%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV824-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:36:10 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.61s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 197 ( 92 ~; 87 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 119 ( 105 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).
tff(v_xb_type,type,
v_xb: $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_com_type,type,
v_com: $i ).
tff(v_fun2_type,type,
v_fun2: ( $i * $i ) > $o ).
tff(v_fun1_type,type,
v_fun1: ( $i * $i ) > $o ).
tff(v_x_type,type,
v_x: $i ).
tff(1,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
refl(( ( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
<=> ( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_Z: $i,V_s_H: $i,V_s: $i] :
trans(monotonicity(rewrite(( ( v_fun2(V_Z,V_s_H)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H) )
<=> ( ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) )),
( ( v_fun2(V_Z,V_s_H)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| ~ v_fun1(V_Z,V_s) )
<=> ( ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H)
| ~ v_fun1(V_Z,V_s) ) )),
rewrite(( ( ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H)
| ~ v_fun1(V_Z,V_s) )
<=> ( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) )),
( ( v_fun2(V_Z,V_s_H)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| ~ v_fun1(V_Z,V_s) )
<=> ( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( v_fun2(V_Z,V_s_H)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| ~ v_fun1(V_Z,V_s) )
<=> ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( v_fun2(V_Z,V_s_H)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| ~ v_fun1(V_Z,V_s) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(7,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ v_fun2(v_x,v_xb)
<=> ~ v_fun2(v_x,v_xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ v_fun2(v_x,v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(13,plain,
~ v_fun2(v_x,v_xb),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( v_fun1(v_x,v_xa)
<=> v_fun1(v_x,v_xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
v_fun1(v_x,v_xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,plain,
v_fun1(v_x,v_xa),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
| ~ v_fun1(v_x,v_xa)
| ~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb)
| v_fun2(v_x,v_xb) )
<=> ( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
| ~ v_fun1(v_x,v_xa)
| ~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb)
| v_fun2(v_x,v_xb) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
| ~ v_fun1(v_x,v_xa)
| ~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb)
| v_fun2(v_x,v_xb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_Z: $i,V_s_H: $i,V_s: $i] :
( ~ v_fun1(V_Z,V_s)
| ~ c_Natural_Oevaln(v_com,V_s,c_Suc(v_n),V_s_H)
| v_fun2(V_Z,V_s_H) )
| ~ v_fun1(v_x,v_xa)
| ~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb)
| v_fun2(v_x,v_xb) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
( c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
<=> c_Natural_Oevaln(v_com,v_xa,v_n,v_xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(23,plain,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
refl(( ( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
<=> ( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
<=> ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
<=> ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
rewrite(( ( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) )
<=> ( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) )
<=> ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
tff(30,plain,
! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
| ~ c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
| c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb) )
<=> ( ~ ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
| ~ c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
| c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
| ~ c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
| c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_c: $i,V_n: $i,V_s_H: $i,V_s: $i] :
( ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) )
| ~ c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
| c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),v_xb) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,33,23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV824-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.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 10:54:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.61 % SZS status Unsatisfiable
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.47/0.64 % E exiting
%------------------------------------------------------------------------------