%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT083-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Thu Sep 24 02:06:54 PM UTC 2026
% Result : Unsatisfiable 102.50s 13.94s
% Output : CNFRefutation 102.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 57 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 83 ( 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f394,axiom,
! [V_P,T_a] : c_Collect(V_P,T_a) = V_P,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f416,axiom,
! [V_P,T_b,T_c,T_a,V_Q,V_R] : hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f612,axiom,
! [T_a,V_A] : c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f710,axiom,
! [V_L] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f711,axiom,
! [T_b,V_f,V_x,V_B,T_a,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f712,axiom,
! [T_a,V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f713,axiom,
! [V_S,V_x,T_a] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f715,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f716,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f717,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1369,plain,
! [X0,X1] : X0 = c_Collect(X0,X1),
inference(cnf_transformation,[status(thm)],[f394]) ).
fof(f1398,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_COMBC(X0,X1,X2,X3),X4),X5) = hAPP(hAPP(X0,X5),X4),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f1705,plain,
! [X0,X1] : c_Collect(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X1),X0) = X1,
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f1879,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(cnf_transformation,[status(thm)],[f710]) ).
fof(f1880,plain,
! [T_b,V_f,V_B,T_a,V_A] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ! [V_x] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) ),
inference(miniscoping,[status(thm)],[f711]) ).
fof(f1881,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X3)),X4),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X3,tc_bool),X0),X0,X3)))
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(X4,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f1880]) ).
fof(f1882,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ),
inference(miniscoping,[status(thm)],[f712]) ).
fof(f1883,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_in(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f1882]) ).
fof(f1884,plain,
! [V_S,V_x] :
( ! [T_a] : ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f713]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1884]) ).
fof(f1887,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[status(thm)],[f715]) ).
fof(f1888,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(cnf_transformation,[status(thm)],[f716]) ).
fof(f1889,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[status(thm)],[f717]) ).
fof(f1950,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))),
inference(resolution,[status(thm)],[f1883,f1889]) ).
fof(f1953,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ),
inference(resolution,[status(thm)],[f1879,f1885]) ).
fof(f1961,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),
inference(resolution,[status(thm)],[f1953,f1887]) ).
fof(f2377,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X5,c_COMBK(X3,tc_fun(X0,tc_bool),X4),X4,X0),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),X3)) ),
inference(resolution,[status(thm)],[f1881,f1883]) ).
fof(f2756,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F)),
inference(resolution,[status(thm)],[f1888,f1885]) ).
fof(f3485,plain,
! [X0,X1] : hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1369,f1705]) ).
fof(f3486,plain,
! [X0,X1,X2] : hAPP(hAPP(c_in(X0),X1),X2) = hAPP(X2,X1),
inference(paramodulation,[status(thm)],[f3485,f1398]) ).
fof(f3550,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(X4,c_COMBK(X0,tc_fun(X5,tc_bool),X3),X3,X5),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| hBOOL(hAPP(X0,hAPP(X1,X2))) ),
inference(backward_demodulation,[status(thm)],[f3486,f2377]) ).
fof(f3614,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(X1,hAPP(X4,X5)))
| ~ hBOOL(hAPP(X0,X5))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),X4)) ),
inference(forward_demodulation,[status(thm)],[f3486,f3550]) ).
fof(f4373,plain,
! [X0] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,X0)))
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X0)) ),
inference(resolution,[status(thm)],[f3614,f2756]) ).
fof(f4385,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),
inference(resolution,[status(thm)],[f4373,f1950]) ).
fof(f4387,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4385,f1961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT083-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 04:30:21 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.14/0.65 % Drodi V4.1.1
% 102.50/13.94 % Refutation found
% 102.50/13.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 102.50/13.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 102.70/14.09 % Elapsed time: 13.500348 seconds
% 102.70/14.09 % CPU time: 105.721844 seconds
% 102.70/14.09 % Total memory used: 682.188 MB
% 102.70/14.09 % Net memory used: 624.595 MB
%------------------------------------------------------------------------------