%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 96.89s 23.74s
% Output : CNFRefutation 96.89s
% 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_n__not__Suc__n,axiom,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
file('theBenchmark.p',fact_n__not__Suc__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_1092,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_1133,plain,
hAPP(c_Nat_OSuc,A) != A,
inference(clausify,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_1235,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_1237,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_10053,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_1092,c_1237]) ).
cnf(c_20138,plain,
hAPP(hAPP(c_COMBB(A,B,C,c_Nat_OSuc),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_1235,c_1133]) ).
cnf(c_20140,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_10053]) ).
cnf(c_20139,plain,
$false,
inference(resolve,[status(thm)],[c_20138,c_20140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n013.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 06:35:04 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 2131410 was started by sandbox on n013,
% 0.09/10.38 % Sat Sep 26 06:35:04 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/10.44
% 0.14/10.44 % From the command line: assign(max_seconds, 300).
% 0.14/10.44
% 0.14/10.44 % SInE: 309 to sos, 223 to usable, of 532 axioms (tolerance 2.00, depth 0 fixpoint).
% 96.89/23.74
% 96.89/23.74 % given #500 (A,wt=128): 955 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) # tptp_name(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094e) # sine_depth(1). [clausify(39)].
% 96.89/23.74
% 96.89/23.74 % given #1000 (F,wt=27): 5004 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_COMBI(B))),A))). [para(4566(a,2),4608(a,1,2,1,2))].
% 96.89/23.74
% 96.89/23.74 % given #1500 (W,wt=15): 16298 c_Set_Oinsert(A,c3,c_Set_Oinsert(B,v_Lab____,c_Arrow__Order__Mirabelle_OLin)) = c_Arrow__Order__Mirabelle_OLin. [para(16275(a,1),10977(a,1,3))].
% 96.89/23.74
% 96.89/23.74 % SZS status Theorem for theBenchmark
% 96.89/23.74
% 96.89/23.74 % Proof 1 at 4.06 (+ 1.03) seconds.
% 96.89/23.74 % Length of proof is 11.
% 96.89/23.74 % Level of proof is 3.
% 96.89/23.74 % Maximum clause weight is 209.000.
% 96.89/23.74 % Given clauses 1790.
% 96.89/23.74
% 96.89/23.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------