%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT141+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 : n002.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 08:28:33 AM UTC 2026
% Result : Theorem 49.94s 7.80s
% Output : CNFRefutation 49.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-3 aty)
% Number of variables : 51 ( 22 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__Cons__self2,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('theBenchmark.p',fact_not__Cons__self2) ).
fof(help_c__COMBC__1,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_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_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(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_781,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C,
inference(clausify,[status(thm)],[fact_not__Cons__self2]) ).
cnf(c_1240,plain,
hAPP(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_1241,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_42585,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_1241,c_781]) ).
cnf(c_43189,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),hAPP(c_COMBS(D,E,F),c_List_Olist_OCons(V6))),V7),V8) != hAPP(V8,V7),
inference(paramod,[status(thm)],[c_1240,c_42585]) ).
cnf(c_43191,plain,
hAPP(hAPP(D,F),hAPP(E,F)) = hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F),
inference(copy,[status(thm)],[c_1241]) ).
cnf(c_43190,plain,
$false,
inference(resolve,[status(thm)],[c_43189,c_43191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT141+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:35:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1033671 was started by sandbox on n002,
% 0.10/0.37 % Sat Sep 26 06:35:20 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.27/0.50
% 0.27/0.50 % From the command line: assign(max_seconds, 300).
% 0.27/0.50
% 0.27/0.50 % SInE: 382 to sos, 140 to usable, of 522 axioms (tolerance 2.00, depth 0 fixpoint).
% 49.94/7.80
% 49.94/7.80 % given #500 (F,wt=89): 4786 -hBOOL(hAPP(hAPP(c_Product__Type_Ointernal__split(A,B,C),c_Product__Type_Ointernal__split(D,E,F)),hAPP(hAPP(c_Product__Type_OPair(A,B),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),hAPP(hAPP(c_Product__Type_Ointernal__split(V6,V7,V8),c_Product__Type_OPair(D,E)),hAPP(hAPP(c_Product__Type_OPair(V6,V7),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V9),V9)),f9(v_b____,v_a____)))))). [para(578(a,2),4221(a,1))].
% 49.94/7.80
% 49.94/7.80 % given #1000 (W,wt=25): 17221 c_Predicate_ORangeP(A,B,c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),f9(v_b____,v_a____)). [resolve(15858,b,740,a)].
% 49.94/7.80
% 49.94/7.80 % given #1500 (F,wt=70): 21705 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_List_Osplice(A,c_List_Osplice(B,c_List_Olist_ONil(B),c_COMBI(C)),c_List_Olist_ONil(A)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),D)))),c_Arrow__Order__Mirabelle_OLin)). [para(21567(a,2),12735(a,1,1,2,1,2))].
% 49.94/7.80
% 49.94/7.80 % given #2000 (T,wt=19): 32589 A = B | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A) | A != C | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B). [resolve(1189,b,708,c),unit_del(c,732)].
% 49.94/7.80
% 49.94/7.80 % SZS status Theorem for theBenchmark
% 49.94/7.80
% 49.94/7.80 % Proof 1 at 6.06 (+ 1.09) seconds.
% 49.94/7.80 % Length of proof is 9.
% 49.94/7.80 % Level of proof is 4.
% 49.94/7.80 % Maximum clause weight is 443.000.
% 49.94/7.80 % Given clauses 2007.
% 49.94/7.80
% 49.94/7.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------