%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SCT061-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:39:55 PM UTC 2026
% Result : Unsatisfiable 7.68s 1.54s
% Output : Proof 7.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 102 ( 62 unt; 0 def)
% Number of atoms : 166 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 222 ( 158 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 248 ( 36 sgn 124 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f569,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I1_J_0) ).
fof(f569_nnf,plain,
v_a____ != v_b____,
inference(nnf_transformation,[status(thm)],[f569]) ).
fof(f569_sk,plain,
v_a____ != v_b____,
inference(skolemisation,[status(esa)],[f569_nnf]) ).
cnf(c569,plain,
v_a____ != v_b____,
inference(cnf_transformation,[status(esa)],[f569_sk]) ).
cnf(hi610,axiom,
ifeq(v_a____,v_b____,false,true) = true,
inference(equality_encoding,[status(esa)],[c569]) ).
cnf(f590,negated_conjecture,
v_b____ = v_a____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f590_nnf,plain,
v_b____ = v_a____,
inference(nnf_transformation,[status(thm)],[f590]) ).
cnf(c590,plain,
v_b____ = v_a____,
inference(cnf_transformation,[status(esa)],[f590_nnf]) ).
cnf(hi567,negated_conjecture,
v_b____ = v_a____,
inference(equality_encoding,[status(esa)],[c590]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi610,hi567]) ).
cnf(t792,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f35,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f35_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)],[f35]) ).
fof(f35_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)],[f35_nnf]) ).
cnf(c35,plain,
c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(f70,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f70_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)],[f70]) ).
fof(f70_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)],[f70_nnf]) ).
cnf(c70,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f71,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/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f71_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)],[f71]) ).
fof(f71_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)],[f71_nnf]) ).
cnf(c71,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)],[f71_sk]) ).
cnf(f176,axiom,
~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f176_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)],[f176]) ).
fof(f176_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)],[f176_nnf]) ).
cnf(c176,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f176_sk]) ).
cnf(f178,axiom,
~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f178_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)],[f178]) ).
fof(f178_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)],[f178_nnf]) ).
cnf(c178,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(f179,axiom,
~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
fof(f179_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)],[f179]) ).
fof(f179_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)],[f179_nnf]) ).
cnf(c179,plain,
~ c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(cnf_transformation,[status(esa)],[f179_sk]) ).
cnf(f183,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/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
fof(f183_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)],[f183]) ).
fof(f183_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)],[f183_nnf]) ).
cnf(c183,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f183_sk]) ).
cnf(f200,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f200_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)],[f200]) ).
fof(f200_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)],[f200_nnf]) ).
cnf(c200,plain,
c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f200_sk]) ).
cnf(f293,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(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),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/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
fof(f293_nnf,plain,
! [T_a,V_r,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(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),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)],[f293]) ).
fof(f293_sk,plain,
! [T_a,V_r,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(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),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)],[f293_nnf]) ).
cnf(c293,plain,
( ~ c_in(c_Pair(X2,X2,X0,X0),c_Transitive__Closure_Otrancl(X1,X0),tc_prod(X0,X0))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X0,X0),X1),c_Transitive__Closure_Ortrancl(X1,X0),tc_fun(tc_prod(X0,X0),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)) ),
inference(cnf_transformation,[status(esa)],[f293_sk]) ).
cnf(f318,axiom,
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| ~ 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f318_nnf,plain,
! [V_x,T_a,V_r] :
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| ~ 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)) ),
inference(nnf_transformation,[status(thm)],[f318]) ).
fof(f318_sk,plain,
! [V_x,T_a,V_r] :
( ~ c_Wellfounded_Oacyclic(V_r,T_a)
| ~ 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)) ),
inference(skolemisation,[status(esa)],[f318_nnf]) ).
cnf(c318,plain,
( ~ c_Wellfounded_Oacyclic(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(X2,X1),tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(esa)],[f318_sk]) ).
cnf(f347,axiom,
( ~ c_Wellfounded_Oacyclic(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/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f347_nnf,plain,
! [V_x,V_y,T_a,V_r] :
( ~ c_Wellfounded_Oacyclic(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)],[f347]) ).
fof(f347_sk,plain,
! [V_x,V_y,T_a,V_r] :
( ~ c_Wellfounded_Oacyclic(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)],[f347_nnf]) ).
cnf(c347,plain,
( ~ c_Wellfounded_Oacyclic(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)],[f347_sk]) ).
cnf(f397,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/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f397_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)],[f397]) ).
fof(f397_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)],[f397_nnf]) ).
cnf(c397,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)],[f397_sk]) ).
cnf(f398,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/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f398_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)],[f398]) ).
fof(f398_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)],[f398_nnf]) ).
cnf(c398,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)],[f398_sk]) ).
cnf(f412,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/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f412_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)],[f412]) ).
fof(f412_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)],[f412_nnf]) ).
cnf(c412,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)],[f412_sk]) ).
cnf(f495,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/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f495_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)],[f495]) ).
fof(f495_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)],[f495_nnf]) ).
cnf(c495,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)],[f495_sk]) ).
cnf(f503,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/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f503_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)],[f503]) ).
fof(f503_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)],[f503_nnf]) ).
cnf(c503,plain,
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(esa)],[f503_sk]) ).
cnf(f517,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/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
fof(f517_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)],[f517]) ).
fof(f517_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)],[f517_nnf]) ).
cnf(c517,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)],[f517_sk]) ).
cnf(f518,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/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f518_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)],[f518]) ).
fof(f518_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)],[f518_nnf]) ).
cnf(c518,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)],[f518_sk]) ).
cnf(f521,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/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
fof(f521_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)],[f521]) ).
fof(f521_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)],[f521_nnf]) ).
cnf(c521,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)],[f521_sk]) ).
cnf(f522,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/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f522_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)],[f522]) ).
fof(f522_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)],[f522_nnf]) ).
cnf(c522,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)],[f522_sk]) ).
cnf(f581,axiom,
v_b____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I2_J_0) ).
fof(f581_nnf,plain,
v_b____ != v_c____,
inference(nnf_transformation,[status(thm)],[f581]) ).
fof(f581_sk,plain,
v_b____ != v_c____,
inference(skolemisation,[status(esa)],[f581_nnf]) ).
cnf(c581,plain,
v_b____ != v_c____,
inference(cnf_transformation,[status(esa)],[f581_sk]) ).
cnf(f588,axiom,
v_a____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I3_J_0) ).
fof(f588_nnf,plain,
v_a____ != v_c____,
inference(nnf_transformation,[status(thm)],[f588]) ).
fof(f588_sk,plain,
v_a____ != v_c____,
inference(skolemisation,[status(esa)],[f588_nnf]) ).
cnf(c588,plain,
v_a____ != v_c____,
inference(cnf_transformation,[status(esa)],[f588_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c35,c70,c71,c176,c178,c179,c183,c200,c293,c318,c347,c397,c398,c412,c495,c503,c517,c518,c521,c522,c569,c581,c588]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t792]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT061-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.52 % Computer : n020.cluster.edu
% 0.07/0.52 % Model : x86_64 x86_64
% 0.07/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.52 % Memory : 8046.5625MB
% 0.07/0.52 % OS : Linux 6.8.0-71-generic
% 0.07/0.52 % CPULimit : 300
% 0.07/0.52 % WCLimit : 300
% 0.07/0.52 % DateTime : Thu Sep 24 08:41:04 UTC 2026
% 0.07/0.52 % CPUTime :
% 0.07/0.52 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.68/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.68/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------