%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 : 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 : Thu Sep 24 09:10:34 AM UTC 2026
% Result : Theorem 215.65s 221.01s
% Output : Proof 216.00s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ( ! [Y,Z] :
( ( Z = f(g(Z))
& Y = f(g(Y)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
<=> ( ! [Y,Z] :
( ( Z = g(f(Z))
& Y = g(f(Y)) )
=> Y = Z )
& ? [X] : X = g(f(X)) ) ),
file('theBenchmark.p',prove_this_cute_thing) ).
fof(f_1_1,negated_conjecture,
~ ( ( ! [Y,Z] :
( ( Z = f(g(Z))
& Y = f(g(Y)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
<=> ( ! [Y,Z] :
( ( Z = g(f(Z))
& Y = g(f(Y)) )
=> Y = Z )
& ? [X] : X = g(f(X)) ) ),
inference(negate,[status(cth)],[prove_this_cute_thing]) ).
fof(f_1_2,negated_conjecture,
( ( ( ? [Y,Z] :
( Y != Z
& Z = f(g(Z))
& Y = f(g(Y)) )
| ! [X] : X != f(g(X)) )
& ! [Y,Z] :
( Y = Z
| Z != g(f(Z))
| Y != g(f(Y)) )
& ? [X] : X = g(f(X)) )
| ( ( ? [Y,Z] :
( Y != Z
& Z = g(f(Z))
& Y = g(f(Y)) )
| ! [X] : X != g(f(X)) )
& ! [Y,Z] :
( Y = Z
| Z != f(g(Z))
| Y != f(g(Y)) )
& ? [X] : X = f(g(X)) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ( ? [U_11,U_10] :
( U_11 != U_10
& U_10 = f(g(U_10))
& U_11 = f(g(U_11)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& ? [U_6] : U_6 = g(f(U_6)) )
| ( ( ? [U_5,U_4] :
( U_5 != U_4
& U_4 = g(f(U_4))
& U_5 = g(f(U_5)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& ? [U_0] : U_0 = f(g(U_0)) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ( ? [U_11,U_10] :
( U_11 != U_10
& U_10 = f(g(U_10))
& U_11 = f(g(U_11)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& ? [U_6] : U_6 = g(f(U_6)) )
| ( ( ? [U_5,U_4] :
( U_5 != U_4
& U_4 = g(f(U_4))
& U_5 = g(f(U_5)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ( ? [U_11,U_10] :
( U_11 != U_10
& U_10 = f(g(U_10))
& U_11 = f(g(U_11)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& ? [U_6] : U_6 = g(f(U_6)) )
| ( ( ? [U_4] :
( sK2 != U_4
& U_4 = g(f(U_4))
& sK2 = g(f(sK2)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ( ? [U_11,U_10] :
( U_11 != U_10
& U_10 = f(g(U_10))
& U_11 = f(g(U_11)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& ? [U_6] : U_6 = g(f(U_6)) )
| ( ( ( sK2 != sK3
& sK3 = g(f(sK3))
& sK2 = g(f(sK2)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ( ? [U_11,U_10] :
( U_11 != U_10
& U_10 = f(g(U_10))
& U_11 = f(g(U_11)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& sK4 = g(f(sK4)) )
| ( ( ( sK2 != sK3
& sK3 = g(f(sK3))
& sK2 = g(f(sK2)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ( ? [U_10] :
( sK5 != U_10
& U_10 = f(g(U_10))
& sK5 = f(g(sK5)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& sK4 = g(f(sK4)) )
| ( ( ( sK2 != sK3
& sK3 = g(f(sK3))
& sK2 = g(f(sK2)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ( ( ( sK5 != sK6
& sK6 = f(g(sK6))
& sK5 = f(g(sK5)) )
| ! [U_9] : U_9 != f(g(U_9)) )
& ! [U_8,U_7] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8)) )
& sK4 = g(f(sK4)) )
| ( ( ( sK2 != sK3
& sK3 = g(f(sK3))
& sK2 = g(f(sK2)) )
| ! [U_3] : U_3 != g(f(U_3)) )
& ! [U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2)) )
& sK1 = f(g(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6)],[f_1_8]) ).
fof(f_1_10,negated_conjecture,
( ( sK5 != sK6
| ~ sP2 )
& ( sK6 = f(g(sK6))
| ~ sP2 )
& ( sK5 = f(g(sK5))
| ~ sP2 )
& ! [U_7,U_8,U_9] :
( sP2
| U_9 != f(g(U_9))
| ~ sP3(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8))
| ~ sP3(U_7,U_8,U_9) )
& ! [U_7,U_8,U_9] :
( sK4 = g(f(sK4))
| ~ sP3(U_7,U_8,U_9) )
& ( sK2 != sK3
| ~ sP0 )
& ( sK3 = g(f(sK3))
| ~ sP0 )
& ( sK2 = g(f(sK2))
| ~ sP0 )
& ! [U_3,U_2,U_1] :
( sP0
| U_3 != g(f(U_3))
| ~ sP1(U_3,U_2,U_1) )
& ! [U_3,U_2,U_1] :
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2))
| ~ sP1(U_3,U_2,U_1) )
& ! [U_3,U_2,U_1] :
( sK1 = f(g(sK1))
| ~ sP1(U_3,U_2,U_1) )
& ! [U_7,U_3,U_2,U_1,U_8,U_9] :
( sP3(U_7,U_8,U_9)
| sP1(U_3,U_2,U_1) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
( sP3(U_7,U_8,U_9)
| sP1(U_3,U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_12,negated_conjecture,
( sK1 = f(g(sK1))
| ~ sP1(U_3,U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_13,negated_conjecture,
( U_2 = U_1
| U_1 != f(g(U_1))
| U_2 != f(g(U_2))
| ~ sP1(U_3,U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_14,negated_conjecture,
( sP0
| U_3 != g(f(U_3))
| ~ sP1(U_3,U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_15,negated_conjecture,
( sK2 = g(f(sK2))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_16,negated_conjecture,
( sK3 = g(f(sK3))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_17,negated_conjecture,
( sK2 != sK3
| ~ sP0 ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_18,negated_conjecture,
( sK4 = g(f(sK4))
| ~ sP3(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_19,negated_conjecture,
( U_8 = U_7
| U_7 != g(f(U_7))
| U_8 != g(f(U_8))
| ~ sP3(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_20,negated_conjecture,
( sP2
| U_9 != f(g(U_9))
| ~ sP3(U_7,U_8,U_9) ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_21,negated_conjecture,
( sK5 = f(g(sK5))
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_22,negated_conjecture,
( sK6 = f(g(sK6))
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_23,negated_conjecture,
( sK5 != sK6
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_10]) ).
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,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| 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 : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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
% 0.08/5.37 % Computer : n007.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 07:01:10 UTC 2026
% 0.08/5.37 % CPUTime :
% 215.65/221.01 % SZS status Theorem for theBenchmark
% 215.65/221.01 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------