%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW248+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 : n001.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 9.67s 2.13s
% Output : CNFRefutation 9.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 26 unt; 0 def)
% Number of atoms : 65 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 47 ( 21 ~; 22 |; 0 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-4 aty)
% Number of variables : 111 ( 28 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__n__not__n,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_m_2] :
( V_m_2 != V_n_2
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_not__add__less2,axiom,
! [V_i,V_j] : ~ 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(fact_nat__size,axiom,
! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n,
file('theBenchmark.p',fact_nat__size) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(help_c__COMBI__1,axiom,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',help_c__COMBI__1) ).
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_1227,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,A) = A,
inference(clausify,[status(thm)],[fact_nat__size]) ).
cnf(c_1330,plain,
( c_Orderings_Oord__class_Oless(A,C,D)
| ~ c_Orderings_Oord__class_Oless(A,B,D)
| B != C
| ~ class_Orderings_Oord(A) ),
inference(clausify,[status(thm)],[fact_ord__eq__less__trans]) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
cnf(c_1812,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(c_1869,plain,
hAPP(c_COMBI(A),B) = B,
inference(clausify,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_1871,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_1872,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_1873,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_1980,plain,
hAPP(c_Nat_OSuc,A) != A,
inference(clausify,[status(thm)],[fact_Suc__n__not__n]) ).
cnf(c_2008,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = hAPP(c_Nat_OSuc,A),
inference(clausify,[status(thm)],[fact_Suc__eq__plus1__left]) ).
cnf(c_2403,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)
| A = B ),
inference(clausify,[status(thm)],[fact_nat__neq__iff]) ).
cnf(c_2404,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)
| A != B ),
inference(clausify,[status(thm)],[fact_nat__neq__iff]) ).
cnf(c_2416,plain,
~ 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_2953,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_COMBC(A,B,C,D),E),F),hAPP(hAPP(D,F),E)),
inference(resolve,[status(thm)],[c_2404,c_1872]) ).
cnf(c_5357,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B)
| A != C
| ~ class_Orderings_Oord(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)
| A = B ),
inference(resolve,[status(thm)],[c_2403,c_1330]) ).
cnf(c_3237,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B)
| A != C
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)
| A = B ),
inference(resolve,[status(thm)],[c_1812,c_5357]) ).
cnf(c_5358,plain,
A = c_Nat_Osize__class_Osize(tc_Nat_Onat,A),
inference(copy,[status(thm)],[c_1227]) ).
cnf(c_3495,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A),B)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)
| A = B ),
inference(resolve,[status(thm)],[c_3237,c_5358]) ).
cnf(c_3744,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_COMBC(A,B,C,c_COMBI(D)),E),F),hAPP(F,E)),
inference(paramod,[status(thm)],[c_1869,c_2953]) ).
cnf(c_3808,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_COMBC(A,B,C,c_COMBI(D)),E),hAPP(hAPP(c_COMBB(F,V6,V7),V8),V9)),hAPP(V8,hAPP(V9,E))),
inference(paramod,[status(thm)],[c_1871,c_3744]) ).
cnf(c_4868,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),A),
inference(paramod,[status(thm)],[c_2008,c_2416]) ).
cnf(c_5359,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,A))
| A = hAPP(c_Nat_OSuc,A) ),
inference(resolve,[status(thm)],[c_3495,c_4868]) ).
cnf(c_5360,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,A))
| hAPP(c_Nat_OSuc,A) = A ),
inference(copy,[status(thm)],[c_5359]) ).
cnf(c_5138,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,A)),
inference(resolve,[status(thm)],[c_1980,c_5360]) ).
cnf(c_5361,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))
| c_Nat_Osize__class_Osize(tc_Nat_Onat,A) != B
| ~ class_Orderings_Oord(tc_Nat_Onat) ),
inference(resolve,[status(thm)],[c_5138,c_1330]) ).
cnf(c_5307,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))
| c_Nat_Osize__class_Osize(tc_Nat_Onat,A) != B ),
inference(resolve,[status(thm)],[c_1812,c_5361]) ).
cnf(c_5351,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))
| A != B ),
inference(paramod,[status(thm)],[c_1227,c_5307]) ).
cnf(c_5355,plain,
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_5351,c_1873]) ).
cnf(c_5356,plain,
$false,
inference(resolve,[status(thm)],[c_5355,c_3808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW248+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n001.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 15:37:43 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 2119257 was started by sandbox2 on n001,
% 0.20/0.46 % Sat Sep 26 15:37:43 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.56/0.83
% 0.56/0.83 % From the command line: assign(max_seconds, 300).
% 0.56/0.83
% 0.56/0.83 % SInE: 652 to sos, 552 to usable, of 1204 axioms (tolerance 2.00, depth 0 fixpoint).
% 9.67/2.13
% 9.67/2.13 % SZS status Theorem for theBenchmark
% 9.67/2.13
% 9.67/2.13 % Proof 1 at 1.04 (+ 0.18) seconds.
% 9.67/2.13 % Length of proof is 33.
% 9.67/2.13 % Level of proof is 8.
% 9.67/2.13 % Maximum clause weight is 115.000.
% 9.67/2.13 % Given clauses 360.
% 9.67/2.13
% 9.67/2.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------