%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT136+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 : 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 08:28:32 AM UTC 2026
% Result : Theorem 44.72s 7.16s
% Output : CNFRefutation 44.72s
% 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 : 5 ( 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 : 40 ( 18 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__Cons__self,axiom,
! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
file('theBenchmark.p',fact_not__Cons__self) ).
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__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_712,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C,
inference(clausify,[status(thm)],[fact_not__Cons__self]) ).
cnf(c_1232,plain,
hAPP(c_COMBI(A),B) = B,
inference(clausify,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_1236,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_19296,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_1236,c_712]) ).
cnf(c_19482,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),c_COMBI(E)),F) = hAPP(hAPP(D,F),F),
inference(paramod,[status(thm)],[c_1232,c_1236]) ).
cnf(c_19484,plain,
hAPP(E,F) != hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F),
inference(copy,[status(thm)],[c_19296]) ).
cnf(c_19483,plain,
$false,
inference(resolve,[status(thm)],[c_19482,c_19484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT136+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 06:34:50 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1032841 was started by sandbox2 on n002,
% 0.18/0.45 % Sat Sep 26 06:34:50 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.42/0.66
% 0.42/0.66 % From the command line: assign(max_seconds, 300).
% 0.42/0.66
% 0.42/0.66 % SInE: 429 to sos, 93 to usable, of 522 axioms (tolerance 2.00, depth 0 fixpoint).
% 44.72/7.16
% 44.72/7.16 % given #500 (F,wt=58): 3891 -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Product__Type_Oprod_Oprod__rec(C,D,E,c_Product__Type_Ocurry(F,V6,V7,hAPP(c_Product__Type_Ointernal__split(F,V6,V8),c_List_Oappend(V9))),hAPP(hAPP(c_Product__Type_OPair(C,D),c_List_Olist_ONil(V9)),B))). [para(810(a,1),2718(a,2))].
% 44.72/7.16
% 44.72/7.16 % given #1000 (W,wt=26): 6508 c_Predicate_ORangeP(A,B,hAPP(c_List_Oappend(C),c_List_Olist_ONil(C)),c_List_Olists(D,E)). [resolve(5907,a,923,a)].
% 44.72/7.16
% 44.72/7.16 % given #1500 (F,wt=39): 11652 c_List_OdropWhile(A,c_List_Olistsp(B,C),D) != hAPP(hAPP(c_List_Olist_OCons(A),c_List_Olist_ONil(B)),E). [resolve(1068,b,951,a)].
% 44.72/7.16
% 44.72/7.16 % given #2000 (T,wt=27): 16896 -c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,A,B) | c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,A),B) | c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,C) = A. [resolve(1192,b,16708,b),unit_del(a,1230)].
% 44.72/7.16
% 44.72/7.16 % SZS status Theorem for theBenchmark
% 44.72/7.16
% 44.72/7.16 % Proof 1 at 5.15 (+ 1.16) seconds.
% 44.72/7.16 % Length of proof is 9.
% 44.72/7.16 % Level of proof is 3.
% 44.72/7.16 % Maximum clause weight is 463.000.
% 44.72/7.16 % Given clauses 2107.
% 44.72/7.16
% 44.72/7.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------