%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW211+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 03:11:44 PM UTC 2026
% Result : Theorem 64.44s 10.03s
% Output : CNFRefutation 64.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 60 unt; 0 def)
% Number of atoms : 74 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-5 aty)
% Number of variables : 105 ( 5 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_real__sum__of__halves,axiom,
! [X27] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_succ__Bit0,axiom,
! [X38] : c_Int_Osucc(c_Int_OBit0(X38)) = c_Int_OBit1(X38),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).
fof(fact_Bit0__def,axiom,
! [X38] : c_Int_OBit0(X38) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X38),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_succ__def,axiom,
! [X38] : c_Int_Osucc(X38) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
fof(fact_add__Pls__right,axiom,
! [X38] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,c_Int_OPls) = X38,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_add__Pls,axiom,
! [X38] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X38) = X38,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact__096abs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ax_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_A_L_Ae_A_P_A2_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ax_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_A_L_Ae_A_P_A2_096) ).
fof(fact_metric__bound__lemma,axiom,
! [X28,X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X27,X28)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X27),c_Complex_ORe(X28))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X27),c_Complex_OIm(X28))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_metric__bound__lemma) ).
fof(fact_Re_Odiff,axiom,
! [X28,X27] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X27,X28)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X27),c_Complex_ORe(X28)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re_Odiff) ).
fof(fact_Im_Odiff,axiom,
! [X28,X27] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X27,X28)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X27),c_Complex_OIm(X28)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im_Odiff) ).
fof(fact_xt1_I7_J,axiom,
! [X34,X27,X28,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X28,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X34,X28)
=> c_Orderings_Oord__class_Oless(X7,X34,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_complex__diff,axiom,
! [X29,X30,X5,X6] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X6,X5),c_Complex_Ocomplex_OComplex(X30,X29)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X30),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff) ).
fof(fact_Re,axiom,
! [X28,X27] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X27,X28)) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re) ).
fof(fact_Im,axiom,
! [X28,X27] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X27,X28)) = X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im) ).
fof(fact_complex__surj,axiom,
! [X34] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X34),c_Complex_OIm(X34)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(fact_o__apply,axiom,
! [X20,X1,X2,X19,X7,X18] : hAPP(c_Fun_Ocomp(X18,X7,X19,X2,X1),X20) = hAPP(X2,hAPP(X1,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(c_0_18,plain,
! [X1100] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1100,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1100,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1100,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
fof(c_0_19,plain,
! [X1468] : c_Int_Osucc(c_Int_OBit0(X1468)) = c_Int_OBit1(X1468),
inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).
fof(c_0_20,plain,
! [X1180] : c_Int_OBit0(X1180) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1180,X1180),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_21,plain,
! [X1469] : c_Int_Osucc(X1469) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1469,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
cnf(c_0_22,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
c_Int_Osucc(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X1182] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1182,c_Int_OPls) = X1182,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_27,plain,
! [X1181] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1181) = X1181,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_28,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_29,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(split_conjunct,[status(thm)],[fact__096abs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ax_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_A_L_Ae_A_P_A2_096]) ).
cnf(c_0_30,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_31,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X966,X967] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X967,X966)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X967),c_Complex_ORe(X966))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X967),c_Complex_OIm(X966))))),
inference(variable_rename,[status(thm)],[fact_metric__bound__lemma]) ).
fof(c_0_34,plain,
! [X995,X996] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X996,X995)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X996),c_Complex_ORe(X995)),
inference(variable_rename,[status(thm)],[fact_Re_Odiff]) ).
fof(c_0_35,plain,
! [X993,X994] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X994,X993)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X994),c_Complex_OIm(X993)),
inference(variable_rename,[status(thm)],[fact_Im_Odiff]) ).
fof(c_0_36,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_37,plain,
! [X235,X236,X237,X238] :
( c_Orderings_Oord__class_Oless(X238,X235,X236)
| ~ c_Orderings_Oord__class_Oless__eq(X238,X235,X237)
| ~ c_Orderings_Oord__class_Oless(X238,X237,X236)
| ~ class_Orderings_Oorder(X238) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])])]) ).
cnf(c_0_38,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_23]),c_0_23]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_39,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_31]),c_0_32]),c_0_31]),c_0_32]),c_0_31]),c_0_32]) ).
cnf(c_0_40,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X2))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X2))))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X2)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X2)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X200,X201,X202,X203] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X203,X202),c_Complex_Ocomplex_OComplex(X201,X200)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X203,X201),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X202,X200)),
inference(variable_rename,[status(thm)],[fact_complex__diff]) ).
fof(c_0_44,plain,
! [X964,X965] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X965,X964)) = X965,
inference(variable_rename,[status(thm)],[fact_Re]) ).
fof(c_0_45,plain,
! [X962,X963] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X963,X962)) = X962,
inference(variable_rename,[status(thm)],[fact_Im]) ).
fof(c_0_46,plain,
! [X930] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X930),c_Complex_OIm(X930)) = X930,
inference(variable_rename,[status(thm)],[fact_complex__surj]) ).
fof(c_0_47,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(fof_nnf,[status(thm)],[c_0_36]) ).
fof(c_0_48,plain,
! [X119,X120,X121,X122,X123,X124] : hAPP(c_Fun_Ocomp(X124,X123,X122,X121,X120),X119) = hAPP(X121,hAPP(X120,X119)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
cnf(c_0_49,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),v_e____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_31]),c_0_32]),c_0_31]),c_0_32]),c_0_31]),c_0_32]),c_0_31]),c_0_32]),c_0_39]) ).
cnf(c_0_51,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_52,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_53,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,plain,
c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_e____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_60,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_61,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),X2),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),X3)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Ocomplex_OComplex(X2,X3)),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW211+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 09:36:28 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 64.44/10.03 % Version: 3.5.1
% 64.44/10.03 % Preprocessing class: FMLMSMSMSSSNFFN.
% 64.44/10.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.44/10.03 % Starting new_bool_3 with 300s (1) cores
% 64.44/10.03 % Starting new_bool_1 with 300s (1) cores
% 64.44/10.03 % Starting sh5l with 300s (1) cores
% 64.44/10.03 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2010882 completed with status 0
% 64.44/10.03 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 64.44/10.03 % Preprocessing class: FMLMSMSMSSSNFFN.
% 64.44/10.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.44/10.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 64.44/10.03 % No SInE strategy applied
% 64.44/10.03 % Search class: FGHSM-SSLM32-DFFFFFNN
% 64.44/10.03 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 64.44/10.03 % Starting SubtermCWHack with 136s (1) cores
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 64.44/10.03 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 64.44/10.03 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 2010891 completed with status 0
% 64.44/10.03 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 64.44/10.03 % Preprocessing class: FMLMSMSMSSSNFFN.
% 64.44/10.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 64.44/10.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 64.44/10.03 % No SInE strategy applied
% 64.44/10.03 % Search class: FGHSM-SSLM32-DFFFFFNN
% 64.44/10.03 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 64.44/10.03 % Starting SubtermCWHack with 136s (1) cores
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 64.44/10.03 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 64.44/10.03 % Preprocessing time : 0.035 s
% 64.44/10.03 % Presaturation interreduction done
% 64.44/10.03
% 64.44/10.03 % Proof found!
% 64.44/10.03 % SZS status Theorem
% 64.44/10.03 % SZS output start CNFRefutation
% See solution above
% 64.44/10.03 % Parsed axioms : 1230
% 64.44/10.03 % Removed by relevancy pruning/SinE : 0
% 64.44/10.03 % Initial clauses : 1668
% 64.44/10.03 % Removed in clause preprocessing : 65
% 64.44/10.03 % Initial clauses in saturation : 1603
% 64.44/10.03 % Processed clauses : 29684
% 64.44/10.03 % ...of these trivial : 581
% 64.44/10.03 % ...subsumed : 20598
% 64.44/10.03 % ...remaining for further processing : 8505
% 64.44/10.03 % Other redundant clauses eliminated : 629
% 64.44/10.03 % Clauses deleted for lack of memory : 0
% 64.44/10.03 % Backward-subsumed : 728
% 64.44/10.03 % Backward-rewritten : 451
% 64.44/10.03 % Generated clauses : 198554
% 64.44/10.03 % ...of the previous two non-redundant : 175715
% 64.44/10.03 % ...aggressively subsumed : 0
% 64.44/10.03 % Contextual simplify-reflections : 23
% 64.44/10.03 % Paramodulations : 197880
% 64.44/10.03 % Factorizations : 16
% 64.44/10.03 % NegExts : 0
% 64.44/10.03 % Equation resolutions : 680
% 64.44/10.03 % Disequality decompositions : 0
% 64.44/10.03 % Total rewrite steps : 159231
% 64.44/10.03 % ...of those cached : 150198
% 64.44/10.03 % Propositional unsat checks : 1
% 64.44/10.03 % Propositional check models : 0
% 64.44/10.03 % Propositional check unsatisfiable : 0
% 64.44/10.03 % Propositional clauses : 0
% 64.44/10.03 % Propositional clauses after purity: 0
% 64.44/10.03 % Propositional unsat core size : 0
% 64.44/10.03 % Propositional preprocessing time : 0.000
% 64.44/10.03 % Propositional encoding time : 0.118
% 64.44/10.03 % Propositional solver time : 0.117
% 64.44/10.03 % Success case prop preproc time : 0.000
% 64.44/10.03 % Success case prop encoding time : 0.000
% 64.44/10.03 % Success case prop solver time : 0.000
% 64.44/10.03 % Current number of processed clauses : 5871
% 64.44/10.03 % Positive orientable unit clauses : 1192
% 64.44/10.03 % Positive unorientable unit clauses: 40
% 64.44/10.03 % Negative unit clauses : 1147
% 64.44/10.03 % Non-unit-clauses : 3492
% 64.44/10.03 % Current number of unprocessed clauses: 148376
% 64.44/10.03 % ...number of literals in the above : 363549
% 64.44/10.03 % Current number of archived formulas : 0
% 64.44/10.03 % Current number of archived clauses : 2510
% 64.44/10.03 % Clause-clause subsumption calls (NU) : 1283351
% 64.44/10.03 % Rec. Clause-clause subsumption calls : 903080
% 64.44/10.03 % Non-unit clause-clause subsumptions : 9074
% 64.44/10.03 % Unit Clause-clause subsumption calls : 209734
% 64.44/10.03 % Rewrite failures with RHS unbound : 3
% 64.44/10.03 % BW rewrite match attempts : 31337
% 64.44/10.03 % BW rewrite match successes : 1081
% 64.44/10.03 % Condensation attempts : 0
% 64.44/10.03 % Condensation successes : 0
% 64.44/10.03 % Termbank termtop insertions : 4309991
% 64.44/10.03 % Search garbage collected termcells : 18561
% 64.44/10.03
% 64.44/10.03 % -------------------------------------------------
% 64.44/10.03 % User time : 9.050 s
% 64.44/10.03 % System time : 0.251 s
% 64.44/10.03 % Total time : 9.301 s
% 64.44/10.03 % Maximum resident set size: 9828 pages
% 64.44/10.03
% 64.44/10.03 % -------------------------------------------------
% 64.44/10.03 % User time : 44.093 s
% 64.44/10.03 % System time : 1.265 s
% 64.44/10.03 % Total time : 45.359 s
% 64.44/10.03 % Maximum resident set size: 6144 pages
% 64.44/10.03 % E exiting
%------------------------------------------------------------------------------