%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW284+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:34 PM UTC 2026
% Result : Theorem 0.23s 0.51s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 88 ( 57 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 97 ( 44 ~; 39 |; 7 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_g_2,V_f_2] :
( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
=> V_f_2 = V_g_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_qa_2,V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_qa_2)
<=> V_pa_2 = V_qa_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_a_2,V_pa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1115,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1122,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1180,hypothesis,
! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1181,conjecture,
v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1182,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(negated_conjecture,[status(cth)],[f1181]) ).
fof(f1183,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f1184,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| hAPP(V_f_2,sK0_skl(V_f_2,V_g_2)) != hAPP(V_g_2,sK0_skl(V_f_2,V_g_2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B_x,sK0_skl(V_f_2,V_g_2))],[f1183]) ).
fof(f1185,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X0,sK0_skl(X0,X1)) != hAPP(X1,sK0_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1184]) ).
fof(f1186,plain,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1195,plain,
! [V_qa_2,V_pa_2,T_a] :
( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_qa_2)
<=> V_pa_2 = V_qa_2 )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f1196,plain,
! [V_qa_2,V_pa_2,T_a] :
( ( ( V_pa_2 != V_qa_2
| c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_qa_2) )
& ( V_pa_2 = V_qa_2
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_qa_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(NNF_transformation,[status(thm)],[f1195]) ).
fof(f1197,plain,
! [T_a] :
( ( ! [V_qa_2,V_pa_2] :
( V_pa_2 != V_qa_2
| c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_qa_2) )
& ! [V_qa_2,V_pa_2] :
( V_pa_2 = V_qa_2
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_qa_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(miniscoping,[status(thm)],[f1196]) ).
fof(f1198,plain,
! [X0,X1,X2] :
( X1 = X2
| c_Polynomial_Opoly(X0,X1) != c_Polynomial_Opoly(X0,X2)
| ~ class_Rings_Oidom(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1197]) ).
fof(f1200,plain,
! [V_a_2,V_pa_2,T_a] :
( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f1201,plain,
! [V_a_2,V_pa_2,T_a] :
( ( ( ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(NNF_transformation,[status(thm)],[f1200]) ).
fof(f1202,plain,
! [T_a] :
( ( ! [V_a_2,V_pa_2] :
( ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ! [V_a_2,V_pa_2] :
( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(miniscoping,[status(thm)],[f1201]) ).
fof(f1204,plain,
! [X0,X1,X2] :
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| hAPP(c_Polynomial_Opoly(X0,X1),X2) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1202]) ).
fof(f4519,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1115]) ).
fof(f4526,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1122]) ).
fof(f4635,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1180]) ).
fof(f4636,plain,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f1182]) ).
fof(f4675,plain,
! [X0,X1] :
( hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Oidom(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f1204]) ).
fof(f4833,plain,
! [X0] :
( X0 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| hAPP(X0,sK0_skl(X0,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f4635,f1185]) ).
fof(f4837,plain,
v_q != v_p,
inference(backward_demodulation,[status(thm)],[f1186,f4636]) ).
fof(f4862,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f4675,f4833]) ).
fof(f4865,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1186,f4862]) ).
fof(f4873,plain,
( v_p = v_q
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f4865,f1198]) ).
fof(f4875,plain,
( v_p = v_q
| ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(duplicate_literals_removal,[status(thm)],[f4873]) ).
fof(f4876,plain,
( ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f4875,f4837]) ).
fof(f5141,plain,
~ class_Rings_Oidom(tc_Complex_Ocomplex),
inference(backward_subsumption_resolution,[status(thm)],[f4876,f4519]) ).
fof(f5264,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4526,f5141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW284+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:40:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.46 % Drodi V4.1.1
% 0.23/0.51 % Refutation found
% 0.23/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.58 % Elapsed time: 0.206550 seconds
% 0.23/0.58 % CPU time: 0.555686 seconds
% 0.23/0.58 % Total memory used: 154.066 MB
% 0.23/0.58 % Net memory used: 152.974 MB
%------------------------------------------------------------------------------