%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW225+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:39 AM UTC 2025
% Result : Theorem 0.48s 0.72s
% Output : Proof 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 58 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 13 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 138 ( 40 ~; 34 |; 0 &)
% ( 61 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 66 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(v_N2_____type,type,
v_N2____: $i ).
tff(v_N1_____type,type,
v_N1____: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(v_f_____type,type,
v_f____: $i ).
tff(c_RComplete_Onatceiling_type,type,
c_RComplete_Onatceiling: $i > $i ).
tff(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(1,plain,
^ [V_n: $i] :
refl(( ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n )
<=> ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n )
<=> ! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n )
<=> ! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
tff(5,plain,
! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_n: $i] : ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n )
| ( c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
^ [V_m_2: $i,V_n_2: $i] :
refl(( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
<=> ! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
<=> ! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
tff(16,plain,
! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [V_m_2: $i,V_n_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
tff(23,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
inference(tautology,[status(thm)],[]) ).
tff(25,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(unit_resolution,[status(thm)],[25,20]) ).
tff(27,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(modus_ponens,[status(thm)],[26,11]) ).
tff(28,plain,
^ [V_n: $i] :
refl(( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
<=> ! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
<=> ! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
tff(32,plain,
! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [V_n: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [V_a_2: $i,V_x_2: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
<=> ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
<=> ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [V_a_2: $i,V_x_2: $i] :
rewrite(( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_a_2: $i,V_x_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
<=> ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [V_a_2: $i,V_x_2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
tff(43,plain,
! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ) )
<=> ( ~ ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_a_2: $i,V_x_2: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ) ),
inference(unit_resolution,[status(thm)],[49,46]) ).
tff(51,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(unit_resolution,[status(thm)],[50,36]) ).
tff(52,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(54,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW225+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 11:21:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.48/0.72 % SZS status Theorem
% 0.48/0.72 % SZS output start Proof
% See solution above
% 0.63/0.80 % E exiting
%------------------------------------------------------------------------------