%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ITP001+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 : Thu Sep 24 08:45:18 AM UTC 2026
% Result : Theorem 0.10s 6.38s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ),
file('theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ),
file('theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
file('theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0),
file('theBenchmark.p',reserved_2Eho_2Ei__thm) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0),
file('theBenchmark.p',reserved_2Eho_2Ek__thm) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))),
file('theBenchmark.p',reserved_2Eho_2Es__thm) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ),
file('theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V1_2E0))
| p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ),
file('theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ),
file('theBenchmark.p',reserved_2Elogic_2E_7E) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ),
file('theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ),
file('theBenchmark.p',reserved_2Elogic_2E_3D) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ),
file('theBenchmark.p',reserved_2Equant_2E_21) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ),
file('theBenchmark.p',reserved_2Equant_2E_3F) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X1_2E0))
& p(s(tyop_2Emin_2Ebool,X0_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ),
file('theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X1_2E0))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ),
file('theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ),
file('theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ),
file('theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ),
file('theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
fof(thm_2Ebool_2ET__DEF,axiom,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
<=> ! [V0x_2E0] : s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) ),
file('theBenchmark.p',thm_2Ebool_2ET__DEF) ).
fof(thm_2Ebool_2ETRUTH,conjecture,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('theBenchmark.p',thm_2Ebool_2ETRUTH) ).
fof(f_1_1,plain,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0)
| ? [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) != s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) ),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eeq__ext]) ).
fof(f_1_2,plain,
! [U_4,U_3,U_2,U_1] :
( s(tyop_2Emin_2Efun(U_4,U_3),U_2) = s(tyop_2Emin_2Efun(U_4,U_3),U_1)
| ? [U_0] : s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_2),s(U_4,U_0))) != s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_1),s(U_4,U_0))) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_4,U_3,U_2,U_1] :
( s(tyop_2Emin_2Efun(U_4,U_3),U_2) = s(tyop_2Emin_2Efun(U_4,U_3),U_1)
| s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_2),s(U_4,sK1(U_4,U_3,U_2,U_1)))) != s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_1),s(U_4,sK1(U_4,U_3,U_2,U_1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_4,U_3,U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( s(tyop_2Emin_2Efun(U_4,U_3),U_2) = s(tyop_2Emin_2Efun(U_4,U_3),U_1)
| s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_2),s(U_4,sK1(U_4,U_3,U_2,U_1)))) != s(U_3,app_2E2(s(tyop_2Emin_2Efun(U_4,U_3),U_1),s(U_4,sK1(U_4,U_3,U_2,U_1)))) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) )
| ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext]) ).
fof(f_2_2,plain,
! [U_6,U_5] :
( s(tyop_2Emin_2Ebool,U_6) = s(tyop_2Emin_2Ebool,U_5)
| ( ~ p(s(tyop_2Emin_2Ebool,U_6))
& p(s(tyop_2Emin_2Ebool,U_5)) )
| ( ~ p(s(tyop_2Emin_2Ebool,U_5))
& p(s(tyop_2Emin_2Ebool,U_6)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( p(s(tyop_2Emin_2Ebool,U_5))
| p(s(tyop_2Emin_2Ebool,U_6))
| s(tyop_2Emin_2Ebool,U_6) = s(tyop_2Emin_2Ebool,U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_6))
| p(s(tyop_2Emin_2Ebool,U_6))
| s(tyop_2Emin_2Ebool,U_6) = s(tyop_2Emin_2Ebool,U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_5,plain,
( p(s(tyop_2Emin_2Ebool,U_5))
| ~ p(s(tyop_2Emin_2Ebool,U_5))
| s(tyop_2Emin_2Ebool,U_6) = s(tyop_2Emin_2Ebool,U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_6,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_6))
| ~ p(s(tyop_2Emin_2Ebool,U_5))
| s(tyop_2Emin_2Ebool,U_6) = s(tyop_2Emin_2Ebool,U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Etruth]) ).
cnf(f_3_2,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
cnf(f_4_2,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
fof(f_5_2,plain,
! [U_7] :
( s(tyop_2Emin_2Ebool,U_7) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,U_7) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( s(tyop_2Emin_2Ebool,U_7) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,U_7) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Ei__thm]) ).
fof(f_6_2,plain,
! [U_9,U_8] : s(U_9,app_2E2(s(tyop_2Emin_2Efun(U_9,U_9),combin_i_2E0),s(U_9,U_8))) = s(U_9,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
s(U_9,app_2E2(s(tyop_2Emin_2Efun(U_9,U_9),combin_i_2E0),s(U_9,U_8))) = s(U_9,U_8),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Ek__thm]) ).
fof(f_7_2,plain,
! [U_13,U_12,U_11,U_10] : s(U_13,app_2E2(s(tyop_2Emin_2Efun(U_12,U_13),app_2E2(s(tyop_2Emin_2Efun(U_13,tyop_2Emin_2Efun(U_12,U_13)),combin_k_2E0),s(U_13,U_11))),s(U_12,U_10))) = s(U_13,U_11),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
s(U_13,app_2E2(s(tyop_2Emin_2Efun(U_12,U_13),app_2E2(s(tyop_2Emin_2Efun(U_13,tyop_2Emin_2Efun(U_12,U_13)),combin_k_2E0),s(U_13,U_11))),s(U_12,U_10))) = s(U_13,U_11),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))),
inference(fof_nnf,[status(thm)],[reserved_2Eho_2Es__thm]) ).
fof(f_8_2,plain,
! [U_19,U_18,U_17,U_16,U_15,U_14] : s(U_17,app_2E2(s(tyop_2Emin_2Efun(U_19,U_17),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,U_18),tyop_2Emin_2Efun(U_19,U_17)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,U_18),tyop_2Emin_2Efun(U_19,U_17))),combin_s_2E0),s(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),U_16))),s(tyop_2Emin_2Efun(U_19,U_18),U_15))),s(U_19,U_14))) = s(U_17,app_2E2(s(tyop_2Emin_2Efun(U_18,U_17),app_2E2(s(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),U_16),s(U_19,U_14))),s(U_18,app_2E2(s(tyop_2Emin_2Efun(U_19,U_18),U_15),s(U_19,U_14))))),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
s(U_17,app_2E2(s(tyop_2Emin_2Efun(U_19,U_17),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,U_18),tyop_2Emin_2Efun(U_19,U_17)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_19,U_18),tyop_2Emin_2Efun(U_19,U_17))),combin_s_2E0),s(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),U_16))),s(tyop_2Emin_2Efun(U_19,U_18),U_15))),s(U_19,U_14))) = s(U_17,app_2E2(s(tyop_2Emin_2Efun(U_18,U_17),app_2E2(s(tyop_2Emin_2Efun(U_19,tyop_2Emin_2Efun(U_18,U_17)),U_16),s(U_19,U_14))),s(U_18,app_2E2(s(tyop_2Emin_2Efun(U_19,U_18),U_15),s(U_19,U_14))))),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) )
& ( ( p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Elogic_2E_2F_5C]) ).
fof(f_9_2,plain,
! [U_21,U_20] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_21),s(tyop_2Emin_2Ebool,U_20))))
| ~ p(s(tyop_2Emin_2Ebool,U_20))
| ~ p(s(tyop_2Emin_2Ebool,U_21)) )
& ( ( p(s(tyop_2Emin_2Ebool,U_20))
& p(s(tyop_2Emin_2Ebool,U_21)) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_21),s(tyop_2Emin_2Ebool,U_20)))) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_25,U_23] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_25),s(tyop_2Emin_2Ebool,U_23))))
| ~ p(s(tyop_2Emin_2Ebool,U_23))
| ~ p(s(tyop_2Emin_2Ebool,U_25)) )
& ! [U_24,U_22] :
( ( p(s(tyop_2Emin_2Ebool,U_22))
& p(s(tyop_2Emin_2Ebool,U_24)) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_24),s(tyop_2Emin_2Ebool,U_22)))) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( p(s(tyop_2Emin_2Ebool,U_24))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_24),s(tyop_2Emin_2Ebool,U_22)))) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( p(s(tyop_2Emin_2Ebool,U_22))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_24),s(tyop_2Emin_2Ebool,U_22)))) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,U_25),s(tyop_2Emin_2Ebool,U_23))))
| ~ p(s(tyop_2Emin_2Ebool,U_23))
| ~ p(s(tyop_2Emin_2Ebool,U_25)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
| ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
& ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) )
& ( p(s(tyop_2Emin_2Ebool,V1_2E0))
| p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Elogic_2E_5C_2F]) ).
fof(f_10_2,plain,
! [U_27,U_26] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_27),s(tyop_2Emin_2Ebool,U_26))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_26))
& ~ p(s(tyop_2Emin_2Ebool,U_27)) ) )
& ( p(s(tyop_2Emin_2Ebool,U_26))
| p(s(tyop_2Emin_2Ebool,U_27))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_27),s(tyop_2Emin_2Ebool,U_26)))) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_31,U_29] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_31),s(tyop_2Emin_2Ebool,U_29))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_29))
& ~ p(s(tyop_2Emin_2Ebool,U_31)) ) )
& ! [U_30,U_28] :
( p(s(tyop_2Emin_2Ebool,U_28))
| p(s(tyop_2Emin_2Ebool,U_30))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_30),s(tyop_2Emin_2Ebool,U_28)))) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( p(s(tyop_2Emin_2Ebool,U_28))
| p(s(tyop_2Emin_2Ebool,U_30))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_30),s(tyop_2Emin_2Ebool,U_28)))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_31))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_31),s(tyop_2Emin_2Ebool,U_29)))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_29))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,U_31),s(tyop_2Emin_2Ebool,U_29)))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
| p(s(tyop_2Emin_2Ebool,V0_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Elogic_2E_7E]) ).
fof(f_11_2,plain,
! [U_32] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_32))))
| p(s(tyop_2Emin_2Ebool,U_32)) )
& ( ~ p(s(tyop_2Emin_2Ebool,U_32))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_32)))) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_34] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_34))))
| p(s(tyop_2Emin_2Ebool,U_34)) )
& ! [U_33] :
( ~ p(s(tyop_2Emin_2Ebool,U_33))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_33)))) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_33))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_33)))) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,U_34))))
| p(s(tyop_2Emin_2Ebool,U_34)) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
| ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) ) )
& ( p(s(tyop_2Emin_2Ebool,V1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Elogic_2E_3D_3D_3E]) ).
fof(f_12_2,plain,
! [U_36,U_35] :
( ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_36),s(tyop_2Emin_2Ebool,U_35))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_35))
& p(s(tyop_2Emin_2Ebool,U_36)) ) )
& ( p(s(tyop_2Emin_2Ebool,U_35))
| ~ p(s(tyop_2Emin_2Ebool,U_36))
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_36),s(tyop_2Emin_2Ebool,U_35)))) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_40,U_38] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_40),s(tyop_2Emin_2Ebool,U_38))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_38))
& p(s(tyop_2Emin_2Ebool,U_40)) ) )
& ! [U_39,U_37] :
( p(s(tyop_2Emin_2Ebool,U_37))
| ~ p(s(tyop_2Emin_2Ebool,U_39))
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_39),s(tyop_2Emin_2Ebool,U_37)))) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( p(s(tyop_2Emin_2Ebool,U_37))
| ~ p(s(tyop_2Emin_2Ebool,U_39))
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_39),s(tyop_2Emin_2Ebool,U_37)))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( p(s(tyop_2Emin_2Ebool,U_40))
| p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_40),s(tyop_2Emin_2Ebool,U_38)))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_38))
| p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,U_40),s(tyop_2Emin_2Ebool,U_38)))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A_27a,V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
| s(A_27a,V0_2E0) != s(A_27a,V1_2E0) )
& ( s(A_27a,V0_2E0) = s(A_27a,V1_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Elogic_2E_3D]) ).
fof(f_13_2,plain,
! [U_43,U_42,U_41] :
( ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_43,U_42),s(U_43,U_41))))
| s(U_43,U_42) != s(U_43,U_41) )
& ( s(U_43,U_42) = s(U_43,U_41)
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_43,U_42),s(U_43,U_41)))) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_49,U_47,U_45] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_49,U_47),s(U_49,U_45))))
| s(U_49,U_47) != s(U_49,U_45) )
& ! [U_48,U_46,U_44] :
( s(U_48,U_46) = s(U_48,U_44)
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_48,U_46),s(U_48,U_44)))) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( s(U_48,U_46) = s(U_48,U_44)
| ~ p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_48,U_46),s(U_48,U_44)))) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(U_49,U_47),s(U_49,U_45))))
| s(U_49,U_47) != s(U_49,U_45) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A_27a,V0f_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
| ? [V1x_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) )
& ( ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Equant_2E_21]) ).
fof(f_14_2,plain,
! [U_53,U_52] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_53,tyop_2Emin_2Ebool),U_52))))
| ? [U_51] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_53,tyop_2Emin_2Ebool),U_52),s(U_53,U_51)))) )
& ( ! [U_50] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_53,tyop_2Emin_2Ebool),U_52),s(U_53,U_50))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_53,tyop_2Emin_2Ebool),U_52)))) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_57,U_55] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55))))
| ? [U_51] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55),s(U_57,U_51)))) )
& ! [U_56,U_54] :
( ! [U_50] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54),s(U_56,U_50))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54)))) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_57,U_55] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55),s(U_57,sK2(U_57,U_55))))) )
& ! [U_56,U_54] :
( ! [U_50] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54),s(U_56,U_50))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_51,sK2(U_57,U_55))],[f_14_3]) ).
cnf(f_14_5,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54),s(U_56,U_50))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_56,tyop_2Emin_2Ebool),U_54)))) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_57,tyop_2Emin_2Ebool),U_55),s(U_57,sK2(U_57,U_55))))) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [A_27a,V0f_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
| ! [V1x_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) )
& ( ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) ) ),
inference(fof_nnf,[status(thm)],[reserved_2Equant_2E_3F]) ).
fof(f_15_2,plain,
! [U_61,U_60] :
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_61,tyop_2Emin_2Ebool),U_60))))
| ! [U_59] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_61,tyop_2Emin_2Ebool),U_60),s(U_61,U_59)))) )
& ( ? [U_58] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_61,tyop_2Emin_2Ebool),U_60),s(U_61,U_58))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_61,tyop_2Emin_2Ebool),U_60)))) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_65,U_63] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63))))
| ! [U_59] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63),s(U_65,U_59)))) )
& ! [U_64,U_62] :
( ? [U_58] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62),s(U_64,U_58))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62)))) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_65,U_63] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63))))
| ! [U_59] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63),s(U_65,U_59)))) )
& ! [U_64,U_62] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62),s(U_64,sK3(U_64,U_62)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_58,sK3(U_64,U_62))],[f_15_3]) ).
cnf(f_15_5,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62),s(U_64,sK3(U_64,U_62)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_64,tyop_2Emin_2Ebool),U_62)))) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_65,tyop_2Emin_2Ebool),U_63),s(U_65,U_59)))) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [X0_2E0,X1_2E0] :
( ( ( p(s(tyop_2Emin_2Ebool,X1_2E0))
& p(s(tyop_2Emin_2Ebool,X0_2E0)) )
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(fof_nnf,[status(thm)],[arityeq2_2Ec_2Ebool_2E_2F_5C_2E2]) ).
fof(f_16_2,plain,
! [U_67,U_66] :
( ( ( p(s(tyop_2Emin_2Ebool,U_66))
& p(s(tyop_2Emin_2Ebool,U_67)) )
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_67))),s(tyop_2Emin_2Ebool,U_66)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_67))),s(tyop_2Emin_2Ebool,U_66))))
| ~ p(s(tyop_2Emin_2Ebool,U_66))
| ~ p(s(tyop_2Emin_2Ebool,U_67)) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_71,U_69] :
( ( p(s(tyop_2Emin_2Ebool,U_69))
& p(s(tyop_2Emin_2Ebool,U_71)) )
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_71))),s(tyop_2Emin_2Ebool,U_69)))) )
& ! [U_70,U_68] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_70))),s(tyop_2Emin_2Ebool,U_68))))
| ~ p(s(tyop_2Emin_2Ebool,U_68))
| ~ p(s(tyop_2Emin_2Ebool,U_70)) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_70))),s(tyop_2Emin_2Ebool,U_68))))
| ~ p(s(tyop_2Emin_2Ebool,U_68))
| ~ p(s(tyop_2Emin_2Ebool,U_70)) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( p(s(tyop_2Emin_2Ebool,U_71))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_71))),s(tyop_2Emin_2Ebool,U_69)))) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( p(s(tyop_2Emin_2Ebool,U_69))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,U_71))),s(tyop_2Emin_2Ebool,U_69)))) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X1_2E0))
| p(s(tyop_2Emin_2Ebool,X0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))))
| ( ~ p(s(tyop_2Emin_2Ebool,X1_2E0))
& ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ) ),
inference(fof_nnf,[status(thm)],[arityeq2_2Ec_2Ebool_2E_5C_2F_2E2]) ).
fof(f_17_2,plain,
! [U_73,U_72] :
( ( p(s(tyop_2Emin_2Ebool,U_72))
| p(s(tyop_2Emin_2Ebool,U_73))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_73))),s(tyop_2Emin_2Ebool,U_72)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_73))),s(tyop_2Emin_2Ebool,U_72))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_72))
& ~ p(s(tyop_2Emin_2Ebool,U_73)) ) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_77,U_75] :
( p(s(tyop_2Emin_2Ebool,U_75))
| p(s(tyop_2Emin_2Ebool,U_77))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_77))),s(tyop_2Emin_2Ebool,U_75)))) )
& ! [U_76,U_74] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_76))),s(tyop_2Emin_2Ebool,U_74))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_74))
& ~ p(s(tyop_2Emin_2Ebool,U_76)) ) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_76))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_76))),s(tyop_2Emin_2Ebool,U_74)))) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_74))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_76))),s(tyop_2Emin_2Ebool,U_74)))) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( p(s(tyop_2Emin_2Ebool,U_75))
| p(s(tyop_2Emin_2Ebool,U_77))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,U_77))),s(tyop_2Emin_2Ebool,U_75)))) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(fof_nnf,[status(thm)],[arityeq1_2Ec_2Ebool_2E_7E_2E1]) ).
fof(f_18_2,plain,
! [U_78] :
( ( ~ p(s(tyop_2Emin_2Ebool,U_78))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_78)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_78))))
| p(s(tyop_2Emin_2Ebool,U_78)) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_80] :
( ~ p(s(tyop_2Emin_2Ebool,U_80))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_80)))) )
& ! [U_79] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_79))))
| p(s(tyop_2Emin_2Ebool,U_79)) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_79))))
| p(s(tyop_2Emin_2Ebool,U_79)) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_80))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,U_80)))) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))))
| ( ~ p(s(tyop_2Emin_2Ebool,X1_2E0))
& p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ) ),
inference(fof_nnf,[status(thm)],[arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2]) ).
fof(f_19_2,plain,
! [U_82,U_81] :
( ( p(s(tyop_2Emin_2Ebool,U_81))
| ~ p(s(tyop_2Emin_2Ebool,U_82))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_82))),s(tyop_2Emin_2Ebool,U_81)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_82))),s(tyop_2Emin_2Ebool,U_81))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_81))
& p(s(tyop_2Emin_2Ebool,U_82)) ) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_86,U_84] :
( p(s(tyop_2Emin_2Ebool,U_84))
| ~ p(s(tyop_2Emin_2Ebool,U_86))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_86))),s(tyop_2Emin_2Ebool,U_84)))) )
& ! [U_85,U_83] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_85))),s(tyop_2Emin_2Ebool,U_83))))
| ( ~ p(s(tyop_2Emin_2Ebool,U_83))
& p(s(tyop_2Emin_2Ebool,U_85)) ) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( p(s(tyop_2Emin_2Ebool,U_85))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_85))),s(tyop_2Emin_2Ebool,U_83)))) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( ~ p(s(tyop_2Emin_2Ebool,U_83))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_85))),s(tyop_2Emin_2Ebool,U_83)))) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( p(s(tyop_2Emin_2Ebool,U_84))
| ~ p(s(tyop_2Emin_2Ebool,U_86))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,U_86))),s(tyop_2Emin_2Ebool,U_84)))) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A_27a,X0_2E0,X1_2E0] :
( ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))))
| s(A_27a,X0_2E0) != s(A_27a,X1_2E0) ) ),
inference(fof_nnf,[status(thm)],[arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a]) ).
fof(f_20_2,plain,
! [U_89,U_88,U_87] :
( ( s(U_89,U_88) = s(U_89,U_87)
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_89,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_89,tyop_2Emin_2Efun(U_89,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_89,U_88))),s(U_89,U_87)))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_89,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_89,tyop_2Emin_2Efun(U_89,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_89,U_88))),s(U_89,U_87))))
| s(U_89,U_88) != s(U_89,U_87) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_95,U_93,U_91] :
( s(U_95,U_93) = s(U_95,U_91)
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_95,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_95,tyop_2Emin_2Efun(U_95,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_95,U_93))),s(U_95,U_91)))) )
& ! [U_94,U_92,U_90] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_94,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_94,tyop_2Emin_2Efun(U_94,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_94,U_92))),s(U_94,U_90))))
| s(U_94,U_92) != s(U_94,U_90) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_94,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_94,tyop_2Emin_2Efun(U_94,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_94,U_92))),s(U_94,U_90))))
| s(U_94,U_92) != s(U_94,U_90) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( s(U_95,U_93) = s(U_95,U_91)
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(U_95,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(U_95,tyop_2Emin_2Efun(U_95,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(U_95,U_93))),s(U_95,U_91)))) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),
inference(fof_nnf,[status(thm)],[arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a]) ).
fof(f_21_2,plain,
! [U_97,U_96] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),U_96))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),U_96))),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),U_96))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(U_97,tyop_2Emin_2Ebool),U_96))),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),
inference(fof_nnf,[status(thm)],[arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a]) ).
fof(f_22_2,plain,
! [U_99,U_98] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),U_98))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),U_98))),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),U_98))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(U_99,tyop_2Emin_2Ebool),U_98))),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ? [V0x_2E0] : s(tyop_2Emin_2Ebool,V0x_2E0) != s(tyop_2Emin_2Ebool,V0x_2E0) )
& ( ! [V0x_2E0] : s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ),
inference(fof_nnf,[status(thm)],[thm_2Ebool_2ET__DEF]) ).
fof(f_23_2,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ? [U_101] : s(tyop_2Emin_2Ebool,U_101) != s(tyop_2Emin_2Ebool,U_101) )
& ( ! [U_100] : s(tyop_2Emin_2Ebool,U_100) = s(tyop_2Emin_2Ebool,U_100)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Emin_2Ebool,sK4) != s(tyop_2Emin_2Ebool,sK4) )
& ( ! [U_100] : s(tyop_2Emin_2Ebool,U_100) = s(tyop_2Emin_2Ebool,U_100)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_101,sK4)],[f_23_2]) ).
cnf(f_23_4,plain,
( s(tyop_2Emin_2Ebool,U_100) = s(tyop_2Emin_2Ebool,U_100)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Emin_2Ebool,sK4) != s(tyop_2Emin_2Ebool,sK4) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(negate,[status(cth)],[thm_2Ebool_2ETRUTH]) ).
fof(f_24_2,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_2_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_4]) ).
cnf(f_2_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( tyop_2Emin_2Efun(Eq_x_0,Eq_x_1) = tyop_2Emin_2Efun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( s(Eq_x_0,Eq_x_1) = s(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( app_2E2(Eq_x_0,Eq_x_1) = app_2E2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_2Ebool_2E_2F_5C_2E2(Eq_x_0,Eq_x_1) = c_2Ebool_2E_2F_5C_2E2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_2Ebool_2E_5C_2F_2E2(Eq_x_0,Eq_x_1) = c_2Ebool_2E_5C_2F_2E2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_2Ebool_2E_7E_2E1(Eq_x_0) = c_2Ebool_2E_7E_2E1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_2Emin_2E_3D_3D_3E_2E2(Eq_x_0,Eq_x_1) = c_2Emin_2E_3D_3D_3E_2E2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_2Emin_2E_3D_2E2(Eq_x_0,Eq_x_1) = c_2Emin_2E_3D_2E2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_2Ebool_2E_21_2E1(Eq_x_0) = c_2Ebool_2E_21_2E1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_2Ebool_2E_3F_2E1(Eq_x_0) = c_2Ebool_2E_3F_2E1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( p(Eq_y_0)
| ~ p(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/6.31 % Computer : n003.cluster.edu
% 0.10/6.31 % Model : x86_64 x86_64
% 0.10/6.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.31 % Memory : 8046.5625MB
% 0.10/6.31 % OS : Linux 6.8.0-71-generic
% 0.10/6.31 % CPULimit : 300
% 0.10/6.31 % WCLimit : 300
% 0.10/6.31 % DateTime : Sat Sep 19 11:19:04 UTC 2026
% 0.10/6.31 % CPUTime :
% 0.10/6.38 % SZS status Theorem for theBenchmark
% 0.10/6.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------