%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:54:51 AM UTC 2026
% Result : Theorem 22.04s 32.34s
% Output : Proof 22.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 31 unt; 0 def)
% Number of atoms : 80 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 25 ~; 16 |; 14 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 21 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('REL001+0.ax',maddux2_join_associativity) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
file('theBenchmark.p',goals) ).
fof(f_1_1,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(fof_nnf,[status(thm)],[maddux1_join_commutativity]) ).
fof(f_1_2,plain,
! [U_1,U_0] : join(U_1,U_0) = join(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
join(U_1,U_0) = join(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(fof_nnf,[status(thm)],[maddux2_join_associativity]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] : join(U_4,join(U_3,U_2)) = join(join(U_4,U_3),U_2),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
join(U_4,join(U_3,U_2)) = join(join(U_4,U_3),U_2),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_14_1,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
inference(negate,[status(cth)],[goals]) ).
fof(f_14_2,negated_conjecture,
? [X0,X1,X2] :
( join(join(X0,X2),X1) != X1
& join(X2,X1) = X1
& join(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[f_14_1]) ).
fof(f_14_3,negated_conjecture,
? [U_27,U_26,U_25] :
( join(join(U_27,U_25),U_26) != U_26
& join(U_25,U_26) = U_26
& join(U_27,U_26) = U_26 ),
inference(variable_rename,[status(thm)],[f_14_2]) ).
fof(f_14_4,negated_conjecture,
? [U_26,U_25] :
( join(join(sK1,U_25),U_26) != U_26
& join(U_25,U_26) = U_26
& join(sK1,U_26) = U_26 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_27,sK1)],[f_14_3]) ).
fof(f_14_5,negated_conjecture,
? [U_25] :
( join(join(sK1,U_25),sK2) != sK2
& join(U_25,sK2) = sK2
& join(sK1,sK2) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_14_4]) ).
fof(f_14_6,negated_conjecture,
( join(join(sK1,sK3),sK2) != sK2
& join(sK3,sK2) = sK2
& join(sK1,sK2) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3)],[f_14_5]) ).
fof(f_14_7,negated_conjecture,
( join(join(sK1,sK3),sK2) != sK2
& join(sK3,sK2) = sK2
& join(sK1,sK2) = sK2 ),
inference(definitional_conversion,[status(esa)],[f_14_6]) ).
cnf(f_14_8,negated_conjecture,
join(sK1,sK2) = sK2,
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_9,negated_conjecture,
join(sK3,sK2) = sK2,
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_10,negated_conjecture,
join(join(sK1,sK3),sK2) != sK2,
inference(clausify,[status(thm)],[f_14_7]) ).
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,
( join(Eq_x_0,Eq_x_1) = join(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
join(join(sK1,sK3),sK2) != sK2,
inference(start,[status(thm),parent(0:0)],[f_14_10]) ).
cnf(t2,plain,
( join(sK3,join(sK1,sK2)) != sK2
| join(join(sK1,sK3),sK2) != join(sK3,join(sK1,sK2))
| join(join(sK1,sK3),sK2) = sK2 ),
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,
( join(join(sK3,sK1),sK2) != join(sK3,join(sK1,sK2))
| join(join(sK1,sK3),sK2) != join(join(sK3,sK1),sK2)
| join(join(sK1,sK3),sK2) = join(sK3,join(sK1,sK2)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK2 != sK2
| join(sK1,sK3) != join(sK3,sK1)
| join(join(sK1,sK3),sK2) = join(join(sK3,sK1),sK2) ),
inference(extension,[status(thm),parent(t4:2)],[equality_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
join(sK1,sK3) = join(sK3,sK1),
inference(extension,[status(thm),parent(t6:2)],[f_1_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t6:3)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( join(sK3,join(sK1,sK2)) != join(join(sK3,sK1),sK2)
| join(join(sK3,sK1),sK2) = join(sK3,join(sK1,sK2)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
join(sK3,join(sK1,sK2)) = join(join(sK3,sK1),sK2),
inference(extension,[status(thm),parent(t12:2)],[f_2_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( join(sK3,sK2) != sK2
| join(sK3,join(sK1,sK2)) != join(sK3,sK2)
| join(sK3,join(sK1,sK2)) = sK2 ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( join(sK1,sK2) != sK2
| sK3 != sK3
| join(sK3,join(sK1,sK2)) = join(sK3,sK2) ),
inference(extension,[status(thm),parent(t16:2)],[equality_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
sK3 = sK3,
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
join(sK1,sK2) = sK2,
inference(extension,[status(thm),parent(t18:3)],[f_14_8]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
join(sK3,sK2) = sK2,
inference(extension,[status(thm),parent(t16:3)],[f_14_9]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/10.40 % Computer : n007.cluster.edu
% 0.10/10.40 % Model : x86_64 x86_64
% 0.10/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.40 % Memory : 8046.5625MB
% 0.10/10.40 % OS : Linux 6.8.0-71-generic
% 0.10/10.40 % CPULimit : 300
% 0.10/10.40 % WCLimit : 300
% 0.10/10.40 % DateTime : Sat Sep 19 20:30:46 UTC 2026
% 0.10/10.40 % CPUTime :
% 22.04/32.34 % SZS status Theorem for theBenchmark
% 22.04/32.34 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------