,V_x,V_B,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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
inference(nnf_transformation,[status(thm)],[f489]) ).
fof(f489_sk,plain,
! [T_a,V_x,V_B,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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
inference(skolemisation,[status(esa)],[f489_nnf]) ).
cnf(c489,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f489_sk]) ).
cnf(f492,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
fof(f492_nnf,plain,
! [V_x,T_a] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)),
inference(nnf_transformation,[status(thm)],[f492]) ).
fof(f492_sk,plain,
! [V_x,T_a] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)),
inference(skolemisation,[status(esa)],[f492_nnf]) ).
cnf(c492,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_fun(X1,tc_bool)),
inference(cnf_transformation,[status(esa)],[f492_sk]) ).
cnf(f493,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f493_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f493]) ).
fof(f493_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f493_nnf]) ).
cnf(c493,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f493_sk]) ).
cnf(f494,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f494_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f494]) ).
fof(f494_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f494_nnf]) ).
cnf(c494,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f494_sk]) ).
cnf(f495,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f495_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f495]) ).
fof(f495_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f495_nnf]) ).
cnf(c495,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f495_sk]) ).
cnf(f501,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
fof(f501_nnf,plain,
! [V_P,T_a,V_x] :
( ~ hBOOL(hAPP(V_P,V_x))
| c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(nnf_transformation,[status(thm)],[f501]) ).
fof(f501_sk,plain,
! [V_P,T_a,V_x] :
( ~ hBOOL(hAPP(V_P,V_x))
| c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(skolemisation,[status(esa)],[f501_nnf]) ).
cnf(c501,plain,
( ~ hBOOL(hAPP(X0,X2))
| c_Collect(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(cnf_transformation,[status(esa)],[f501_sk]) ).
cnf(f518,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(f518_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)],[f518]) ).
fof(f518_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)],[f518_nnf]) ).
cnf(c518,plain,
c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f518_sk]) ).
cnf(f519,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f519_nnf,plain,
! [V_x,V_y,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(nnf_transformation,[status(thm)],[f519]) ).
fof(f519_sk,plain,
! [V_x,V_y,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(skolemisation,[status(esa)],[f519_nnf]) ).
cnf(c519,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X2,X0))),
inference(cnf_transformation,[status(esa)],[f519_sk]) ).
cnf(f520,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
fof(f520_nnf,plain,
! [V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(nnf_transformation,[status(thm)],[f520]) ).
fof(f520_sk,plain,
! [V_x,V_L] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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))),
inference(skolemisation,[status(esa)],[f520_nnf]) ).
cnf(c520,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X1,X0))),
inference(cnf_transformation,[status(esa)],[f520_sk]) ).
cnf(f526,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
fof(f526_nnf,plain,
! [T_a,V_P,V_x] :
( ~ hBOOL(hAPP(V_P,V_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a) ),
inference(nnf_transformation,[status(thm)],[f526]) ).
fof(f526_sk,plain,
! [T_a,V_P,V_x] :
( ~ hBOOL(hAPP(V_P,V_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a) ),
inference(skolemisation,[status(esa)],[f526_nnf]) ).
cnf(c526,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f526_sk]) ).
cnf(f561,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f561_nnf,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f561]) ).
fof(f561_sk,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f561_nnf]) ).
cnf(c561,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f561_sk]) ).
cnf(f562,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f562_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f562]) ).
fof(f562_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f562_nnf]) ).
cnf(c562,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f562_sk]) ).
cnf(f563,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f563_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f563]) ).
fof(f563_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f563_nnf]) ).
cnf(c563,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f563_sk]) ).
cnf(f564,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f564_nnf,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f564]) ).
fof(f564_sk,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f564_nnf]) ).
cnf(c564,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f564_sk]) ).
cnf(f568,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
fof(f568_nnf,plain,
! [T_a,V_c,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ),
inference(nnf_transformation,[status(thm)],[f568]) ).
fof(f568_sk,plain,
! [T_a,V_c,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ),
inference(skolemisation,[status(esa)],[f568_nnf]) ).
cnf(c568,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f568_sk]) ).
cnf(f592,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
fof(f592_nnf,plain,
! [V_P,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x)) ),
inference(nnf_transformation,[status(thm)],[f592]) ).
fof(f592_sk,plain,
! [V_P,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x)) ),
inference(skolemisation,[status(esa)],[f592_nnf]) ).
cnf(c592,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f592_sk]) ).
cnf(f650,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
fof(f650_nnf,plain,
! [V_b,V_a,V_L] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
inference(nnf_transformation,[status(thm)],[f650]) ).
fof(f650_sk,plain,
! [V_b,V_a,V_L] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
inference(skolemisation,[status(esa)],[f650_nnf]) ).
cnf(c650,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X2),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X2)) ),
inference(cnf_transformation,[status(esa)],[f650_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c187,c189,c191,c193,c194,c312,c313,c329,c388,c451,c453,c454,c460,c470,c483,c489,c492,c493,c494,c495,c501,c518,c519,c520,c526,c561,c562,c563,c564,c568,c592,c650,c666]) ).
cnf(g0_0,plain,
v_thesis____ != false,
inference(rw,[status(thm)],[goal_0,t2994]) ).
cnf(g0_1,plain,
v_thesis____ != v_thesis____,
inference(rw,[status(thm)],[g0_0,t2972]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT027-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 08:35:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.82/3.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.82/3.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------