%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT167+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 : 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 : Sun Sep 27 08:28:35 AM UTC 2026
% Result : Theorem 87.50s 12.20s
% Output : CNFRefutation 87.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-5 aty)
% Number of variables : 43 ( 15 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_plus__nat_Oadd__0) ).
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(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
cnf(c_1083,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A,
inference(clausify,[status(thm)],[fact_plus__nat_Oadd__0]) ).
cnf(c_1116,plain,
hAPP(c_Nat_OSuc,A) != A,
inference(clausify,[status(thm)],[fact_Suc__n__not__n]) ).
cnf(c_1249,plain,
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_1251,plain,
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_10235,plain,
hAPP(c_COMBS(A,B,C,D,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),E) = hAPP(hAPP(D,E),E),
inference(paramod,[status(thm)],[c_1083,c_1251]) ).
cnf(c_22319,plain,
hAPP(hAPP(c_COMBB(A,B,C,c_Nat_OSuc),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_1249,c_1116]) ).
cnf(c_22321,plain,
hAPP(hAPP(D,E),E) = hAPP(c_COMBS(A,B,C,D,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),E),
inference(copy,[status(thm)],[c_10235]) ).
cnf(c_22320,plain,
$false,
inference(resolve,[status(thm)],[c_22319,c_22321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT167+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n011.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 06:35:15 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3995193 was started by sandbox2 on n011,
% 0.16/0.44 % Sat Sep 26 06:35:15 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.39/0.67
% 0.39/0.67 % From the command line: assign(max_seconds, 300).
% 0.39/0.67
% 0.39/0.67 % SInE: 336 to sos, 196 to usable, of 532 axioms (tolerance 2.00, depth 0 fixpoint).
% 87.50/12.20
% 87.50/12.20 % given #500 (W,wt=19): 2439 hBOOL(hAPP(c_Nat_Onat_Onat__case(A,hAPP(c_fequal,B),C,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(1761,a,893,a)].
% 87.50/12.20
% 87.50/12.20 % given #1000 (T,wt=14): 7865 c_Set_Oinsert(A,c_Nat_Osize__class_Osize(tc_Nat_Onat,c4),c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin. [resolve(1055,a,2664,a)].
% 87.50/12.20
% 87.50/12.20 % given #1500 (F,wt=16): 15424 c_Nat_Osize__class_Osize(tc_Nat_Onat,f9(A,A)) != c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)). [para(15216(a,1),10750(a,1,2)),flip(a)].
% 87.50/12.20
% 87.50/12.20 % SZS status Theorem for theBenchmark
% 87.50/12.20
% 87.50/12.20 % Proof 1 at 2.66 (+ 0.69) seconds.
% 87.50/12.20 % Length of proof is 11.
% 87.50/12.20 % Level of proof is 3.
% 87.50/12.20 % Maximum clause weight is 209.000.
% 87.50/12.20 % Given clauses 1929.
% 87.50/12.20
% 87.50/12.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------