%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 08:49:53 AM UTC 2026
% Result : Theorem 0.22s 0.48s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 67 ( 33 unt; 0 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 460 ( 169 ~; 138 |; 153 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 124 ( 12 sgn 59 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X),
file('theBenchmark.p',reflexivity) ).
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(f_1_1,plain,
! [X] : r1(X,X),
inference(fof_nnf,[status(thm)],[reflexivity]) ).
fof(f_1_2,plain,
! [U_0] : r1(U_0,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
r1(U_0,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_3_1,negated_conjecture,
? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
inference(negate,[status(cth)],[main]) ).
fof(f_3_2,negated_conjecture,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(Y)
| ~ p2(Y) )
& ( p2(Y)
| p1(Y) )
& r1(X,Y) )
& ? [Y] :
( ~ p3(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ~ $false
& r1(X,Y) ) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p3(Y)
& r1(X,Y) ) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_12] :
( ? [U_11] :
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] :
( ~ $false
& r1(U_10,U_6) ) )
| ~ r1(U_11,U_10) )
& r1(U_12,U_11) )
& ? [U_5] :
( ? [U_4] :
( p1(U_4)
& r1(U_5,U_4) )
& p3(U_5)
& r1(U_12,U_5) ) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
? [U_12] :
( ? [U_11] :
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] : r1(U_10,U_6)
& ~ $false )
| ~ r1(U_11,U_10) )
& r1(U_12,U_11) )
& ? [U_5] :
( ? [U_4] :
( p1(U_4)
& r1(U_5,U_4) )
& p3(U_5)
& r1(U_12,U_5) ) ),
inference(miniscope,[status(thm)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ? [U_11] :
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] : r1(U_10,U_6)
& ~ $false )
| ~ r1(U_11,U_10) )
& r1(sK1,U_11) )
& ? [U_5] :
( ? [U_4] :
( p1(U_4)
& r1(U_5,U_4) )
& p3(U_5)
& r1(sK1,U_5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1)],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ? [U_11] :
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] : r1(U_10,U_6)
& ~ $false )
| ~ r1(U_11,U_10) )
& r1(sK1,U_11) )
& ? [U_4] :
( p1(U_4)
& r1(sK2,U_4) )
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_3_5]) ).
fof(f_3_7,negated_conjecture,
( ? [U_11] :
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] : r1(U_10,U_6)
& ~ $false )
| ~ r1(U_11,U_10) )
& r1(sK1,U_11) )
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3)],[f_3_6]) ).
fof(f_3_8,negated_conjecture,
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& ? [U_6] : r1(U_10,U_6)
& ~ $false )
| ~ r1(sK4,U_10) )
& r1(sK1,sK4)
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_11,sK4)],[f_3_7]) ).
fof(f_3_9,negated_conjecture,
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ? [U_8] :
( ~ p3(U_8)
& r1(U_10,U_8) )
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& r1(U_10,sK5(U_10))
& ~ $false )
| ~ r1(sK4,U_10) )
& r1(sK1,sK4)
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_6,sK5(U_10))],[f_3_8]) ).
fof(f_3_10,negated_conjecture,
( ! [U_10] :
( ( ? [U_9] :
( ( ~ p1(U_9)
| ~ p2(U_9) )
& ( p2(U_9)
| p1(U_9) )
& r1(U_10,U_9) )
& ~ p3(sK6(U_10))
& r1(U_10,sK6(U_10))
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& r1(U_10,sK5(U_10))
& ~ $false )
| ~ r1(sK4,U_10) )
& r1(sK1,sK4)
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_8,sK6(U_10))],[f_3_9]) ).
fof(f_3_11,negated_conjecture,
( ! [U_10] :
( ( ( ~ p1(sK7(U_10))
| ~ p2(sK7(U_10)) )
& ( p2(sK7(U_10))
| p1(sK7(U_10)) )
& r1(U_10,sK7(U_10))
& ~ p3(sK6(U_10))
& r1(U_10,sK6(U_10))
& ! [U_7] :
( ( ( ~ p1(U_7)
| p2(U_7) )
& ( p1(U_7)
| ~ p2(U_7) ) )
| ~ r1(U_10,U_7) )
& r1(U_10,sK5(U_10))
& ~ $false )
| ~ r1(sK4,U_10) )
& r1(sK1,sK4)
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_9,sK7(U_10))],[f_3_10]) ).
fof(f_3_12,negated_conjecture,
( ! [U_7] :
( ~ p1(U_7)
| p2(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( p1(U_7)
| ~ p2(U_7)
| ~ sP0(U_7) )
& ! [U_10,U_7] :
( ~ p1(sK7(U_10))
| ~ p2(sK7(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( p2(sK7(U_10))
| p1(sK7(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( r1(U_10,sK7(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( ~ p3(sK6(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( r1(U_10,sK6(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( sP0(U_7)
| ~ r1(U_10,U_7)
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( r1(U_10,sK5(U_10))
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( ~ $false
| ~ sP1(U_10,U_7) )
& ! [U_10,U_7] :
( sP1(U_10,U_7)
| ~ r1(sK4,U_10) )
& r1(sK1,sK4)
& p1(sK3)
& r1(sK2,sK3)
& p3(sK2)
& r1(sK1,sK2) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_3_11]) ).
cnf(f_3_18,negated_conjecture,
( sP1(U_10,U_7)
| ~ r1(sK4,U_10) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_21,negated_conjecture,
( sP0(U_7)
| ~ r1(U_10,U_7)
| ~ sP1(U_10,U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_24,negated_conjecture,
( r1(U_10,sK7(U_10))
| ~ sP1(U_10,U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_25,negated_conjecture,
( p2(sK7(U_10))
| p1(sK7(U_10))
| ~ sP1(U_10,U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_26,negated_conjecture,
( ~ p1(sK7(U_10))
| ~ p2(sK7(U_10))
| ~ sP1(U_10,U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_27,negated_conjecture,
( p1(U_7)
| ~ p2(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(f_3_28,negated_conjecture,
( ~ p1(U_7)
| p2(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_3_12]) ).
cnf(t1,plain,
( ~ p2(sK7(sK4))
| ~ p1(sK7(sK4))
| ~ sP1(sK4,U_132) ),
inference(start,[status(thm),parent(0:0)],[f_3_26]) ).
cnf(t2,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,U_132) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_18]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
r1(sK4,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,
( ~ p2(sK7(sK4))
| ~ sP0(sK7(sK4))
| p1(sK7(sK4)) ),
inference(extension,[status(thm),parent(t1:2)],[f_3_27]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:2]) ).
cnf(t8,plain,
( ~ r1(sK4,sK7(sK4))
| ~ sP1(sK4,sK7(sK4))
| sP0(sK7(sK4)) ),
inference(extension,[status(thm),parent(t6:2)],[f_3_21]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,sK7(sK4)) ),
inference(extension,[status(thm),parent(t8:2)],[f_3_18]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
r1(sK4,sK4),
inference(extension,[status(thm),parent(t10:2)],[f_1_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sP1(sK4,U_143)
| r1(sK4,sK7(sK4)) ),
inference(extension,[status(thm),parent(t8:3)],[f_3_24]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,U_143) ),
inference(extension,[status(thm),parent(t14:2)],[f_3_18]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
r1(sK4,sK4),
inference(extension,[status(thm),parent(t16:2)],[f_1_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( p1(sK7(sK4))
| ~ sP1(sK4,U_148)
| p2(sK7(sK4)) ),
inference(extension,[status(thm),parent(t6:3)],[f_3_25]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:3]) ).
cnf(t22,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,U_148) ),
inference(extension,[status(thm),parent(t20:2)],[f_3_18]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
r1(sK4,sK4),
inference(extension,[status(thm),parent(t22:2)],[f_1_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t20:3)],[t20:3,t1:2]) ).
cnf(l3,lemma,
p1(sK7(sK4)),
inference(lemma,[status(cth),parent(t1:2),below(0:0)],[t1:2]) ).
cnf(t27,plain,
( ~ p1(sK7(sK4))
| ~ sP0(sK7(sK4))
| p2(sK7(sK4)) ),
inference(extension,[status(thm),parent(t1:3)],[f_3_28]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t1:3]) ).
cnf(t29,plain,
( ~ r1(sK4,sK7(sK4))
| ~ sP1(sK4,sK7(sK4))
| sP0(sK7(sK4)) ),
inference(extension,[status(thm),parent(t27:2)],[f_3_21]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
cnf(t31,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,sK7(sK4)) ),
inference(extension,[status(thm),parent(t29:2)],[f_3_18]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
r1(sK4,sK4),
inference(extension,[status(thm),parent(t31:2)],[f_1_3]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
( ~ sP1(sK4,U_159)
| r1(sK4,sK7(sK4)) ),
inference(extension,[status(thm),parent(t29:3)],[f_3_24]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t29:3]) ).
cnf(t37,plain,
( ~ r1(sK4,sK4)
| sP1(sK4,U_159) ),
inference(extension,[status(thm),parent(t35:2)],[f_3_18]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
r1(sK4,sK4),
inference(extension,[status(thm),parent(t37:2)],[f_1_3]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t37:2]) ).
cnf(t41,plain,
p1(sK7(sK4)),
inference(lemma_extension,[status(thm),parent(t27:3)],[l3:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t27:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ 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
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 15:45:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------