%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV689-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:35:56 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.55s
% Output : Proof 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(v_k_type,type,
v_k: $i ).
tff(v_i_type,type,
v_i: $i ).
tff(1,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
<=> c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
tff(6,plain,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_n: $i,V_j: $i,V_k: $i] :
refl(( ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_n: $i,V_j: $i,V_k: $i] :
rewrite(( ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_n: $i,V_j: $i,V_k: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) )
<=> ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_n: $i,V_j: $i,V_k: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
tff(13,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) )
<=> ( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_n: $i,V_j: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) )
| ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SWV689-1 : TPTP v9.0.0. Released v4.1.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 10:39:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.55 % SZS status Unsatisfiable
% 0.19/0.55 % SZS output start Proof
% See solution above
% 0.43/0.59 % E exiting
%------------------------------------------------------------------------------