%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 09:13:56 AM UTC 2026
% Result : Theorem 3.09s 1.03s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 25 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 2 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 26 ( 3 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096,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('theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096,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('theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(fact_o__apply,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('theBenchmark.p',fact_o__apply) ).
fof(conj_0,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('theBenchmark.p',conj_0) ).
fof(conj_0_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(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_1818,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A),hAPP(v_f____,B))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) ),
inference(clausify,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096]) ).
cnf(c_1819,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,A),hAPP(v_ga____,B))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) ),
inference(clausify,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096]) ).
cnf(c_1823,plain,
hAPP(hAPP(c_Fun_Ocomp(A,B,C,D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[fact_o__apply]) ).
fof(nnf_973,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(fof_nnf,[status(thm)],[conj_0_neg]) ).
fof(sk_conj_0_neg,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____),sK0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK1))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B_m,sK0),skolemize(B_n,sK1)],[nnf_973]) ).
cnf(c_2730,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_conj_0_neg]) ).
cnf(c_2731,negated_conjecture,
~ 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____),sK0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK1)),
inference(split_conjunct,[status(thm)],[sk_conj_0_neg]) ).
cnf(c_3085,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK0)),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK1)),
inference(paramod,[status(thm)],[c_1823,c_2731]) ).
cnf(c_2732,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK0)),hAPP(v_f____,hAPP(v_ga____,sK1))),
inference(paramod,[status(thm)],[c_1823,c_3085]) ).
cnf(c_2929,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK0),hAPP(v_ga____,sK1)),
inference(resolve,[status(thm)],[c_1819,c_2730]) ).
cnf(c_3086,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK0)),hAPP(v_f____,hAPP(v_ga____,sK1))),
inference(resolve,[status(thm)],[c_2929,c_1818]) ).
cnf(c_3084,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2732,c_3086]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 15:24:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1064047 was started by sandbox2 on n017,
% 0.10/0.37 % Sat Sep 26 15:24:05 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.32/0.61
% 0.32/0.61 % From the command line: assign(max_seconds, 300).
% 0.32/0.61
% 0.32/0.61 % SInE: 544 to sos, 616 to usable, of 1160 axioms (tolerance 2.00, depth 0 fixpoint).
% 3.09/1.03
% 3.09/1.03 % SZS status Theorem for theBenchmark
% 3.09/1.03
% 3.09/1.03 % Proof 1 at 0.31 (+ 0.06) seconds.
% 3.09/1.03 % Length of proof is 12.
% 3.09/1.03 % Level of proof is 3.
% 3.09/1.03 % Maximum clause weight is 15.000.
% 3.09/1.03 % Given clauses 50.
% 3.09/1.03
% 3.09/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------