%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG391-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 04:59:02 AM UTC 2025
% Result : Unsatisfiable 0.44s 0.61s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 119 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 187 ( 87 ~; 78 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_cs_____type,type,
v_cs____: $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(1,plain,
^ [V_xa: $i] :
refl(( ( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
<=> ( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
<=> ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
<=> ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_xa: $i] :
trans(monotonicity(rewrite(( ( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) ) )
<=> ( ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) )),
( ( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )),
rewrite(( ( ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) )),
( ( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_xa: $i] :
( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_xa: $i] :
( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(7,plain,
! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
<=> ( v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(13,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
<=> ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| $false
| $false )
<=> ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) = c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) )
<=> $false ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
( ( c_Polynomial_Odegree(v_cs____,t_a) = c_Polynomial_Odegree(v_cs____,t_a) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
<=> $false ),
inference(transitivity,[status(thm)],[21,16]) ).
tff(23,plain,
( ( ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) ) )
<=> ( ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[22,19]) ).
tff(24,plain,
( ( ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) ) )
<=> ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(transitivity,[status(thm)],[23,15]) ).
tff(25,plain,
( ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) ) )
<=> ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) ) )
<=> ( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
inference(transitivity,[status(thm)],[25,14]) ).
tff(27,plain,
( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) != c_Polynomial_Opoly(v_cs____,hAPP(v_x,v_cs____),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_xa: $i] :
( ( V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a) )
| ( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a) ) )
| ( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ALG391-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n008.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 11:12:48 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.44/0.61 % SZS status Unsatisfiable
% 0.44/0.61 % SZS output start Proof
% See solution above
% 0.46/0.66 % E exiting
%------------------------------------------------------------------------------