%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:03:15 PM UTC 2026
% Result : Unsatisfiable 8.53s 1.57s
% Output : Proof 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 114 ( 110 unt; 0 def)
% Number of atoms : 118 ( 90 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 79 ( 75 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-5 aty)
% Number of variables : 202 ( 82 sgn 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f157,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
fof(f157_nnf,plain,
! [V_t] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(nnf_transformation,[status(thm)],[f157]) ).
fof(f157_sk,plain,
! [V_t] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) ),
inference(skolemisation,[status(esa)],[f157_nnf]) ).
cnf(c157,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),X0)) ),
inference(cnf_transformation,[status(esa)],[f157_sk]) ).
cnf(t104,plain,
ifeq(hBOOL(hAPP(c_InductTermi_OIT,X1)),true,hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),X1)),true) = true,
inference(equality_encoding,[status(esa)],[c157]) ).
cnf(t227,axiom,
sF0 = c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),
introduced(definition) ).
cnf(t246,plain,
c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB) = sF0,
inference(orient,[status(thm)],[t227]) ).
cnf(t2147,plain,
ifeq(hBOOL(hAPP(c_InductTermi_OIT,X1)),true,hBOOL(hAPP(c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB),X1)),true) = true,
inference(step,[status(thm)],[t104,t246]) ).
cnf(t228,axiom,
sF1 = c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
introduced(definition) ).
cnf(t1866,plain,
sF1 = c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB),
inference(step,[status(thm)],[t228,t246]) ).
cnf(t260,plain,
c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB) = sF1,
inference(orient,[status(thm)],[t1866]) ).
cnf(t2148,plain,
ifeq(hBOOL(hAPP(c_InductTermi_OIT,X1)),true,hBOOL(hAPP(sF1,X1)),true) = true,
inference(step,[status(thm)],[t2147,t260]) ).
cnf(t1420,plain,
ifeq(hBOOL(hAPP(c_InductTermi_OIT,X1)),true,hBOOL(hAPP(sF1,X1)),true) = true,
inference(orient,[status(thm)],[t2148]) ).
cnf(f188,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f188_nnf,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(nnf_transformation,[status(thm)],[f188]) ).
cnf(c188,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(cnf_transformation,[status(esa)],[f188_nnf]) ).
cnf(t13,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)) = true,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t245,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t1421,plain,
true = ifeq(true,true,hBOOL(hAPP(sF1,v_t)),true),
inference(cp,[status(thm)],[t1420,t245]) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t252,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t2149,plain,
true = hBOOL(hAPP(sF1,v_t)),
inference(step,[status(thm)],[t1421,t252]) ).
cnf(t229,axiom,
sF2 = hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t),
introduced(definition) ).
cnf(t1867,plain,
sF2 = hAPP(c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB),v_t),
inference(step,[status(thm)],[t229,t246]) ).
cnf(t1868,plain,
sF2 = hAPP(sF1,v_t),
inference(step,[status(thm)],[t1867,t260]) ).
cnf(t302,plain,
hAPP(sF1,v_t) = sF2,
inference(orient,[status(thm)],[t1868]) ).
cnf(t2150,plain,
true = hBOOL(sF2),
inference(step,[status(thm)],[t2149,t302]) ).
cnf(f189,negated_conjecture,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f189_nnf,plain,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(nnf_transformation,[status(thm)],[f189]) ).
fof(f189_sk,plain,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(skolemisation,[status(esa)],[f189_nnf]) ).
cnf(c189,plain,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(cnf_transformation,[status(esa)],[f189_sk]) ).
cnf(t47,plain,
hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)) = false,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t1869,plain,
hBOOL(hAPP(c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB),v_t)) = false,
inference(step,[status(thm)],[t47,t246]) ).
cnf(t1870,plain,
hBOOL(hAPP(sF1,v_t)) = false,
inference(step,[status(thm)],[t1869,t260]) ).
cnf(t1871,plain,
hBOOL(sF2) = false,
inference(step,[status(thm)],[t1870,t302]) ).
cnf(t311,plain,
hBOOL(sF2) = false,
inference(orient,[status(thm)],[t1871]) ).
cnf(t230,axiom,
sF3 = hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
introduced(definition) ).
cnf(t1908,plain,
sF3 = hBOOL(hAPP(c_Wellfounded_Oaccp(sF0,tc_Lambda_OdB),v_t)),
inference(step,[status(thm)],[t230,t246]) ).
cnf(t1909,plain,
sF3 = hBOOL(hAPP(sF1,v_t)),
inference(step,[status(thm)],[t1908,t260]) ).
cnf(t1910,plain,
sF3 = hBOOL(sF2),
inference(step,[status(thm)],[t1909,t302]) ).
cnf(t1911,plain,
sF3 = false,
inference(step,[status(thm)],[t1910,t311]) ).
cnf(t416,plain,
false = sF3,
inference(orient,[status(thm)],[t1911]) ).
cnf(t1944,plain,
hBOOL(sF2) = sF3,
inference(step,[status(thm)],[t311,t416]) ).
cnf(t449,plain,
hBOOL(sF2) = sF3,
inference(orient,[status(thm)],[t1944]) ).
cnf(t2151,plain,
true = sF3,
inference(step,[status(thm)],[t2150,t449]) ).
cnf(t1517,plain,
true = sF3,
inference(orient,[status(thm)],[t2151]) ).
cnf(f4,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f4_nnf,plain,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f9,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
fof(f9_nnf,plain,
! [V_x,V_xa,T_a] : c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_x,V_xa,T_a] : c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f10,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f10_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(T_a),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_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(T_a),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f12,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f12_nnf,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f13,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
fof(f13_nnf,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(f37,axiom,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f37_nnf,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(X0,X1),X2),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(f38,axiom,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f38_nnf,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [V_r,T_a,V_xs] : ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(X0,X1),c_List_Olist_ONil(X1)),X2)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(f52,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f52_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)],[f52]) ).
fof(f52_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)],[f52_nnf]) ).
cnf(c52,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OVar(X2),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(f55,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f55_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)],[f55]) ).
fof(f55_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)],[f55_nnf]) ).
cnf(c55,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)],[f55_sk]) ).
cnf(f91,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f91_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)],[f91]) ).
fof(f91_sk,plain,
! [V_nat,V_dB_H] : c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
inference(skolemisation,[status(esa)],[f91_nnf]) ).
cnf(c91,plain,
c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X1),
inference(cnf_transformation,[status(esa)],[f91_sk]) ).
cnf(f98,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f98_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)],[f98]) ).
fof(f98_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)],[f98_nnf]) ).
cnf(c98,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)],[f98_sk]) ).
cnf(f104,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f104_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)],[f104]) ).
fof(f104_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)],[f104_nnf]) ).
cnf(c104,plain,
c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f104_sk]) ).
cnf(f130,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f130_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)],[f130]) ).
fof(f130_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)],[f130_nnf]) ).
cnf(c130,plain,
c_Lambda_OdB_OAbs(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(cnf_transformation,[status(esa)],[f130_sk]) ).
cnf(f133,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f133_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)],[f133]) ).
fof(f133_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)],[f133_nnf]) ).
cnf(c133,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1) != c_Lambda_OdB_OAbs(X2),
inference(cnf_transformation,[status(esa)],[f133_sk]) ).
cnf(f134,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f134_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)],[f134]) ).
fof(f134_sk,plain,
! [V_dB_H,V_nat] : c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
inference(skolemisation,[status(esa)],[f134_nnf]) ).
cnf(c134,plain,
c_Lambda_OdB_OAbs(X0) != c_Lambda_OdB_OVar(X1),
inference(cnf_transformation,[status(esa)],[f134_sk]) ).
cnf(f149,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f149_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)],[f149]) ).
fof(f149_sk,plain,
! [V_i,V_t] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
inference(skolemisation,[status(esa)],[f149_nnf]) ).
cnf(c149,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f149_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c9,c10,c12,c13,c37,c38,c52,c55,c91,c98,c104,c130,c133,c134,c149,c189]) ).
cnf(g0_0,plain,
sF3 != false,
inference(rw,[status(thm)],[goal_0,t1517]) ).
cnf(g0_1,plain,
sF3 != sF3,
inference(rw,[status(thm)],[g0_0,t416]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.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 00:38:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.53/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.53/1.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------