%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 42.16s 6.54s
% Output : Proof 42.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 34 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 6 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 3 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_0_h4789540cac4ff9e3) ).
fof(f2_nnf,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1160,conjecture,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1160_neg,negated_conjecture,
~ ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n)) ),
inference(negated_conjecture,[status(cth)],[f1160]) ).
fof(f1160_nnf,plain,
? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(nnf_transformation,[status(thm)],[f1160_neg]) ).
fof(f1160_sk,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sk52),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sk53))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk52,sk53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk52,sk53])],[f1160_nnf]) ).
cnf(c1654,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk52,sk53),
inference(cnf_transformation,[status(esa)],[f1160_sk]) ).
cnf(p927,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sk52),hAPP(v_ga____,sk53)),
inference(resolution,[status(thm)],[c2,c1654]) ).
fof(f1,axiom,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_0_ha316c8249076c2bf) ).
fof(f1_nnf,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p928,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sk52)),hAPP(v_f____,hAPP(v_ga____,sk53))),
inference(resolution,[status(thm)],[p927,c1]) ).
fof(f6,axiom,
! [V_xa_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
fof(f6_nnf,plain,
! [V_xa_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T_b,T_a,T_c,V_fa_2,V_gb_2,V_xa_2] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
hAPP(hAPP(c_Fun_Ocomp(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c1655,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sk52),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sk53)),
inference(cnf_transformation,[status(esa)],[f1160_sk]) ).
cnf(p930,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sk52)),hAPP(v_f____,hAPP(v_ga____,sk53))),
inference(superposition,[status(thm)],[c6,c1655]) ).
cnf(p946,plain,
$false,
inference(resolution,[status(thm)],[p928,p930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.39 % Computer : n011.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Thu Sep 24 21:44:13 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.16/6.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.16/6.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------