%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG428-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 04:59:06 AM UTC 2025
% Result : Unsatisfiable 15.44s 15.62s
% Output : Proof 15.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 69 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 251 ( 100 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 279 ( 110 ~; 139 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 77 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_p_type,type,
v_p: $i ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) )
<=> ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
tff(3,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)) = c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
^ [V_n: $i] :
refl(( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat)
<=> ! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat)
<=> ! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
tff(12,plain,
! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [V_n: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dp_0) ).
tff(19,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
^ [V_n: $i,V_m: $i] :
refl(( ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
<=> ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [V_n: $i,V_m: $i] :
trans(monotonicity(rewrite(( ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
<=> ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) )),
( ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) )
<=> ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) )),
rewrite(( ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) )
<=> ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) )),
( ( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) )
<=> ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
tff(26,plain,
! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) )
<=> ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_n: $i,V_m: $i] :
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ( V_m = V_n )
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) )
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)),tc_nat) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat),
inference(unit_resolution,[status(thm)],[35,29,19,16]) ).
tff(37,plain,
^ [V_n: $i] :
refl(( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
<=> ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
<=> ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [V_n: $i] :
rewrite(( ( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_n: $i] :
( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) )
<=> ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [V_n: $i] :
( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
tff(43,plain,
! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_n: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)),
inference(transitivity,[status(thm)],[51,7]) ).
tff(53,plain,
^ [V_x: $i] :
refl(( ( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
<=> ( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
<=> ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
<=> ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
^ [V_x: $i] :
rewrite(( ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) )
| v_thesis____ )
<=> ( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [V_x: $i] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) )
| v_thesis____ )
<=> ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [V_x: $i] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) )
| v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(59,plain,
! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(65,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ( ~ ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
| v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)) ) )
<=> ( ~ ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
| v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
| v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_x: $i] :
( v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) ) )
| v_thesis____
| ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,65,62,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ALG428-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 11:15:26 EDT 2025
% 0.15/0.36 % CPUTime :
% 15.44/15.62 % SZS status Unsatisfiable
% 15.44/15.62 % SZS output start Proof
% See solution above
% 15.48/15.67 % E exiting
%------------------------------------------------------------------------------