%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 03:26:49 PM UTC 2026
% Result : Theorem 71.71s 11.07s
% Output : Proof 71.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 53 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 18 ~; 18 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_A_Is_A0_J_096) ).
fof(f14_nnf,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(nnf_transformation,[status(thm)],[f14]) ).
cnf(c17,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(cnf_transformation,[status(esa)],[f14_nnf]) ).
fof(f8,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f8_nnf,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f7_nnf,plain,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_z,V_w] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f1263,conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1263_neg,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(negated_conjecture,[status(cth)],[f1263]) ).
fof(f1263_nnf,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(nnf_transformation,[status(thm)],[f1263_neg]) ).
fof(f1263_sk,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(skolemisation,[status(esa)],[f1263_nnf]) ).
cnf(c1708,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(cnf_transformation,[status(esa)],[f1263_sk]) ).
cnf(p1050,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(resolution,[status(thm)],[c7,c1708]) ).
cnf(p1053,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
inference(resolution,[status(thm)],[c8,p1050]) ).
cnf(p1119,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(resolution,[status(thm)],[c17,p1053]) ).
fof(f9,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
=> V_z = V_w ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f9_nnf,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_z,V_w] :
( V_z = V_w
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( X1 = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p1130,plain,
( v_r = 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)) ),
inference(resolution,[status(thm)],[p1119,c9]) ).
fof(f3,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(f3_nnf,plain,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1132,plain,
v_r = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(resolution,[status(thm)],[p1130,c3]) ).
cnf(p1133,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(superposition,[status(thm)],[p1132,c17]) ).
cnf(p1134,plain,
$false,
inference(resolution,[status(thm)],[p1133,c1708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n004.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 21:44:53 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 71.71/11.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.71/11.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------