%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW249+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 : n015.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 09:13:59 AM UTC 2026
% Result : Theorem 6.71s 6.75s
% Output : CNFRefutation 6.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 13 unt; 0 def)
% Number of atoms : 18 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 75 ( 31 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> ( V_m_2 = V_n_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_not__add__less2,axiom,
! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
file('theBenchmark.p',fact_not__add__less2) ).
fof(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBC__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_COMBC(T_c,T_d,T_b,V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
file('theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
cnf(c_1856,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_1857,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(D,F),E),
inference(clausify,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_1858,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[help_c__COMBS__1]) ).
cnf(c_1978,plain,
( B != A
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B))) ),
inference(clausify,[status(thm)],[fact_less__Suc__eq]) ).
cnf(c_2002,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),B)),
inference(clausify,[status(thm)],[fact_not__add__less2]) ).
cnf(c_3030,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),D),E)),hAPP(D,E))),
inference(paramod,[status(thm)],[c_1858,c_2002]) ).
cnf(c_3132,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_COMBC(A,B,C,hAPP(c_COMBS(D,E,F),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),V6),V7)),hAPP(V7,V6))),
inference(paramod,[status(thm)],[c_1857,c_3030]) ).
cnf(c_3317,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_COMBC(A,B,C,hAPP(c_COMBS(D,E,F),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),V6),hAPP(hAPP(c_COMBB(V7,V8,V9),V10),V11))),hAPP(V10,hAPP(V11,V6)))),
inference(paramod,[status(thm)],[c_1856,c_3132]) ).
cnf(c_3782,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(A,B),hAPP(C,B))),hAPP(c_Nat_OSuc,hAPP(hAPP(hAPP(c_COMBS(D,E,F),A),C),B)))),
inference(resolve,[status(thm)],[c_1978,c_1858]) ).
cnf(c_3783,plain,
$false,
inference(resolve,[status(thm)],[c_3782,c_3317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW249+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 15:35:50 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.39 % Process 205212 was started by sandbox2 on n015,
% 0.12/5.39 % Sat Sep 26 15:35:50 2026
% 0.12/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.67
% 0.15/5.67 % From the command line: assign(max_seconds, 300).
% 0.15/5.67
% 0.15/5.67 % SInE: 657 to sos, 557 to usable, of 1214 axioms (tolerance 2.00, depth 0 fixpoint).
% 6.71/6.75
% 6.71/6.75 % SZS status Theorem for theBenchmark
% 6.71/6.75
% 6.71/6.75 % Proof 1 at 0.57 (+ 0.09) seconds.
% 6.71/6.75 % Length of proof is 15.
% 6.71/6.75 % Level of proof is 5.
% 6.71/6.75 % Maximum clause weight is 31.000.
% 6.71/6.75 % Given clauses 219.
% 6.71/6.75
% 6.71/6.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------