%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW225+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 : n026.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 09:13:57 AM UTC 2026
% Result : Theorem 18.75s 8.16s
% Output : CNFRefutation 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 3 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_seq__suble,axiom,
! [V_n_2,V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
file('theBenchmark.p',fact_seq__suble) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(fact_fz_I1_J,axiom,
c_SEQ_Osubseq(v_f____),
file('theBenchmark.p',fact_fz_I1_J) ).
cnf(c_1896,plain,
c_SEQ_Osubseq(v_f____),
inference(clausify,[status(thm)],[fact_fz_I1_J]) ).
cnf(c_1912,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B)) ),
inference(clausify,[status(thm)],[fact_Suc__le__mono]) ).
cnf(c_1948,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)) ),
inference(clausify,[status(thm)],[fact_real__of__nat__le__iff]) ).
cnf(c_1949,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B))
| ~ c_SEQ_Osubseq(A) ),
inference(clausify,[status(thm)],[fact_seq__suble]) ).
cnf(c_2800,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_5129,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(v_f____,A)),
inference(resolve,[status(thm)],[c_1949,c_1896]) ).
cnf(c_5200,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(hAPP(v_f____,A))),
inference(resolve,[status(thm)],[c_5129,c_1912]) ).
cnf(c_14471,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(A)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,A)))),
inference(resolve,[status(thm)],[c_5200,c_1948]) ).
cnf(c_14472,plain,
$false,
inference(resolve,[status(thm)],[c_14471,c_2800]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW225+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 15:32:15 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1365356 was started by sandbox2 on n026,
% 0.11/5.39 % Sat Sep 26 15:32:15 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.64
% 0.15/5.64 % From the command line: assign(max_seconds, 300).
% 0.15/5.64
% 0.15/5.64 % SInE: 686 to sos, 582 to usable, of 1268 axioms (tolerance 2.00, depth 0 fixpoint).
% 18.75/8.16
% 18.75/8.16 % given #500 (T,wt=13): 6246 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(6228,a,1214,b),unit_del(a,1764)].
% 18.75/8.16
% 18.75/8.16 % given #1000 (F,wt=14): 14229 -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5095,a,1144,c),unit_del(a,1741)].
% 18.75/8.16
% 18.75/8.16 % SZS status Theorem for theBenchmark
% 18.75/8.16
% 18.75/8.16 % Proof 1 at 1.92 (+ 0.35) seconds.
% 18.75/8.16 % Length of proof is 13.
% 18.75/8.16 % Level of proof is 5.
% 18.75/8.16 % Maximum clause weight is 112.000.
% 18.75/8.16 % Given clauses 1028.
% 18.75/8.16
% 18.75/8.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------