%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN080+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n012.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 09:09:26 AM UTC 2026
% Result : Theorem 0.03s 0.30s
% Output : Proof 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 16 unt; 0 def)
% Number of atoms : 20 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 10 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 2 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel58_1,axiom,
! [X,Y] : f(X) = g(Y),
file('theBenchmark.p',pel58_1) ).
fof(pel58,conjecture,
! [X,Y] : f(f(X)) = f(g(Y)),
file('theBenchmark.p',pel58) ).
fof(f_1_1,plain,
! [X,Y] : f(X) = g(Y),
inference(fof_nnf,[status(thm)],[pel58_1]) ).
fof(f_1_2,plain,
! [U_1,U_0] : f(U_1) = g(U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
f(U_1) = g(U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,negated_conjecture,
~ ! [X,Y] : f(f(X)) = f(g(Y)),
inference(negate,[status(cth)],[pel58]) ).
fof(f_2_2,negated_conjecture,
? [X,Y] : f(f(X)) != f(g(Y)),
inference(fof_nnf,[status(thm)],[f_2_1]) ).
fof(f_2_3,negated_conjecture,
? [U_3,U_2] : f(f(U_3)) != f(g(U_2)),
inference(variable_rename,[status(thm)],[f_2_2]) ).
fof(f_2_4,negated_conjecture,
? [U_2] : f(f(sK1)) != f(g(U_2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_2_3]) ).
fof(f_2_5,negated_conjecture,
f(f(sK1)) != f(g(sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_2_4]) ).
fof(f_2_6,negated_conjecture,
f(f(sK1)) != f(g(sK2)),
inference(definitional_conversion,[status(esa)],[f_2_5]) ).
cnf(f_2_7,negated_conjecture,
f(f(sK1)) != f(g(sK2)),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(equality_4,axiom,
( f(Eq_x_0) = f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
f(f(sK1)) != f(g(sK2)),
inference(start,[status(thm),parent(0:0)],[f_2_7]) ).
cnf(t2,plain,
( f(sK1) != g(sK2)
| f(f(sK1)) = f(g(sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
f(sK1) = g(sK2),
inference(extension,[status(thm),parent(t2:2)],[f_1_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN080+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.01 This is a FOF_THM_RFO_PEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 06:24:06 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % SZS status Theorem for theBenchmark
% 0.03/0.30 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------