%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG396-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.40s 0.57s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(v_c_____type,type,
v_c____: $i ).
tff(v_x_____type,type,
v_x____: $i ).
tff(v_q_____type,type,
v_q____: $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(1,plain,
^ [V_x: $i] :
refl(( ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) )
<=> ! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) )
<=> ! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th_0) ).
tff(5,plain,
! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i] : ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_x,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,V_x,tc_Complex_Ocomplex) )
| ( c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(13,plain,
c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
$false,
inference(unit_resolution,[status(thm)],[13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG396-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 11:14:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.40/0.57 % SZS status Unsatisfiable
% 0.40/0.57 % SZS output start Proof
% See solution above
% 0.42/0.61 % E exiting
%------------------------------------------------------------------------------