%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:04:49 AM UTC 2026
% Result : Theorem 234.85s 240.16s
% Output : Proof 234.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 24 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096cmod_A_Is_A0_J_A_060_061_Ar_096,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
file('theBenchmark.p',fact__096cmod_A_Is_A0_J_A_060_061_Ar_096) ).
fof(fact__0960_A_060_061_Acmod_A_Is_A0_J_096,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('theBenchmark.p',fact__0960_A_060_061_Acmod_A_Is_A0_J_096) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(conj_0,conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('theBenchmark.p',conj_0) ).
fof(f_5_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(fof_nnf,[status(thm)],[fact__096cmod_A_Is_A0_J_A_060_061_Ar_096]) ).
fof(f_5_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_15_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(fof_nnf,[status(thm)],[fact__0960_A_060_061_Acmod_A_Is_A0_J_096]) ).
fof(f_15_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_18_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).
fof(f_18_2,plain,
! [U_40,U_39,U_38,U_37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_39))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_38))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_38),U_39))
| ~ class_Orderings_Oorder(U_37) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_37,U_38,U_39,U_40] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_39))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_38))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_38),U_39))
| ~ class_Orderings_Oorder(U_37) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_39))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_40),U_38))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_37,U_38),U_39))
| ~ class_Orderings_Oorder(U_37) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_1161_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(f_1161_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1161_1]) ).
cnf(f_1161_3,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1264_1,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_1264_2,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(definitional_conversion,[status(esa)],[f_1264_1]) ).
cnf(f_1264_3,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(clausify,[status(thm)],[f_1264_2]) ).
cnf(t1,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(start,[status(thm),parent(0:0)],[f_1264_3]) ).
cnf(t2,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(extension,[status(thm),parent(t1:1)],[f_18_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(extension,[status(thm),parent(t2:2)],[f_5_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(extension,[status(thm),parent(t2:3)],[f_15_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(extension,[status(thm),parent(t2:4)],[f_1161_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n001.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Sun Sep 20 05:13:18 UTC 2026
% 0.09/5.39 % CPUTime :
% 234.85/240.16 % SZS status Theorem for theBenchmark
% 234.85/240.16 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------