%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SCT052-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 02:39:54 PM UTC 2026
% Result : Unsatisfiable 9.57s 1.65s
% Output : Proof 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 82 ( 42 unt; 0 def)
% Number of atoms : 146 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 198 ( 134 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-4 aty)
% Number of variables : 194 ( 18 sgn 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f596,negated_conjecture,
v_b____ != v_c____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f596_nnf,plain,
v_b____ != v_c____,
inference(nnf_transformation,[status(thm)],[f596]) ).
fof(f596_sk,plain,
v_b____ != v_c____,
inference(skolemisation,[status(esa)],[f596_nnf]) ).
cnf(c596,plain,
v_b____ != v_c____,
inference(cnf_transformation,[status(esa)],[f596_sk]) ).
cnf(t4,plain,
eq(v_b____,v_c____) = false,
inference(equality_encoding,[status(esa)],[c596]) ).
cnf(f597,negated_conjecture,
v_b____ = v_c____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f597_nnf,plain,
v_b____ = v_c____,
inference(nnf_transformation,[status(thm)],[f597]) ).
cnf(c597,plain,
v_b____ = v_c____,
inference(cnf_transformation,[status(esa)],[f597_nnf]) ).
cnf(t0,plain,
v_c____ = v_b____,
inference(equality_encoding,[status(esa)],[c597]) ).
cnf(t256,plain,
v_b____ = v_c____,
inference(orient,[status(thm)],[t0]) ).
cnf(t263,plain,
eq(v_c____,v_c____) = false,
inference(step,[status(thm)],[t4,t256]) ).
cnf(t1,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t257,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t264,plain,
true = false,
inference(step,[status(thm)],[t263,t257]) ).
cnf(t259,plain,
false = true,
inference(orient,[status(thm)],[t264]) ).
cnf(f173,axiom,
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f173_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
( ~ c_in(X0,c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(f257,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/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f257_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)],[f257]) ).
fof(f257_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)],[f257_nnf]) ).
cnf(c257,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)],[f257_sk]) ).
cnf(f307,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/sandbox2/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f307_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)],[f307]) ).
fof(f307_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)],[f307_nnf]) ).
cnf(c307,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)],[f307_sk]) ).
cnf(f341,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(f341_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)],[f341]) ).
fof(f341_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)],[f341_nnf]) ).
cnf(c341,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)],[f341_sk]) ).
cnf(f342,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(f342_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)],[f342]) ).
fof(f342_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)],[f342_nnf]) ).
cnf(c342,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)],[f342_sk]) ).
cnf(f356,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(f356_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)],[f356]) ).
fof(f356_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)],[f356_nnf]) ).
cnf(c356,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)],[f356_sk]) ).
cnf(f399,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(f399_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)],[f399]) ).
fof(f399_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)],[f399_nnf]) ).
cnf(c399,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)],[f399_sk]) ).
cnf(f505,axiom,
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f505_nnf,plain,
! [V_x,T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f505]) ).
fof(f505_sk,plain,
! [V_x,T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f505_nnf]) ).
cnf(c505,plain,
( ~ c_Relation_Oirrefl(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(esa)],[f505_sk]) ).
cnf(f514,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(f514_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)],[f514]) ).
fof(f514_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)],[f514_nnf]) ).
cnf(c514,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)],[f514_sk]) ).
cnf(f522,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(f522_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)],[f522]) ).
fof(f522_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)],[f522_nnf]) ).
cnf(c522,plain,
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(esa)],[f522_sk]) ).
cnf(f536,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(f536_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)],[f536]) ).
fof(f536_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)],[f536_nnf]) ).
cnf(c536,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)],[f536_sk]) ).
cnf(f537,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(f537_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)],[f537]) ).
fof(f537_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)],[f537_nnf]) ).
cnf(c537,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)],[f537_sk]) ).
cnf(f540,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(f540_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)],[f540]) ).
fof(f540_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)],[f540_nnf]) ).
cnf(c540,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)],[f540_sk]) ).
cnf(f541,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(f541_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)],[f541]) ).
fof(f541_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)],[f541_nnf]) ).
cnf(c541,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)],[f541_sk]) ).
cnf(f594,negated_conjecture,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f594_nnf,plain,
v_a____ != v_b____,
inference(nnf_transformation,[status(thm)],[f594]) ).
fof(f594_sk,plain,
v_a____ != v_b____,
inference(skolemisation,[status(esa)],[f594_nnf]) ).
cnf(c594,plain,
v_a____ != v_b____,
inference(cnf_transformation,[status(esa)],[f594_sk]) ).
cnf(f595,negated_conjecture,
v_a____ != v_c____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f595_nnf,plain,
v_a____ != v_c____,
inference(nnf_transformation,[status(thm)],[f595]) ).
fof(f595_sk,plain,
v_a____ != v_c____,
inference(skolemisation,[status(esa)],[f595_nnf]) ).
cnf(c595,plain,
v_a____ != v_c____,
inference(cnf_transformation,[status(esa)],[f595_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c173,c257,c307,c341,c342,c356,c399,c505,c514,c522,c536,c537,c540,c541,c594,c595,c596]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t259]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT052-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 08:39:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.57/1.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.57/1.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------