%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT137+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 247.03s 38.10s
% Output : CNFRefutation 247.03s
% 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__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__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_761,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C,
inference(clausify,[status(thm)],[fact_not__Cons__self2]) ).
cnf(c_1236,plain,
hAPP(c_COMBI(A),B) = B,
inference(clausify,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_1240,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_53686,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_1240,c_761]) ).
cnf(c_57130,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),c_COMBI(E)),F) = hAPP(hAPP(D,F),F),
inference(paramod,[status(thm)],[c_1236,c_1240]) ).
cnf(c_57132,plain,
hAPP(E,F) != hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F),
inference(copy,[status(thm)],[c_53686]) ).
cnf(c_57131,plain,
$false,
inference(resolve,[status(thm)],[c_57130,c_57132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT137+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n002.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 06:34:43 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 1032450 was started by sandbox on n002,
% 0.18/5.46 % Sat Sep 26 06:34:43 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/5.57
% 0.23/5.57 % From the command line: assign(max_seconds, 300).
% 0.23/5.57
% 0.23/5.57 % SInE: 391 to sos, 131 to usable, of 522 axioms (tolerance 2.00, depth 0 fixpoint).
% 247.03/38.10
% 247.03/38.10 % given #500 (F,wt=50): 3599 -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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),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(c_fequal,c_List_Osplice(V9,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V10),V10),c_List_Olist_ONil(V9)))),c_Arrow__Order__Mirabelle_OLin))))). [resolve(2304,a,1390,b)].
% 247.03/38.10
% 247.03/38.10 % given #1000 (W,wt=13): 9168 c_Predicate_ODomainP(A,B,hAPP(c_List_Oappend(C),c_List_Olist_ONil(C)),hAPP(c_fconj,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))). [resolve(9042,a,1455,a)].
% 247.03/38.10
% 247.03/38.10 % given #1500 (F,wt=33): 9654 hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Oappend(A),C),hAPP(hAPP(c_Product__Type_Ointernal__split(D,E,F),c_List_Olist_OCons(A)),hAPP(hAPP(c_Product__Type_OPair(D,E),V6),c_List_Olist_ONil(A))))) != hAPP(hAPP(c_List_Oappend(A),B),C). [para(823(a,1),9645(a,1))].
% 247.03/38.10
% 247.03/38.10 % given #2000 (T,wt=11): 22326 hBOOL(hAPP(hAPP(c_member(A),B),c_Wellfounded_Oacc(tc_Arrow__Order__Mirabelle_Oalt,c_Arrow__Order__Mirabelle_Omkbot(C,B)))). [resolve(22303,a,745,b)].
% 247.03/38.10
% 247.03/38.10 % given #2500 (F,wt=30): 17384 hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),hAPP(hAPP(c_List_Oappend(A),D),hAPP(hAPP(hAPP(c_COMBC(E,F,V6),c_List_Olist_OCons(A)),c_List_Olist_ONil(A)),V7)))) != c_List_Olist_ONil(A). [para(1239(a,2),9209(a,1,2,2,2))].
% 247.03/38.10
% 247.03/38.10 % given #3000 (T,wt=10): 33749 hBOOL(hAPP(c_Set_Oimage(A,B,C,c_Arrow__Order__Mirabelle_OProf),hAPP(C,v_P____))). [resolve(33674,a,744,a)].
% 247.03/38.10
% 247.03/38.10 % given #3500 (F,wt=30): 21302 -hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBC(A,B,C),c_COMBC(D,E,F)),c_Arrow__Order__Mirabelle_OLin),c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Relation_ORange(tc_List_Olist(V6),tc_List_Olist(V6),c_List_Olistrel(V6,c_Transitive__Closure_Ortrancl(V6,V7))))). [para(1239(a,2),21209(a,1,1))].
% 247.03/38.10
% 247.03/38.10 % given #4000 (T,wt=14): 41704 c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,A,B),C),c_List_Osplice(D,c_List_Olist_ONil(D),A)). [resolve(41672,a,2035,a)].
% 247.03/38.10
% 247.03/38.10 % given #4500 (A,wt=222): 1208 A = B | c_Nat_Osize__class_Osize(tc_List_Olist(C),A) != c_Nat_Osize__class_Osize(tc_List_Olist(C),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f79(C,B,A),c_Nat_Osize__class_Osize(tc_List_Olist(C),A)) # tptp_name(fact_list__eq__iff__nth__eq) # sine_depth(3). [clausify(352)].
% 247.03/38.10
% 247.03/38.10 % SZS status Theorem for theBenchmark
% 247.03/38.10
% 247.03/38.10 % Proof 1 at 27.11 (+ 4.91) seconds.
% 247.03/38.10 % Length of proof is 9.
% 247.03/38.10 % Level of proof is 3.
% 247.03/38.10 % Maximum clause weight is 618.000.
% 247.03/38.10 % Given clauses 4808.
% 247.03/38.10
% 247.03/38.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------