%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW292+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 : n003.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 09:14:03 AM UTC 2026
% Result : Theorem 39.10s 6.43s
% Output : CNFRefutation 39.10s
% 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 : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-6 aty)
% Number of variables : 54 ( 18 sgn 17 !; 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(help_c__COMBS__1,axiom,
! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
fof(fact_map__fun__apply,axiom,
! [V_x_2,V_h_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(c_Fun_Omap__fun(T_c,T_d,T_e,T_b,V_f_2,V_g_2),V_h_2),V_x_2) = hAPP(V_g_2,hAPP(V_h_2,hAPP(V_f_2,V_x_2))),
file('theBenchmark.p',fact_map__fun__apply) ).
fof(fact_rev__rev__ident,axiom,
! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
file('theBenchmark.p',fact_rev__rev__ident) ).
cnf(c_2511,plain,
hAPP(hAPP(c_Fun_Omap__fun(A,B,C,D,E,F),V6),V7) = hAPP(F,hAPP(V6,hAPP(E,V7))),
inference(clausify,[status(thm)],[fact_map__fun__apply]) ).
cnf(c_4721,plain,
hAPP(c_List_Orev(A),hAPP(c_List_Orev(A),B)) = B,
inference(clausify,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_5974,plain,
hAPP(c_Nat_OSuc,A) != A,
inference(clausify,[status(thm)],[fact_Suc__n__not__n]) ).
cnf(c_6626,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_6963,plain,
hAPP(hAPP(c_Fun_Omap__fun(A,B,C,D,E,c_Nat_OSuc),F),V6) != hAPP(F,hAPP(E,V6)),
inference(paramod,[status(thm)],[c_2511,c_5974]) ).
cnf(c_8322,plain,
hAPP(hAPP(c_Fun_Omap__fun(A,B,C,D,c_List_Orev(E),c_Nat_OSuc),F),hAPP(c_List_Orev(E),V6)) != hAPP(F,V6),
inference(paramod,[status(thm)],[c_4721,c_6963]) ).
cnf(c_8324,plain,
hAPP(hAPP(D,F),hAPP(E,F)) = hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F),
inference(copy,[status(thm)],[c_6626]) ).
cnf(c_8323,plain,
$false,
inference(resolve,[status(thm)],[c_8322,c_8324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW292+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 15:38:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3213481 was started by sandbox2 on n003,
% 0.09/0.36 % Sat Sep 26 15:38:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 39.10/6.43
% 39.10/6.43 % SInE (scan): 2133 to sos (tol 1.5x), 417 to usable (tol 2.0x), 2671 zapped, of 5221 axioms (depth 3).
% 39.10/6.43
% 39.10/6.43 % From the command line: assign(max_seconds, 300).
% 39.10/6.43
% 39.10/6.43 % SZS status Theorem for theBenchmark
% 39.10/6.43
% 39.10/6.43 % Proof 1 at 4.53 (+ 0.76) seconds.
% 39.10/6.43 % Length of proof is 11.
% 39.10/6.43 % Level of proof is 4.
% 39.10/6.43 % Maximum clause weight is 109.000.
% 39.10/6.43 % Given clauses 90.
% 39.10/6.43
% 39.10/6.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------