%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN551+3 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 : n015.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 48.65s 48.92s
% Output : Proof 48.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 72 ( 30 unt; 0 def)
% Number of atoms : 217 ( 149 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 244 ( 99 ~; 89 |; 50 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 93 ( 12 sgn 48 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> Y = X )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> Y = X )
& X = g(f(X)) ) ),
file('theBenchmark.p',prove_this_cute_thing) ).
fof(f_1_1,negated_conjecture,
~ ( ? [X] :
( ! [Y] :
( Y = f(g(Y))
=> Y = X )
& X = f(g(X)) )
<=> ? [X] :
( ! [Y] :
( Y = g(f(Y))
=> Y = X )
& X = g(f(X)) ) ),
inference(negate,[status(cth)],[prove_this_cute_thing]) ).
fof(f_1_2,negated_conjecture,
( ( ! [X] :
( ? [Y] :
( Y != X
& Y = f(g(Y)) )
| X != f(g(X)) )
& ? [X] :
( ! [Y] :
( Y = X
| Y != g(f(Y)) )
& X = g(f(X)) ) )
| ( ! [X] :
( ? [Y] :
( Y != X
& Y = g(f(Y)) )
| X != g(f(X)) )
& ? [X] :
( ! [Y] :
( Y = X
| 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_6 != U_7
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_4 = U_5
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ? [U_2] :
( U_2 != U_3
& U_2 = g(f(U_2)) )
| U_3 != g(f(U_3)) )
& ? [U_1] :
( ! [U_0] :
( U_0 = U_1
| 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_6 != U_7
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_4 = U_5
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ? [U_2] :
( U_2 != U_3
& U_2 = g(f(U_2)) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( U_0 = sK1
| 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_6 != U_7
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ? [U_5] :
( ! [U_4] :
( U_4 = U_5
| U_4 != g(f(U_4)) )
& U_5 = g(f(U_5)) ) )
| ( ! [U_3] :
( ( sK2(U_3) != U_3
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( U_0 = sK1
| 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_6 != U_7
& U_6 = f(g(U_6)) )
| U_7 != f(g(U_7)) )
& ! [U_4] :
( U_4 = sK3
| U_4 != g(f(U_4)) )
& sK3 = g(f(sK3)) )
| ( ! [U_3] :
( ( sK2(U_3) != U_3
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( U_0 = sK1
| 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] :
( ( sK4(U_7) != U_7
& sK4(U_7) = f(g(sK4(U_7))) )
| U_7 != f(g(U_7)) )
& ! [U_4] :
( U_4 = sK3
| U_4 != g(f(U_4)) )
& sK3 = g(f(sK3)) )
| ( ! [U_3] :
( ( sK2(U_3) != U_3
& sK2(U_3) = g(f(sK2(U_3))) )
| U_3 != g(f(U_3)) )
& ! [U_0] :
( U_0 = sK1
| 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] :
( sK4(U_7) != U_7
| ~ sP2(U_7) )
& ! [U_7] :
( sK4(U_7) = f(g(sK4(U_7)))
| ~ sP2(U_7) )
& ! [U_4,U_7] :
( sP2(U_7)
| U_7 != f(g(U_7))
| ~ sP3(U_4,U_7) )
& ! [U_4,U_7] :
( U_4 = sK3
| U_4 != g(f(U_4))
| ~ sP3(U_4,U_7) )
& ! [U_4,U_7] :
( sK3 = g(f(sK3))
| ~ sP3(U_4,U_7) )
& ! [U_3] :
( sK2(U_3) != U_3
| ~ sP0(U_3) )
& ! [U_3] :
( sK2(U_3) = g(f(sK2(U_3)))
| ~ sP0(U_3) )
& ! [U_3,U_0] :
( sP0(U_3)
| U_3 != g(f(U_3))
| ~ sP1(U_3,U_0) )
& ! [U_3,U_0] :
( U_0 = sK1
| U_0 != f(g(U_0))
| ~ sP1(U_3,U_0) )
& ! [U_3,U_0] :
( sK1 = f(g(sK1))
| ~ sP1(U_3,U_0) )
& ! [U_4,U_7,U_3,U_0] :
( sP3(U_4,U_7)
| sP1(U_3,U_0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( sP3(U_4,U_7)
| sP1(U_3,U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
( sK1 = f(g(sK1))
| ~ sP1(U_3,U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
( U_0 = sK1
| U_0 != f(g(U_0))
| ~ sP1(U_3,U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
( sP0(U_3)
| U_3 != g(f(U_3))
| ~ sP1(U_3,U_0) ),
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,
( sK2(U_3) != U_3
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
( sK3 = g(f(sK3))
| ~ sP3(U_4,U_7) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
( U_4 = sK3
| U_4 != g(f(U_4))
| ~ sP3(U_4,U_7) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
( sP2(U_7)
| U_7 != f(g(U_7))
| ~ sP3(U_4,U_7) ),
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,
( sK4(U_7) != U_7
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_1_8]) ).
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(t1,plain,
( sP3(g(sK4(f(sK3))),f(sK3))
| sP1(g(sK1),f(sK2(g(sK1)))) ),
inference(start,[status(thm),parent(0:0)],[f_1_9]) ).
cnf(t2,plain,
( g(sK1) != g(f(g(sK1)))
| sP0(g(sK1))
| ~ sP1(g(sK1),f(sK2(g(sK1)))) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK2(g(sK1)) != g(sK1)
| ~ sP0(g(sK1)) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_14]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( g(f(sK2(g(sK1)))) != g(sK1)
| sK2(g(sK1)) != g(f(sK2(g(sK1))))
| sK2(g(sK1)) = g(sK1) ),
inference(extension,[status(thm),parent(t4:2)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP0(g(sK1))
| sK2(g(sK1)) = g(f(sK2(g(sK1)))) ),
inference(extension,[status(thm),parent(t6:2)],[f_1_13]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t2:2]) ).
cnf(l4,lemma,
sK2(g(sK1)) = g(f(sK2(g(sK1)))),
inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).
cnf(t11,plain,
( f(sK2(g(sK1))) != sK1
| g(f(sK2(g(sK1)))) = g(sK1) ),
inference(extension,[status(thm),parent(t6:3)],[equality_4]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t6:3]) ).
cnf(t13,plain,
( f(sK2(g(sK1))) != f(g(f(sK2(g(sK1)))))
| ~ sP1(g(sK1),f(sK2(g(sK1))))
| f(sK2(g(sK1))) = sK1 ),
inference(extension,[status(thm),parent(t11:2)],[f_1_11]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t1:1]) ).
cnf(t16,plain,
( sK2(g(sK1)) != g(f(sK2(g(sK1))))
| f(sK2(g(sK1))) = f(g(f(sK2(g(sK1))))) ),
inference(extension,[status(thm),parent(t13:3)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t13:3]) ).
cnf(t18,plain,
sK2(g(sK1)) = g(f(sK2(g(sK1)))),
inference(lemma_extension,[status(thm),parent(t16:2)],[l4:1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( sK1 != f(g(sK1))
| g(sK1) = g(f(g(sK1))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
( ~ sP1(g(sK1),f(sK2(g(sK1))))
| sK1 = f(g(sK1)) ),
inference(extension,[status(thm),parent(t20:2)],[f_1_10]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
$false,
inference(reduction,[status(thm),parent(t22:2)],[t22:2,t1:1]) ).
cnf(t25,plain,
( f(sK3) != f(g(f(sK3)))
| sP2(f(sK3))
| ~ sP3(g(sK4(f(sK3))),f(sK3)) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_17]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t1:2]) ).
cnf(t27,plain,
( sK4(f(sK3)) != f(sK3)
| ~ sP2(f(sK3)) ),
inference(extension,[status(thm),parent(t25:2)],[f_1_19]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
( f(g(sK4(f(sK3)))) != f(sK3)
| sK4(f(sK3)) != f(g(sK4(f(sK3))))
| sK4(f(sK3)) = f(sK3) ),
inference(extension,[status(thm),parent(t27:2)],[equality_3]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
cnf(t31,plain,
( ~ sP2(f(sK3))
| sK4(f(sK3)) = f(g(sK4(f(sK3)))) ),
inference(extension,[status(thm),parent(t29:2)],[f_1_18]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t31:2)],[t31:2,t25:2]) ).
cnf(l16,lemma,
sK4(f(sK3)) = f(g(sK4(f(sK3)))),
inference(lemma,[status(cth),parent(t29:2),below(t27:2)],[t29:2]) ).
cnf(t34,plain,
( g(sK4(f(sK3))) != sK3
| f(g(sK4(f(sK3)))) = f(sK3) ),
inference(extension,[status(thm),parent(t29:3)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t29:3]) ).
cnf(t36,plain,
( g(sK4(f(sK3))) != g(f(g(sK4(f(sK3)))))
| ~ sP3(g(sK4(f(sK3))),f(sK3))
| g(sK4(f(sK3))) = sK3 ),
inference(extension,[status(thm),parent(t34:2)],[f_1_16]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
$false,
inference(reduction,[status(thm),parent(t36:2)],[t36:2,t1:2]) ).
cnf(t39,plain,
( sK4(f(sK3)) != f(g(sK4(f(sK3))))
| g(sK4(f(sK3))) = g(f(g(sK4(f(sK3))))) ),
inference(extension,[status(thm),parent(t36:3)],[equality_4]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t36:3]) ).
cnf(t41,plain,
sK4(f(sK3)) = f(g(sK4(f(sK3)))),
inference(lemma_extension,[status(thm),parent(t39:2)],[l16:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
( sK3 != g(f(sK3))
| f(sK3) = f(g(f(sK3))) ),
inference(extension,[status(thm),parent(t25:3)],[equality_5]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t25:3]) ).
cnf(t45,plain,
( ~ sP3(g(sK4(f(sK3))),f(sK3))
| sK3 = g(f(sK3)) ),
inference(extension,[status(thm),parent(t43:2)],[f_1_15]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
cnf(t47,plain,
$false,
inference(reduction,[status(thm),parent(t45:2)],[t45:2,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+3 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n015.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 07:06:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 48.65/48.92 % SZS status Theorem for theBenchmark
% 48.65/48.92 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------