%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL447-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:02:03 PM UTC 2026
% Result : Unsatisfiable 29.29s 4.28s
% Output : Proof 29.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 51
% Syntax : Number of formulae : 219 ( 191 unt; 0 def)
% Number of atoms : 251 ( 135 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 254 ( 222 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 45 ( 45 usr; 18 con; 0-4 aty)
% Number of variables : 541 ( 152 sgn 258 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1368,axiom,
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f1368_nnf,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f1368]) ).
fof(f1368_sk,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f1368_nnf]) ).
cnf(c1368,plain,
( c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f1368_sk]) ).
cnf(t8,plain,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c1368]) ).
cnf(t18,plain,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(f1369,negated_conjecture,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1369_nnf,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1369]) ).
cnf(c1369,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1369_nnf]) ).
cnf(t1,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(equality_encoding,[status(esa)],[c1369]) ).
cnf(t13,plain,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t20,plain,
true = ifeq(true,true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,X1,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(X1,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),true),
inference(cp,[status(thm)],[t18,t13]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t81,plain,
true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,X1,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(X1,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(step,[status(thm)],[t20,t9]) ).
cnf(t62,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,X1,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(X1,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(orient,[status(thm)],[t81]) ).
cnf(f1370,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1370_nnf,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1370]) ).
fof(f1370_sk,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f1370_nnf]) ).
cnf(c1370,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1370_sk]) ).
cnf(t2,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = false,
inference(equality_encoding,[status(esa)],[c1370]) ).
cnf(t25,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t65,plain,
true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,false,true),
inference(cp,[status(thm)],[t62,t25]) ).
cnf(f1367,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OK_0) ).
fof(f1367_nnf,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f1367]) ).
fof(f1367_sk,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemisation,[status(esa)],[f1367_nnf]) ).
cnf(c1367,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Oop_A_N_62(X1,X0,X2),X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
inference(cnf_transformation,[status(esa)],[f1367_sk]) ).
cnf(t5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(equality_encoding,[status(esa)],[c1367]) ).
cnf(t12,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t82,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t65,t12]) ).
cnf(t83,plain,
true = false,
inference(step,[status(thm)],[t82,t9]) ).
cnf(t67,plain,
false = true,
inference(orient,[status(thm)],[t83]) ).
cnf(f0,axiom,
c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(V_a_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__1__iff1_0) ).
fof(f0_nnf,plain,
! [V_a_H,T_a] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(V_a_H,T_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_a_H,T_a] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(V_a_H,T_a),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(X0,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f1,axiom,
c_PropLog_Opl_Ovar(V_a_H,T_a) != c_PropLog_Opl_Ofalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__2__iff1_0) ).
fof(f1_nnf,plain,
! [V_a_H,T_a] : c_PropLog_Opl_Ovar(V_a_H,T_a) != c_PropLog_Opl_Ofalse,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_a_H,T_a] : c_PropLog_Opl_Ovar(V_a_H,T_a) != c_PropLog_Opl_Ofalse,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
c_PropLog_Opl_Ovar(X0,X1) != c_PropLog_Opl_Ofalse,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f2,axiom,
c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__3__iff1_0) ).
fof(f2_nnf,plain,
! [V_pl1_H,V_pl2_H,T_a] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_pl1_H,V_pl2_H,T_a] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f3,axiom,
c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ofalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__4__iff1_0) ).
fof(f3_nnf,plain,
! [V_pl1_H,V_pl2_H,T_a] : c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ofalse,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_pl1_H,V_pl2_H,T_a] : c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ofalse,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
c_PropLog_Opl_Oop_A_N_62(X0,X1,X2) != c_PropLog_Opl_Ofalse,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f4,axiom,
c_PropLog_Opl_Ovar(V_a,T_a) != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__5__iff1_0) ).
fof(f4_nnf,plain,
! [V_a,T_a,V_pl1_H,V_pl2_H] : c_PropLog_Opl_Ovar(V_a,T_a) != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_a,T_a,V_pl1_H,V_pl2_H] : c_PropLog_Opl_Ovar(V_a,T_a) != c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_PropLog_Opl_Ovar(X0,X1) != c_PropLog_Opl_Oop_A_N_62(X2,X3,X1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f5,axiom,
c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ovar(V_a,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__6__iff1_0) ).
fof(f5_nnf,plain,
! [V_pl1_H,V_pl2_H,T_a,V_a] : c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ovar(V_a,T_a),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_pl1_H,V_pl2_H,T_a,V_a] : c_PropLog_Opl_Oop_A_N_62(V_pl1_H,V_pl2_H,T_a) != c_PropLog_Opl_Ovar(V_a,T_a),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_PropLog_Opl_Oop_A_N_62(X0,X1,X2) != c_PropLog_Opl_Ovar(X3,X2),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f14,axiom,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).
fof(f14_nnf,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X0,X1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f15,axiom,
c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).
fof(f15_nnf,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
c_Datatype_Ooption_OSome(X0,X1) != c_Datatype_Ooption_ONone,
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f18,axiom,
c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons__iff1_0) ).
fof(f18_nnf,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
c_Datatype__Universe_OAtom(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(f20,axiom,
c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
fof(f20_nnf,plain,
! [V_M,T_a,T_b,V_N] : c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [V_M,T_a,T_b,V_N] : c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
c_Datatype__Universe_OIn0(X0,X1,X2) != c_Datatype__Universe_OIn1(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f22,axiom,
c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
fof(f22_nnf,plain,
! [V_N,T_a,T_b,V_M] : c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [V_N,T_a,T_b,V_M] : c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
c_Datatype__Universe_OIn1(X0,X1,X2) != c_Datatype__Universe_OIn0(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(f23,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).
fof(f23_nnf,plain,
! [V_a,T_a,T_b,V_k] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [V_a,T_a,T_b,V_k] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f24,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).
fof(f24_nnf,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(f25,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf__iff1_0) ).
fof(f25_nnf,plain,
! [V_k,T_a,T_b,V_a] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [V_k,T_a,T_b,V_a] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(f26,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).
fof(f26_nnf,plain,
! [V_k,T_a,T_b,V_M,V_N] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [V_k,T_a,T_b,V_M,V_N] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(f29,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).
fof(f29_nnf,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_OAtom(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f30,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).
fof(f30_nnf,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f31,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).
fof(f31_nnf,plain,
! [V_M,V_N,T_a,T_b,V_k] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [V_M,V_N,T_a,T_b,V_k] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(f38,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).
fof(f38_nnf,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(f39,axiom,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).
fof(f39_nnf,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(f52,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
fof(f52_nnf,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(f60,axiom,
~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
fof(f60_nnf,plain,
! [V_xs,T_a,V_r] : ~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(nnf_transformation,[status(thm)],[f60]) ).
fof(f60_sk,plain,
! [V_xs,T_a,V_r] : ~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(skolemisation,[status(esa)],[f60_nnf]) ).
cnf(c60,plain,
~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X2,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(f66,axiom,
~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
fof(f66_nnf,plain,
! [V_ys,T_a,V_r] : ~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [V_ys,T_a,V_r] : ~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
~ c_in(c_Pair(c_List_Olist_ONil,X0,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X2,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(f84,axiom,
~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
fof(f84_nnf,plain,
! [T_a] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
inference(nnf_transformation,[status(thm)],[f84]) ).
fof(f84_sk,plain,
! [T_a] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
inference(skolemisation,[status(esa)],[f84_nnf]) ).
cnf(c84,plain,
~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)),tc_nat),
inference(cnf_transformation,[status(esa)],[f84_sk]) ).
cnf(f88,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
fof(f88_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(nnf_transformation,[status(thm)],[f88]) ).
fof(f88_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c88,plain,
c_List_Olist_ONil != c_List_Olist_OCons(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(f89,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
fof(f89_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
inference(nnf_transformation,[status(thm)],[f89]) ).
fof(f89_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
inference(skolemisation,[status(esa)],[f89_nnf]) ).
cnf(c89,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil,
inference(cnf_transformation,[status(esa)],[f89_sk]) ).
cnf(f111,axiom,
c_Suc(V_m) != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
fof(f111_nnf,plain,
! [V_m] : c_Suc(V_m) != c_0,
inference(nnf_transformation,[status(thm)],[f111]) ).
fof(f111_sk,plain,
! [V_m] : c_Suc(V_m) != c_0,
inference(skolemisation,[status(esa)],[f111_nnf]) ).
cnf(c111,plain,
c_Suc(X0) != c_0,
inference(cnf_transformation,[status(esa)],[f111_sk]) ).
cnf(f112,axiom,
c_0 != c_Suc(V_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
fof(f112_nnf,plain,
! [V_m] : c_0 != c_Suc(V_m),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
! [V_m] : c_0 != c_Suc(V_m),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
c_0 != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(f126,axiom,
~ c_less(c_0,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
fof(f126_nnf,plain,
~ c_less(c_0,c_0,tc_nat),
inference(nnf_transformation,[status(thm)],[f126]) ).
fof(f126_sk,plain,
~ c_less(c_0,c_0,tc_nat),
inference(skolemisation,[status(esa)],[f126_nnf]) ).
cnf(c126,plain,
~ c_less(c_0,c_0,tc_nat),
inference(cnf_transformation,[status(esa)],[f126_sk]) ).
cnf(f127,axiom,
~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
fof(f127_nnf,plain,
! [V_i,V_j] : ~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f127]) ).
fof(f127_sk,plain,
! [V_i,V_j] : ~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f127_nnf]) ).
cnf(c127,plain,
~ c_less(c_plus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f127_sk]) ).
cnf(f128,axiom,
~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
fof(f128_nnf,plain,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f128]) ).
fof(f128_sk,plain,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f128_nnf]) ).
cnf(c128,plain,
~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
inference(cnf_transformation,[status(esa)],[f128_sk]) ).
cnf(f129,axiom,
~ c_less(V_n,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
fof(f129_nnf,plain,
! [V_n] : ~ c_less(V_n,c_0,tc_nat),
inference(nnf_transformation,[status(thm)],[f129]) ).
fof(f129_sk,plain,
! [V_n] : ~ c_less(V_n,c_0,tc_nat),
inference(skolemisation,[status(esa)],[f129_nnf]) ).
cnf(c129,plain,
~ c_less(X0,c_0,tc_nat),
inference(cnf_transformation,[status(esa)],[f129_sk]) ).
cnf(f130,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).
fof(f130_nnf,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(nnf_transformation,[status(thm)],[f130]) ).
fof(f130_sk,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(skolemisation,[status(esa)],[f130_nnf]) ).
cnf(c130,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(cnf_transformation,[status(esa)],[f130_sk]) ).
cnf(f131,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).
fof(f131_nnf,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(nnf_transformation,[status(thm)],[f131]) ).
fof(f131_sk,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(skolemisation,[status(esa)],[f131_nnf]) ).
cnf(c131,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(cnf_transformation,[status(esa)],[f131_sk]) ).
cnf(f132,axiom,
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f132_nnf,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f132]) ).
fof(f132_sk,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f132_nnf]) ).
cnf(c132,plain,
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f132_sk]) ).
cnf(f161,axiom,
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f161_nnf,plain,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f161]) ).
fof(f161_sk,plain,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f161_nnf]) ).
cnf(c161,plain,
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f161_sk]) ).
cnf(f166,axiom,
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
fof(f166_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f166]) ).
fof(f166_sk,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f166_nnf]) ).
cnf(c166,plain,
( ~ c_in(X0,c_minus(X3,X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f166_sk]) ).
cnf(f175,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
fof(f175_nnf,plain,
c_UNIV != c_emptyset,
inference(nnf_transformation,[status(thm)],[f175]) ).
fof(f175_sk,plain,
c_UNIV != c_emptyset,
inference(skolemisation,[status(esa)],[f175_nnf]) ).
cnf(c175,plain,
c_UNIV != c_emptyset,
inference(cnf_transformation,[status(esa)],[f175_sk]) ).
cnf(f183,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f183_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f183]) ).
fof(f183_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f183_nnf]) ).
cnf(c183,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f183_sk]) ).
cnf(f187,axiom,
~ c_less(V_A,c_emptyset,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
fof(f187_nnf,plain,
! [V_A,T_a] : ~ c_less(V_A,c_emptyset,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f187]) ).
fof(f187_sk,plain,
! [V_A,T_a] : ~ c_less(V_A,c_emptyset,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f187_nnf]) ).
cnf(c187,plain,
~ c_less(X0,c_emptyset,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f187_sk]) ).
cnf(f195,axiom,
c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
fof(f195_nnf,plain,
! [V_a,T_a,T_b,V_b] : c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
! [V_a,T_a,T_b,V_b] : c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInr(X3,X2,X1),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(f197,axiom,
c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
fof(f197_nnf,plain,
! [V_b,T_b,T_a,V_a] : c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
! [V_b,T_b,T_a,V_a] : c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
c_Sum__Type_OInr(X0,X1,X2) != c_Sum__Type_OInl(X3,X2,X1),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(f201,axiom,
( ~ 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))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
fof(f201_nnf,plain,
! [V_y,V_x,T_a,V_r] :
( ~ 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))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(nnf_transformation,[status(thm)],[f201]) ).
fof(f201_sk,plain,
! [V_y,V_x,T_a,V_r] :
( ~ 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))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(skolemisation,[status(esa)],[f201_nnf]) ).
cnf(c201,plain,
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[status(esa)],[f201_sk]) ).
cnf(f204,axiom,
( ~ 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))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
fof(f204_nnf,plain,
! [V_y,V_x,T_a,V_r] :
( ~ 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))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(nnf_transformation,[status(thm)],[f204]) ).
fof(f204_sk,plain,
! [V_y,V_x,T_a,V_r] :
( ~ 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))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(skolemisation,[status(esa)],[f204_nnf]) ).
cnf(c204,plain,
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[status(esa)],[f204_sk]) ).
cnf(f273,axiom,
~ c_less(V_n,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f273_nnf,plain,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f273]) ).
fof(f273_sk,plain,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f273_nnf]) ).
cnf(c273,plain,
~ c_less(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f273_sk]) ).
cnf(f309,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f309_nnf,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f309]) ).
fof(f309_sk,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f309_nnf]) ).
cnf(c309,plain,
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_less(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f309_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c3,c4,c5,c14,c15,c18,c20,c22,c23,c24,c25,c26,c29,c30,c31,c38,c39,c52,c60,c66,c84,c88,c89,c111,c112,c126,c127,c128,c129,c130,c131,c132,c161,c166,c175,c183,c187,c195,c197,c201,c204,c273,c309,c1370]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t67]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL447-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 23:24:59 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.29/4.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.29/4.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------