%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV675-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:35:55 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.72s
% Output : Proof 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 135 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 214 ( 103 ~; 89 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 88 ( 78 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
<=> c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i,V_m: $i] :
refl(( ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_n: $i,V_m: $i] :
rewrite(( ( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_lessequals(V_m,V_n,tc_nat) )
<=> ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_lessequals(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
tff(10,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_n: $i] :
refl(( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
tff(22,plain,
! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_n: $i] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_n: $i,V_m: $i] :
refl(( ( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [V_n: $i,V_m: $i] :
trans(monotonicity(rewrite(( ( ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
( ( ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) )
<=> ( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) ) )),
rewrite(( ( ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) )
<=> ( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
( ( ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) )
<=> ( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) )
<=> ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
tff(33,plain,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_y) )
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_y) )
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_y) )
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_y) )
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(v_y),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_y),
inference(unit_resolution,[status(thm)],[39,36,26,17]) ).
tff(41,plain,
^ [V_m: $i] :
refl(( ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) )
<=> ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) )
<=> ! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) )
<=> ! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
tff(45,plain,
! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [V_m: $i] : ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) )
| ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(v_y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,47,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV675-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:42:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.48/0.72 % SZS status Unsatisfiable
% 0.48/0.72 % SZS output start Proof
% See solution above
% 0.64/0.79 % E exiting
%------------------------------------------------------------------------------