%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW211+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 : Tue May 5 05:30:03 PM UTC 2026
% Result : Theorem 39.21s 25.21s
% Output : CNFRefutation 39.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 57 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 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 : 63 ( 5 sgn 40 !; 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_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_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(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__096cmod_A_Is_A_If_A_Ig_An_J_J_A_N_AComplex_Ax_Ay_J_060_061_Aabs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_ARe_A_IComplex_Ax_Ay_J_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_AIm_A_IComplex_Ax_Ay_J_J_096,axiom,
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,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),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____)))),c_Complex_ORe(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),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____)))),c_Complex_OIm(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Is_A_If_A_Ig_An_J_J_A_N_AComplex_Ax_Ay_J_060_061_Aabs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_ARe_A_IComplex_Ax_Ay_J_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_AIm_A_IComplex_Ax_Ay_J_J_096) ).
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(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_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_14,plain,
! [X3593] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3593,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,X3593,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X3593,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
fof(c_0_15,plain,
! [X3961] : c_Int_Osucc(c_Int_OBit0(X3961)) = c_Int_OBit1(X3961),
inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).
fof(c_0_16,plain,
! [X3673] : c_Int_OBit0(X3673) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3673,X3673),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_17,plain,
! [X3962] : c_Int_Osucc(X3962) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3962,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
fof(c_0_18,plain,
! [X3457,X3458] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X3458,X3457)) = X3458,
inference(variable_rename,[status(thm)],[fact_Re]) ).
fof(c_0_19,plain,
! [X3455,X3456] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X3456,X3455)) = X3455,
inference(variable_rename,[status(thm)],[fact_Im]) ).
cnf(c_0_20,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_14]) ).
cnf(c_0_21,plain,
c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
fof(c_0_24,plain,
! [X3675] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3675,c_Int_OPls) = X3675,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_25,plain,
! [X3674] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X3674) = X3674,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_26,plain,
! [X2728,X2729,X2730,X2731] :
( ~ class_Orderings_Oorder(X2731)
| ~ c_Orderings_Oord__class_Oless(X2731,X2730,X2729)
| ~ c_Orderings_Oord__class_Oless__eq(X2731,X2728,X2730)
| c_Orderings_Oord__class_Oless(X2731,X2728,X2729) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
cnf(c_0_27,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,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),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____)))),c_Complex_ORe(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),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____)))),c_Complex_OIm(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))))),
inference(split_conjunct,[status(thm)],[fact__096cmod_A_Is_A_If_A_Ig_An_J_J_A_N_AComplex_Ax_Ay_J_060_061_Aabs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_ARe_A_IComplex_Ax_Ay_J_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_AIm_A_IComplex_Ax_Ay_J_J_096]) ).
cnf(c_0_28,plain,
c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,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_31,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_20,c_0_21]),c_0_21]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_32,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_35,plain,
! [X2612,X2613,X2614,X2615,X2616,X2617] : hAPP(c_Fun_Ocomp(X2617,X2616,X2615,X2614,X2613),X2612) = hAPP(X2614,hAPP(X2613,X2612)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,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,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),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____)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_38,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_39,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_30,c_0_21]),c_0_21]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_40,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_31,c_0_32]),c_0_33]),c_0_32]),c_0_33]),c_0_32]),c_0_33]),c_0_32]),c_0_33]) ).
cnf(c_0_41,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_34]) ).
cnf(c_0_42,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( 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____))),X1)
| ~ 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____))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_44,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_39,c_0_32]),c_0_33]),c_0_32]),c_0_33]),c_0_32]),c_0_33]),c_0_32]),c_0_33]),c_0_40]) ).
cnf(c_0_45,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(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW211+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 06:27:48 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 39.21/25.21 % Version : CSE_E---1.7
% 39.21/25.21 % Problem : theBenchmark.p
% 39.21/25.21 % SZS status Theorem for theBenchmark.p
% 39.21/25.21 % SZS output start CNFRefutation
% See solution above
% 39.30/25.34 % Total time : 19.655s
%------------------------------------------------------------------------------