%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT102+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 : n007.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 08:28:30 AM UTC 2026
% Result : Theorem 0.17s 5.89s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-5 aty)
% Number of variables : 65 ( 31 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(fact_append__Nil,axiom,
! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
file('theBenchmark.p',fact_append__Nil) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
cnf(c_719,plain,
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_733,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),C) != C,
inference(clausify,[status(thm)],[fact_not__Cons__self]) ).
cnf(c_772,plain,
hAPP(hAPP(c_List_Oappend(A),c_List_Olist_ONil(A)),B) = B,
inference(clausify,[status(thm)],[fact_append__Nil]) ).
cnf(c_1367,plain,
hAPP(c_COMBS(A,B,C,c_List_Olist_OCons(D),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_719,c_733]) ).
cnf(c_1406,plain,
hAPP(c_COMBS(A,B,C,c_List_Olist_OCons(D),c_COMBS(E,F,V6,V7,V8)),V9) != hAPP(hAPP(V7,V9),hAPP(V8,V9)),
inference(paramod,[status(thm)],[c_719,c_1367]) ).
cnf(c_1614,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(c_COMBS(C,D,E,F,V6),B)) != hAPP(hAPP(F,B),hAPP(V6,B)),
inference(paramod,[status(thm)],[c_719,c_1406]) ).
cnf(c_1633,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(c_COMBS(C,D,E,hAPP(c_List_Oappend(F),c_List_Olist_ONil(F)),V6),B)) != hAPP(B,hAPP(V6,B)),
inference(paramod,[status(thm)],[c_772,c_1614]) ).
cnf(c_1760,plain,
hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(c_COMBS(C,D,E,hAPP(c_List_Oappend(F),c_List_Olist_ONil(F)),hAPP(c_List_Oappend(V6),c_List_Olist_ONil(V6))),B)) != hAPP(B,B),
inference(paramod,[status(thm)],[c_772,c_1633]) ).
cnf(c_1762,plain,
hAPP(hAPP(D,F),hAPP(E,F)) = hAPP(c_COMBS(A,B,C,D,E),F),
inference(copy,[status(thm)],[c_719]) ).
cnf(c_1761,plain,
$false,
inference(resolve,[status(thm)],[c_1760,c_1762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT102+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.39 % Computer : n007.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Sat Sep 26 06:25:47 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.39 % Process 2998428 was started by sandbox on n007,
% 0.13/5.39 % Sat Sep 26 06:25:47 2026
% 0.13/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.56
% 0.17/5.56 % From the command line: assign(max_seconds, 300).
% 0.17/5.56
% 0.17/5.56 % SInE: 422 to sos, 152 to usable, of 574 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.17/5.89
% 0.17/5.89 % SZS status Theorem for theBenchmark
% 0.17/5.89
% 0.17/5.89 % Proof 1 at 0.22 (+ 0.07) seconds.
% 0.17/5.89 % Length of proof is 12.
% 0.17/5.89 % Level of proof is 7.
% 0.17/5.89 % Maximum clause weight is 25.000.
% 0.17/5.89 % Given clauses 80.
% 0.17/5.89
% 0.17/5.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------