%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT139+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 : 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 08:28:33 AM UTC 2026
% Result : Theorem 54.40s 8.56s
% Output : CNFRefutation 54.40s
% 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_699,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C,
inference(clausify,[status(thm)],[fact_not__Cons__self2]) ).
cnf(c_1231,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_1232,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_20119,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_List_Olist_OCons(D)),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_1232,c_699]) ).
cnf(c_24144,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_1231,c_20119]) ).
cnf(c_24146,plain,
hAPP(hAPP(D,F),hAPP(E,F)) = hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F),
inference(copy,[status(thm)],[c_1232]) ).
cnf(c_24145,plain,
$false,
inference(resolve,[status(thm)],[c_24144,c_24146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT139+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 06:33:53 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2238176 was started by sandbox on n003,
% 0.18/0.45 % Sat Sep 26 06:33:53 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.41/0.64
% 0.41/0.64 % From the command line: assign(max_seconds, 300).
% 0.41/0.64
% 0.41/0.64 % SInE: 436 to sos, 86 to usable, of 522 axioms (tolerance 2.00, depth 0 fixpoint).
% 54.40/8.56
% 54.40/8.56 % given #500 (F,wt=68): 1476 -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),hAPP(hAPP(B,C),D),hAPP(hAPP(c_Product__Type_Ointernal__split(E,F,V6),B),hAPP(hAPP(c_Product__Type_OPair(E,F),C),D))). [resolve(1205,b,557,a)].
% 54.40/8.56
% 54.40/8.56 % given #1000 (W,wt=26): 6942 c_Predicate_ODomainP(A,B,c_List_Oappend(C),hAPP(c_List_Olistsp(D,E),c_List_Olist_ONil(D))). [resolve(939,a,3375,a)].
% 54.40/8.56
% 54.40/8.56 % given #1500 (F,wt=39): 12875 c_List_OdropWhile(A,hAPP(c_member(B),v_P_H____),C) != hAPP(hAPP(c_List_Olist_OCons(A),c_Arrow__Order__Mirabelle_OProf),D). [resolve(1065,b,1555,a)].
% 54.40/8.56
% 54.40/8.56 % given #2000 (T,wt=26): 17409 -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool,D,C)). [resolve(1163,b,17270,a)].
% 54.40/8.56
% 54.40/8.56 % given #2500 (F,wt=44): 21272 c_List_OdropWhile(A,c_COMBI(B),C) != hAPP(hAPP(c_List_Olist_OCons(A),hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),D). [resolve(19367,b,1319,a)].
% 54.40/8.56
% 54.40/8.56 % SZS status Theorem for theBenchmark
% 54.40/8.56
% 54.40/8.56 % Proof 1 at 6.35 (+ 1.22) seconds.
% 54.40/8.56 % Length of proof is 9.
% 54.40/8.56 % Level of proof is 4.
% 54.40/8.56 % Maximum clause weight is 563.000.
% 54.40/8.56 % Given clauses 2710.
% 54.40/8.56
% 54.40/8.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------