%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 03:10:13 PM UTC 2026
% Result : Theorem 3.20s 6.10s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 22 unt; 0 def)
% Number of atoms : 99 ( 75 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 95 ( 37 ~; 38 |; 8 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__eq__plus1,axiom,
! [X8] : c_Nat_OSuc(X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(conj_0,conjecture,
( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_pe,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).
fof(fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096,axiom,
! [X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096) ).
fof(fact_n,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n) ).
fof(fact_nat__add__commute,axiom,
! [X8,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096,axiom,
( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096) ).
fof(fact_dp,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dp) ).
fof(c_0_8,plain,
! [X1190] : c_Nat_OSuc(X1190) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1190,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_9,negated_conjecture,
~ ( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_10,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_simplification,[status(thm)],[fact_pe]) ).
fof(c_0_11,plain,
! [X454] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X454) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X454) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096])])]) ).
cnf(c_0_12,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
inference(split_conjunct,[status(thm)],[fact_n]) ).
cnf(c_0_13,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X1317,X1318] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1318,X1317) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1317,X1318),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_15,negated_conjecture,
! [X90] :
( ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X90) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X90) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X90) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X90) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk1_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk1_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
& ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk1_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk1_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).
fof(c_0_16,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(fof_simplification,[status(thm)],[fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096]) ).
fof(c_0_18,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_simplification,[status(thm)],[fact_dp]) ).
cnf(c_0_19,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk11_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk11_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
fof(c_0_25,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_27,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_n____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk11_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk11_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21]),c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk11_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk11_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(sr,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk1_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk1_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_38,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk1_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),esk1_0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n026.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Mon Sep 21 09:48:42 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/5.54 Running first-order theorem proving
% 0.23/5.54 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.20/6.09 % Version: 3.5.1
% 3.20/6.09 % Preprocessing class: FMLMSMSSSSSNFFN.
% 3.20/6.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/6.09 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 3.20/6.09 % Starting new_bool_3 with 300s (1) cores
% 3.20/6.09 % Starting new_bool_1 with 300s (1) cores
% 3.20/6.09 % Starting sh5l with 300s (1) cores
% 3.20/6.09 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 1966003 completed with status 0
% 3.20/6.09 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 3.20/6.09 % Preprocessing class: FMLMSMSSSSSNFFN.
% 3.20/6.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/6.09 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 3.20/6.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.20/6.09 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 3.20/6.09 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.20/6.09 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.20/6.09 % Starting SubtermCWHack with 136s (1) cores
% 3.20/6.09 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 3.20/6.09 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 3.20/6.10 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 3.20/6.10 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 3.20/6.10 % G-E--_208_B07_F1_SE_CS_SP_PS_S4d with pid 1966013 completed with status 0
% 3.20/6.10 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S4d
% 3.20/6.10 % Preprocessing class: FMLMSMSSSSSNFFN.
% 3.20/6.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/6.10 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 3.20/6.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.20/6.10 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 3.20/6.10 % Search class: FGHSM-SSLM32-DFFFFFNN
% 3.20/6.10 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 3.20/6.10 % Starting SubtermCWHack with 136s (1) cores
% 3.20/6.10 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 3.20/6.10 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 3.20/6.10 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 3.20/6.10 % Preprocessing time : 0.038 s
% 3.20/6.10 % Presaturation interreduction done
% 3.20/6.10
% 3.20/6.10 % Proof found!
% 3.20/6.10 % SZS status Theorem
% 3.20/6.10 % SZS output start CNFRefutation
% See solution above
% 3.20/6.10 % Parsed axioms : 1206
% 3.20/6.10 % Removed by relevancy pruning/SinE : 115
% 3.20/6.10 % Initial clauses : 1486
% 3.20/6.10 % Removed in clause preprocessing : 73
% 3.20/6.10 % Initial clauses in saturation : 1413
% 3.20/6.10 % Processed clauses : 1668
% 3.20/6.10 % ...of these trivial : 9
% 3.20/6.10 % ...subsumed : 267
% 3.20/6.10 % ...remaining for further processing : 1392
% 3.20/6.10 % Other redundant clauses eliminated : 184
% 3.20/6.10 % Clauses deleted for lack of memory : 0
% 3.20/6.10 % Backward-subsumed : 1
% 3.20/6.10 % Backward-rewritten : 11
% 3.20/6.10 % Generated clauses : 160
% 3.20/6.10 % ...of the previous two non-redundant : 125
% 3.20/6.10 % ...aggressively subsumed : 0
% 3.20/6.10 % Contextual simplify-reflections : 4
% 3.20/6.10 % Paramodulations : 5
% 3.20/6.10 % Factorizations : 0
% 3.20/6.10 % NegExts : 0
% 3.20/6.10 % Equation resolutions : 184
% 3.20/6.10 % Disequality decompositions : 0
% 3.20/6.10 % Total rewrite steps : 180
% 3.20/6.10 % ...of those cached : 109
% 3.20/6.10 % Propositional unsat checks : 0
% 3.20/6.10 % Propositional check models : 0
% 3.20/6.10 % Propositional check unsatisfiable : 0
% 3.20/6.10 % Propositional clauses : 0
% 3.20/6.10 % Propositional clauses after purity: 0
% 3.20/6.10 % Propositional unsat core size : 0
% 3.20/6.10 % Propositional preprocessing time : 0.000
% 3.20/6.10 % Propositional encoding time : 0.000
% 3.20/6.10 % Propositional solver time : 0.000
% 3.20/6.10 % Success case prop preproc time : 0.000
% 3.20/6.10 % Success case prop encoding time : 0.000
% 3.20/6.10 % Success case prop solver time : 0.000
% 3.20/6.10 % Current number of processed clauses : 132
% 3.20/6.10 % Positive orientable unit clauses : 112
% 3.20/6.10 % Positive unorientable unit clauses: 0
% 3.20/6.10 % Negative unit clauses : 8
% 3.20/6.10 % Non-unit-clauses : 12
% 3.20/6.10 % Current number of unprocessed clauses: 963
% 3.20/6.10 % ...number of literals in the above : 2623
% 3.20/6.10 % Current number of archived formulas : 0
% 3.20/6.10 % Current number of archived clauses : 1106
% 3.20/6.10 % Clause-clause subsumption calls (NU) : 99583
% 3.20/6.10 % Rec. Clause-clause subsumption calls : 60144
% 3.20/6.10 % Non-unit clause-clause subsumptions : 240
% 3.20/6.10 % Unit Clause-clause subsumption calls : 27
% 3.20/6.10 % Rewrite failures with RHS unbound : 0
% 3.20/6.10 % BW rewrite match attempts : 534
% 3.20/6.10 % BW rewrite match successes : 72
% 3.20/6.10 % Condensation attempts : 0
% 3.20/6.10 % Condensation successes : 0
% 3.20/6.10 % Termbank termtop insertions : 155333
% 3.20/6.10 % Search garbage collected termcells : 20596
% 3.20/6.10
% 3.20/6.10 % -------------------------------------------------
% 3.20/6.10 % User time : 0.448 s
% 3.20/6.10 % System time : 0.037 s
% 3.20/6.10 % Total time : 0.486 s
% 3.20/6.10 % Maximum resident set size: 10184 pages
% 3.20/6.10
% 3.20/6.10 % -------------------------------------------------
% 3.20/6.10 % User time : 1.674 s
% 3.20/6.10 % System time : 0.125 s
% 3.20/6.10 % Total time : 1.799 s
% 3.20/6.10 % Maximum resident set size: 5888 pages
% 3.20/6.10 % E exiting
%------------------------------------------------------------------------------