%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 09:10:34 AM UTC 2026
% Result : Theorem 5.26s 5.58s
% Output : Proof 5.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_of_reachable,axiom,
! [X] : reachable(X,X),
file('theBenchmark.p',reflexivity_of_reachable) ).
fof(transitivity_of_reachable,axiom,
! [X,Y,Z] :
( ( reachable(Y,Z)
& reachable(X,Y) )
=> reachable(X,Z) ),
file('theBenchmark.p',transitivity_of_reachable) ).
fof(prove_this,conjecture,
? [X] :
( ! [Y] :
( reachable(X,Y)
=> ( ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
<=> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) ) )
& reachable(initial_world,X) ),
file('theBenchmark.p',prove_this) ).
fof(f_1_1,plain,
! [X] : reachable(X,X),
inference(fof_nnf,[status(thm)],[reflexivity_of_reachable]) ).
fof(f_1_2,plain,
! [U_0] : reachable(U_0,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
reachable(U_0,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [X,Y,Z] :
( reachable(X,Z)
| ~ reachable(Y,Z)
| ~ reachable(X,Y) ),
inference(fof_nnf,[status(thm)],[transitivity_of_reachable]) ).
fof(f_2_2,plain,
! [U_3,U_2,U_1] :
( reachable(U_3,U_1)
| ~ reachable(U_2,U_1)
| ~ reachable(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( reachable(U_3,U_1)
| ~ reachable(U_2,U_1)
| ~ reachable(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,negated_conjecture,
~ ? [X] :
( ! [Y] :
( reachable(X,Y)
=> ( ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) )
<=> ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) ) )
& reachable(initial_world,X) ),
inference(negate,[status(cth)],[prove_this]) ).
fof(f_3_2,negated_conjecture,
! [X] :
( ? [Y] :
( ( ( ! [Z] :
( ( ! [V] :
( ~ q(V)
| ~ reachable(Z,V) )
& ~ p(Z) )
| ~ reachable(Y,Z) )
& ( ? [W] :
( q(W)
& reachable(Y,W) )
| ? [W] :
( p(W)
& reachable(Y,W) ) ) )
| ( ! [W] :
( ~ q(W)
| ~ reachable(Y,W) )
& ! [W] :
( ~ p(W)
| ~ reachable(Y,W) )
& ? [Z] :
( ( ? [V] :
( q(V)
& reachable(Z,V) )
| p(Z) )
& reachable(Y,Z) ) ) )
& reachable(X,Y) )
| ~ reachable(initial_world,X) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
! [U_13] :
( ? [U_12] :
( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(U_12,U_11) )
& ( ? [U_9] :
( q(U_9)
& reachable(U_12,U_9) )
| ? [U_8] :
( p(U_8)
& reachable(U_12,U_8) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(U_12,U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(U_12,U_6) )
& ? [U_5] :
( ( ? [U_4] :
( q(U_4)
& reachable(U_5,U_4) )
| p(U_5) )
& reachable(U_12,U_5) ) ) )
& reachable(U_13,U_12) )
| ~ reachable(initial_world,U_13) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
! [U_13] :
( ( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(sK1(U_13),U_11) )
& ( ? [U_9] :
( q(U_9)
& reachable(sK1(U_13),U_9) )
| ? [U_8] :
( p(U_8)
& reachable(sK1(U_13),U_8) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6) )
& ? [U_5] :
( ( ? [U_4] :
( q(U_4)
& reachable(U_5,U_4) )
| p(U_5) )
& reachable(sK1(U_13),U_5) ) ) )
& reachable(U_13,sK1(U_13)) )
| ~ reachable(initial_world,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1(U_13))],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
! [U_13] :
( ( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(sK1(U_13),U_11) )
& ( ? [U_9] :
( q(U_9)
& reachable(sK1(U_13),U_9) )
| ? [U_8] :
( p(U_8)
& reachable(sK1(U_13),U_8) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6) )
& ( ? [U_4] :
( q(U_4)
& reachable(sK2(U_13),U_4) )
| p(sK2(U_13)) )
& reachable(sK1(U_13),sK2(U_13)) ) )
& reachable(U_13,sK1(U_13)) )
| ~ reachable(initial_world,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2(U_13))],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
! [U_13] :
( ( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(sK1(U_13),U_11) )
& ( ? [U_9] :
( q(U_9)
& reachable(sK1(U_13),U_9) )
| ? [U_8] :
( p(U_8)
& reachable(sK1(U_13),U_8) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6) )
& ( ( q(sK3(U_13))
& reachable(sK2(U_13),sK3(U_13)) )
| p(sK2(U_13)) )
& reachable(sK1(U_13),sK2(U_13)) ) )
& reachable(U_13,sK1(U_13)) )
| ~ reachable(initial_world,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3(U_13))],[f_3_5]) ).
fof(f_3_7,negated_conjecture,
! [U_13] :
( ( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(sK1(U_13),U_11) )
& ( ? [U_9] :
( q(U_9)
& reachable(sK1(U_13),U_9) )
| ( p(sK4(U_13))
& reachable(sK1(U_13),sK4(U_13)) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6) )
& ( ( q(sK3(U_13))
& reachable(sK2(U_13),sK3(U_13)) )
| p(sK2(U_13)) )
& reachable(sK1(U_13),sK2(U_13)) ) )
& reachable(U_13,sK1(U_13)) )
| ~ reachable(initial_world,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_8,sK4(U_13))],[f_3_6]) ).
fof(f_3_8,negated_conjecture,
! [U_13] :
( ( ( ( ! [U_11] :
( ( ! [U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10) )
& ~ p(U_11) )
| ~ reachable(sK1(U_13),U_11) )
& ( ( q(sK5(U_13))
& reachable(sK1(U_13),sK5(U_13)) )
| ( p(sK4(U_13))
& reachable(sK1(U_13),sK4(U_13)) ) ) )
| ( ! [U_7] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7) )
& ! [U_6] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6) )
& ( ( q(sK3(U_13))
& reachable(sK2(U_13),sK3(U_13)) )
| p(sK2(U_13)) )
& reachable(sK1(U_13),sK2(U_13)) ) )
& reachable(U_13,sK1(U_13)) )
| ~ reachable(initial_world,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_9,sK5(U_13))],[f_3_7]) ).
fof(f_3_9,negated_conjecture,
( ! [U_11,U_10] :
( ~ q(U_10)
| ~ reachable(U_11,U_10)
| ~ sP4(U_11,U_10) )
& ! [U_11,U_10] :
( ~ p(U_11)
| ~ sP4(U_11,U_10) )
& ! [U_13] :
( q(sK5(U_13))
| ~ sP3(U_13) )
& ! [U_13] :
( reachable(sK1(U_13),sK5(U_13))
| ~ sP3(U_13) )
& ! [U_13] :
( p(sK4(U_13))
| ~ sP2(U_13) )
& ! [U_13] :
( reachable(sK1(U_13),sK4(U_13))
| ~ sP2(U_13) )
& ! [U_13,U_11,U_10] :
( sP4(U_11,U_10)
| ~ reachable(sK1(U_13),U_11)
| ~ sP5(U_13,U_11,U_10) )
& ! [U_13,U_11,U_10] :
( sP3(U_13)
| sP2(U_13)
| ~ sP5(U_13,U_11,U_10) )
& ! [U_13] :
( q(sK3(U_13))
| ~ sP0(U_13) )
& ! [U_13] :
( reachable(sK2(U_13),sK3(U_13))
| ~ sP0(U_13) )
& ! [U_7,U_6,U_13] :
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7)
| ~ sP1(U_7,U_6,U_13) )
& ! [U_7,U_6,U_13] :
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6)
| ~ sP1(U_7,U_6,U_13) )
& ! [U_7,U_6,U_13] :
( sP0(U_13)
| p(sK2(U_13))
| ~ sP1(U_7,U_6,U_13) )
& ! [U_7,U_6,U_13] :
( reachable(sK1(U_13),sK2(U_13))
| ~ sP1(U_7,U_6,U_13) )
& ! [U_7,U_6,U_13,U_11,U_10] :
( sP5(U_13,U_11,U_10)
| sP1(U_7,U_6,U_13)
| ~ sP6(U_7,U_6,U_13,U_11,U_10) )
& ! [U_7,U_6,U_13,U_11,U_10] :
( reachable(U_13,sK1(U_13))
| ~ sP6(U_7,U_6,U_13,U_11,U_10) )
& ! [U_7,U_6,U_13,U_11,U_10] :
( sP6(U_7,U_6,U_13,U_11,U_10)
| ~ reachable(initial_world,U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4,sP5,sP6])],[f_3_8]) ).
cnf(f_3_10,negated_conjecture,
( sP6(U_7,U_6,U_13,U_11,U_10)
| ~ reachable(initial_world,U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_11,negated_conjecture,
( reachable(U_13,sK1(U_13))
| ~ sP6(U_7,U_6,U_13,U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_12,negated_conjecture,
( sP5(U_13,U_11,U_10)
| sP1(U_7,U_6,U_13)
| ~ sP6(U_7,U_6,U_13,U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_13,negated_conjecture,
( reachable(sK1(U_13),sK2(U_13))
| ~ sP1(U_7,U_6,U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_14,negated_conjecture,
( sP0(U_13)
| p(sK2(U_13))
| ~ sP1(U_7,U_6,U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_15,negated_conjecture,
( ~ p(U_6)
| ~ reachable(sK1(U_13),U_6)
| ~ sP1(U_7,U_6,U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_16,negated_conjecture,
( ~ q(U_7)
| ~ reachable(sK1(U_13),U_7)
| ~ sP1(U_7,U_6,U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_17,negated_conjecture,
( reachable(sK2(U_13),sK3(U_13))
| ~ sP0(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_18,negated_conjecture,
( q(sK3(U_13))
| ~ sP0(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_19,negated_conjecture,
( sP3(U_13)
| sP2(U_13)
| ~ sP5(U_13,U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_20,negated_conjecture,
( sP4(U_11,U_10)
| ~ reachable(sK1(U_13),U_11)
| ~ sP5(U_13,U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_21,negated_conjecture,
( reachable(sK1(U_13),sK4(U_13))
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_22,negated_conjecture,
( p(sK4(U_13))
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_23,negated_conjecture,
( reachable(sK1(U_13),sK5(U_13))
| ~ sP3(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_24,negated_conjecture,
( q(sK5(U_13))
| ~ sP3(U_13) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_25,negated_conjecture,
( ~ p(U_11)
| ~ sP4(U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_26,negated_conjecture,
( ~ q(U_10)
| ~ reachable(U_11,U_10)
| ~ sP4(U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.09/0.36 % Computer : n007.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 07:00:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 5.26/5.58 % SZS status Theorem for theBenchmark
% 5.26/5.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------