%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL854-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:03:13 PM UTC 2026
% Result : Unsatisfiable 6.76s 1.41s
% Output : Proof 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 114 ( 98 unt; 0 def)
% Number of atoms : 142 ( 87 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 157 ( 129 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-5 aty)
% Number of variables : 202 ( 84 sgn 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f255,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
fof(f255_nnf,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
inference(nnf_transformation,[status(thm)],[f255]) ).
cnf(c255,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
inference(cnf_transformation,[status(esa)],[f255_nnf]) ).
cnf(t7,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)) = true,
inference(equality_encoding,[status(esa)],[c255]) ).
cnf(t476,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f261,axiom,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I1_J_0) ).
fof(f261_nnf,plain,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(nnf_transformation,[status(thm)],[f261]) ).
cnf(c261,plain,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(cnf_transformation,[status(esa)],[f261_nnf]) ).
cnf(t39,plain,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)) = true,
inference(equality_encoding,[status(esa)],[c261]) ).
cnf(t523,plain,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t135,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(f30,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f30_nnf,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f85,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f85_nnf,plain,
! [V_r,T_a,V_xs] : ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [V_r,T_a,V_xs] : ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
inference(skolemisation,[status(esa)],[f85_nnf]) ).
cnf(c85,plain,
~ c_ListOrder_Ostep1(X0,c_List_Olist_ONil(X1),X2,X1),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(f86,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f86_nnf,plain,
! [V_r,V_xs,T_a] : ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [V_r,V_xs,T_a] : ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
inference(skolemisation,[status(esa)],[f86_nnf]) ).
cnf(c86,plain,
~ c_ListOrder_Ostep1(X0,X1,c_List_Olist_ONil(X2),X2),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(f91,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f91_nnf,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f91]) ).
fof(f91_sk,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(f95,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f95_nnf,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f95]) ).
fof(f95_sk,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f95_nnf]) ).
cnf(c95,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(f134,axiom,
V_n != c_Suc(V_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f134_nnf,plain,
! [V_n] : V_n != c_Suc(V_n),
inference(nnf_transformation,[status(thm)],[f134]) ).
fof(f134_sk,plain,
! [V_n] : V_n != c_Suc(V_n),
inference(skolemisation,[status(esa)],[f134_nnf]) ).
cnf(c134,plain,
X0 != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f134_sk]) ).
cnf(f135,axiom,
c_Suc(V_n) != V_n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f135_nnf,plain,
! [V_n] : c_Suc(V_n) != V_n,
inference(nnf_transformation,[status(thm)],[f135]) ).
fof(f135_sk,plain,
! [V_n] : c_Suc(V_n) != V_n,
inference(skolemisation,[status(esa)],[f135_nnf]) ).
cnf(c135,plain,
c_Suc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f135_sk]) ).
cnf(f143,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
fof(f143_nnf,plain,
! [V_m] : c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
! [V_m] : c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
c_Suc(X0) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(f144,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f144_nnf,plain,
! [V_nat_H] : c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f144]) ).
fof(f144_sk,plain,
! [V_nat_H] : c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f144_nnf]) ).
cnf(c144,plain,
c_Suc(X0) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f144_sk]) ).
cnf(f157,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f157_nnf,plain,
! [V_m] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
inference(nnf_transformation,[status(thm)],[f157]) ).
fof(f157_sk,plain,
! [V_m] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
inference(skolemisation,[status(esa)],[f157_nnf]) ).
cnf(c157,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f157_sk]) ).
cnf(f158,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f158_nnf,plain,
! [V_nat_H] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
inference(nnf_transformation,[status(thm)],[f158]) ).
fof(f158_sk,plain,
! [V_nat_H] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
inference(skolemisation,[status(esa)],[f158_nnf]) ).
cnf(c158,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f158_sk]) ).
cnf(f183,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f183_nnf,plain,
! [V_dB1_H,V_dB2_H,V_nat] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(nnf_transformation,[status(thm)],[f183]) ).
fof(f183_sk,plain,
! [V_dB1_H,V_dB2_H,V_nat] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f183_nnf]) ).
cnf(c183,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f183_sk]) ).
cnf(f187,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f187_nnf,plain,
! [V_s,V_t,V_n,V_ss] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(nnf_transformation,[status(thm)],[f187]) ).
fof(f187_sk,plain,
! [V_s,V_t,V_n,V_ss] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(skolemisation,[status(esa)],[f187_nnf]) ).
cnf(c187,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),
inference(cnf_transformation,[status(esa)],[f187_sk]) ).
cnf(f203,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f203_nnf,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f203]) ).
fof(f203_sk,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f203_nnf]) ).
cnf(c203,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f203_sk]) ).
cnf(f215,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f215_nnf,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(nnf_transformation,[status(thm)],[f215]) ).
fof(f215_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f215_nnf]) ).
cnf(c215,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f215_sk]) ).
cnf(f218,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f218_nnf,plain,
! [V_n,V_ts,V_r,V_ss] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(nnf_transformation,[status(thm)],[f218]) ).
fof(f218_sk,plain,
! [V_n,V_ts,V_r,V_ss] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
inference(skolemisation,[status(esa)],[f218_nnf]) ).
cnf(c218,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),
inference(cnf_transformation,[status(esa)],[f218_sk]) ).
cnf(f220,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f220_nnf,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
inference(nnf_transformation,[status(thm)],[f220]) ).
fof(f220_sk,plain,
! [V_nat,V_dB1_H,V_dB2_H] : c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
inference(skolemisation,[status(esa)],[f220_nnf]) ).
cnf(c220,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f220_sk]) ).
cnf(f232,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f232_nnf,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(nnf_transformation,[status(thm)],[f232]) ).
fof(f232_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f232_nnf]) ).
cnf(c232,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f232_sk]) ).
cnf(f240,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f240_nnf,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
inference(nnf_transformation,[status(thm)],[f240]) ).
fof(f240_sk,plain,
! [V_dB_H,V_dB1,V_dB2] : c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
inference(skolemisation,[status(esa)],[f240_nnf]) ).
cnf(c240,plain,
c_Lambda_OdB_OAbs(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f240_sk]) ).
cnf(f242,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f242_nnf,plain,
! [V_dB1,V_dB2,V_dB_H] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(nnf_transformation,[status(thm)],[f242]) ).
fof(f242_sk,plain,
! [V_dB1,V_dB2,V_dB_H] : hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f242_nnf]) ).
cnf(c242,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f242_sk]) ).
cnf(f243,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f243_nnf,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(nnf_transformation,[status(thm)],[f243]) ).
fof(f243_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f243_nnf]) ).
cnf(c243,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f243_sk]) ).
cnf(f247,axiom,
hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
fof(f247_nnf,plain,
! [V_type1_H,V_type2_H,V_nat] : hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
inference(nnf_transformation,[status(thm)],[f247]) ).
fof(f247_sk,plain,
! [V_type1_H,V_type2_H,V_nat] : hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
inference(skolemisation,[status(esa)],[f247_nnf]) ).
cnf(c247,plain,
hAPP(hAPP(c_Type_Otype_OFun,X0),X1) != c_Type_Otype_OAtom(X2),
inference(cnf_transformation,[status(esa)],[f247_sk]) ).
cnf(f265,axiom,
c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
fof(f265_nnf,plain,
! [V_nat,V_type1_H,V_type2_H] : c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
inference(nnf_transformation,[status(thm)],[f265]) ).
fof(f265_sk,plain,
! [V_nat,V_type1_H,V_type2_H] : c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
inference(skolemisation,[status(esa)],[f265_nnf]) ).
cnf(c265,plain,
c_Type_Otype_OAtom(X0) != hAPP(hAPP(c_Type_Otype_OFun,X1),X2),
inference(cnf_transformation,[status(esa)],[f265_sk]) ).
cnf(f267,negated_conjecture,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f267_nnf,plain,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(nnf_transformation,[status(thm)],[f267]) ).
fof(f267_sk,plain,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(skolemisation,[status(esa)],[f267_nnf]) ).
cnf(c267,plain,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(cnf_transformation,[status(esa)],[f267_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c30,c85,c86,c91,c95,c134,c135,c143,c144,c157,c158,c183,c187,c203,c215,c218,c220,c232,c240,c242,c243,c247,c265,c267]) ).
cnf(g0_0,plain,
true != ifeq(c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),true,false,hBOOL(hAPP(c_InductTermi_OIT,v_s____))),
inference(rw,[status(thm)],[g0_0,t476]) ).
cnf(g0_2,plain,
true != ifeq(c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),false,hBOOL(hAPP(c_InductTermi_OIT,v_s____))),
inference(rw,[status(thm)],[g0_1,t523]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t135]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL854-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 00:41:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.76/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.76/1.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------