%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT126+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 : n012.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 23.09s 8.98s
% Output : CNFRefutation 23.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 28 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 5 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 6 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(fact_PiE,axiom,
! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_PiE) ).
fof(help_c__COMBK__1,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P,
file('theBenchmark.p',help_c__COMBK__1) ).
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(fact__096Q_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',fact__096Q_A_058_AProf_096) ).
cnf(c_706,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[fact__096Q_A_058_AProf_096]) ).
cnf(c_714,plain,
( hBOOL(hAPP(C,B))
| ~ hBOOL(hAPP(hAPP(c_member(A),B),C)) ),
inference(clausify,[status(thm)],[fact_mem__def]) ).
cnf(c_715,plain,
( ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(hAPP(c_member(A),B),C)) ),
inference(clausify,[status(thm)],[fact_mem__def]) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('theBenchmark.p',fact_assms_I1_J) ).
cnf(c_755,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(clausify,[status(thm)],[fact_assms_I1_J]) ).
cnf(c_772,plain,
( ~ hBOOL(hAPP(hAPP(c_member(A),F),D))
| hBOOL(hAPP(hAPP(c_member(B),hAPP(C,F)),hAPP(E,F)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(A,B)),C),c_FuncSet_OPi(A,B,D,E))) ),
inference(clausify,[status(thm)],[fact_PiE]) ).
cnf(c_1261,plain,
hAPP(c_COMBK(A,B,C),D) = C,
inference(clausify,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_1270,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_1350,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)),
inference(resolve,[status(thm)],[c_706,c_714]) ).
cnf(c_1369,plain,
hBOOL(hAPP(hAPP(c_member(A),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(resolve,[status(thm)],[c_715,c_1350]) ).
cnf(c_6269,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,A)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),A))) ),
inference(resolve,[status(thm)],[c_772,c_755]) ).
cnf(c_6270,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),v_Q____))),
inference(resolve,[status(thm)],[c_6269,c_1369]) ).
cnf(c_6271,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(paramod,[status(thm)],[c_1261,c_6270]) ).
cnf(c_6268,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1270,c_6271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT126+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.52 % Computer : n012.cluster.edu
% 0.05/5.52 % Model : x86_64 x86_64
% 0.05/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.52 % Memory : 8046.5625MB
% 0.05/5.52 % OS : Linux 6.8.0-71-generic
% 0.05/5.52 % CPULimit : 300
% 0.05/5.52 % WCLimit : 300
% 0.05/5.52 % DateTime : Sat Sep 26 06:30:45 UTC 2026
% 0.05/5.53 % CPUTime :
% 0.05/5.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/5.53 % Process 4091887 was started by sandbox on n012,
% 0.05/5.53 % Sat Sep 26 06:30:45 2026
% 0.05/5.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/5.59
% 0.05/5.59 % From the command line: assign(max_seconds, 300).
% 0.05/5.59
% 0.05/5.59 % SInE: 400 to sos, 124 to usable, of 524 axioms (tolerance 2.00, depth 0 fixpoint).
% 23.09/8.98
% 23.09/8.98 % SZS status Theorem for theBenchmark
% 23.09/8.98
% 23.09/8.98 % Proof 1 at 2.86 (+ 0.43) seconds.
% 23.09/8.98 % Length of proof is 14.
% 23.09/8.98 % Level of proof is 4.
% 23.09/8.98 % Maximum clause weight is 181.000.
% 23.09/8.98 % Given clauses 468.
% 23.09/8.98
% 23.09/8.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------