%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN417+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 09:10:19 AM UTC 2026
% Result : Theorem 64.77s 65.04s
% Output : Proof 65.61s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(cute,conjecture,
( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> X = Y )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> X = Y )
& X = g(f(X)) ) ),
file('theBenchmark.p',cute) ).
fof(f_1_1,negated_conjecture,
~ ( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> X = Y )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> X = Y )
& X = g(f(X)) ) ),
inference(negate,[status(cth)],[cute]) ).
fof(f_1_2,negated_conjecture,
( ( ! [X] :
( ? [Y] :
( X != Y
& Y = f(g(Y)) )
| X != f(g(X)) )
& ? [X] :
( ! [Y] :
( X = Y
| Y != g(f(Y)) )
& X = g(f(X)) ) )
| ( ! [X] :
( ? [Y] :
( X != Y
& Y = g(f(Y)) )
| X != g(f(X)) )
& ? [X] :
( ! [Y] :
( X = Y
| Y != f(g(Y)) )
& X = f(g(X)) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ! [U_7] :
( ? [U_6] :
( U_7 != U_6
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_5 = U_4
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ? [U_2] :
( U_3 != U_2
& U_2 = g(f(U_2)) )
| U_3 != g(f(U_3)) )
& ? [U_1] :
( ! [U_0] :
( U_1 = U_0
| U_0 != f(g(U_0)) )
& U_1 = f(g(U_1)) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ! [U_7] :
( ? [U_6] :
( U_7 != U_6
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_5 = U_4
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ? [U_2] :
( U_3 != U_2
& U_2 = g(f(U_2)) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( sK1 = U_0
| U_0 != f(g(U_0)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ! [U_7] :
( ? [U_6] :
( U_7 != U_6
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_5 = U_4
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ( U_3 != sK2(U_3)
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( sK1 = U_0
| U_0 != f(g(U_0)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2(U_3))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ! [U_7] :
( ? [U_6] :
( U_7 != U_6
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ! [U_4] :
( sK3 = U_4
| U_4 != g(f(U_4)) )
& sK3 = g(f(sK3)) )
| ( ! [U_3] :
( ( U_3 != sK2(U_3)
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( sK1 = U_0
| U_0 != f(g(U_0)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ! [U_7] :
( ( U_7 != sK4(U_7)
& sK4(U_7) = f(g(sK4(U_7))) )
| U_7 != f(g(U_7)) )
& ! [U_4] :
( sK3 = U_4
| U_4 != g(f(U_4)) )
& sK3 = g(f(sK3)) )
| ( ! [U_3] :
( ( U_3 != sK2(U_3)
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( sK1 = U_0
| U_0 != f(g(U_0)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4(U_7))],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ! [U_7] :
( U_7 != sK4(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( sK4(U_7) = f(g(sK4(U_7)))
| ~ sP2(U_7) )
& ! [U_7,U_4] :
( sP2(U_7)
| U_7 != f(g(U_7))
| ~ sP3(U_7,U_4) )
& ! [U_7,U_4] :
( sK3 = U_4
| U_4 != g(f(U_4))
| ~ sP3(U_7,U_4) )
& ! [U_7,U_4] :
( sK3 = g(f(sK3))
| ~ sP3(U_7,U_4) )
& ! [U_3] :
( U_3 != sK2(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sK2(U_3) = g(f(sK2(U_3)))
| ~ sP0(U_3) )
& ! [U_0,U_3] :
( sP0(U_3)
| U_3 != g(f(U_3))
| ~ sP1(U_0,U_3) )
& ! [U_0,U_3] :
( sK1 = U_0
| U_0 != f(g(U_0))
| ~ sP1(U_0,U_3) )
& ! [U_0,U_3] :
( sK1 = f(g(sK1))
| ~ sP1(U_0,U_3) )
& ! [U_7,U_4,U_0,U_3] :
( sP3(U_7,U_4)
| sP1(U_0,U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( sP3(U_7,U_4)
| sP1(U_0,U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
( sK1 = f(g(sK1))
| ~ sP1(U_0,U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
( sK1 = U_0
| U_0 != f(g(U_0))
| ~ sP1(U_0,U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
( sP0(U_3)
| U_3 != g(f(U_3))
| ~ sP1(U_0,U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
( sK2(U_3) = g(f(sK2(U_3)))
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
( U_3 != sK2(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
( sK3 = g(f(sK3))
| ~ sP3(U_7,U_4) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
( sK3 = U_4
| U_4 != g(f(U_4))
| ~ sP3(U_7,U_4) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
( sP2(U_7)
| U_7 != f(g(U_7))
| ~ sP3(U_7,U_4) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
( sK4(U_7) = f(g(sK4(U_7)))
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
( U_7 != sK4(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_1_8]) ).
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,
( g(Eq_x_0) = g(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( f(Eq_x_0) = f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : SYN417+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_PEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 06:32:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 64.77/65.04 % SZS status Theorem for theBenchmark
% 64.77/65.04 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------