%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN083+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 : n016.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 09:09:27 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 20 unt; 0 def)
% Number of atoms : 26 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 14 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 17 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p61_1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
file('theBenchmark.p',p61_1) ).
fof(pel61,conjecture,
! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
file('theBenchmark.p',pel61) ).
fof(f_1_1,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(fof_nnf,[status(thm)],[p61_1]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] : f(U_2,f(U_1,U_0)) = f(f(U_2,U_1),U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
f(U_2,f(U_1,U_0)) = f(f(U_2,U_1),U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,negated_conjecture,
~ ! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
inference(negate,[status(cth)],[pel61]) ).
fof(f_2_2,negated_conjecture,
? [X,Y,Z,W] : f(X,f(Y,f(Z,W))) != f(f(f(X,Y),Z),W),
inference(fof_nnf,[status(thm)],[f_2_1]) ).
fof(f_2_3,negated_conjecture,
? [U_6,U_5,U_4,U_3] : f(U_6,f(U_5,f(U_4,U_3))) != f(f(f(U_6,U_5),U_4),U_3),
inference(variable_rename,[status(thm)],[f_2_2]) ).
fof(f_2_4,negated_conjecture,
? [U_5,U_4,U_3] : f(sK1,f(U_5,f(U_4,U_3))) != f(f(f(sK1,U_5),U_4),U_3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_2_3]) ).
fof(f_2_5,negated_conjecture,
? [U_4,U_3] : f(sK1,f(sK2,f(U_4,U_3))) != f(f(f(sK1,sK2),U_4),U_3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_2_4]) ).
fof(f_2_6,negated_conjecture,
? [U_3] : f(sK1,f(sK2,f(sK3,U_3))) != f(f(f(sK1,sK2),sK3),U_3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3)],[f_2_5]) ).
fof(f_2_7,negated_conjecture,
f(sK1,f(sK2,f(sK3,sK4))) != f(f(f(sK1,sK2),sK3),sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_3,sK4)],[f_2_6]) ).
fof(f_2_8,negated_conjecture,
f(sK1,f(sK2,f(sK3,sK4))) != f(f(f(sK1,sK2),sK3),sK4),
inference(definitional_conversion,[status(esa)],[f_2_7]) ).
cnf(f_2_9,negated_conjecture,
f(sK1,f(sK2,f(sK3,sK4))) != f(f(f(sK1,sK2),sK3),sK4),
inference(clausify,[status(thm)],[f_2_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(t1,plain,
f(sK1,f(sK2,f(sK3,sK4))) != f(f(f(sK1,sK2),sK3),sK4),
inference(start,[status(thm),parent(0:0)],[f_2_9]) ).
cnf(t2,plain,
( f(f(sK1,sK2),f(sK3,sK4)) != f(f(f(sK1,sK2),sK3),sK4)
| f(sK1,f(sK2,f(sK3,sK4))) != f(f(sK1,sK2),f(sK3,sK4))
| f(sK1,f(sK2,f(sK3,sK4))) = f(f(f(sK1,sK2),sK3),sK4) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
f(sK1,f(sK2,f(sK3,sK4))) = f(f(sK1,sK2),f(sK3,sK4)),
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]) ).
cnf(t6,plain,
f(f(sK1,sK2),f(sK3,sK4)) = f(f(f(sK1,sK2),sK3),sK4),
inference(extension,[status(thm),parent(t2:3)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN083+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 06:29:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------