%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% 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 : n009.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 09:07:52 AM UTC 2026
% Result : Theorem 0.94s 1.20s
% Output : Proof 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 18 unt; 0 def)
% Number of atoms : 50 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 16 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 16 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_state__not__singleton__def,axiom,
( hBOOL(hoare_1883395792gleton)
<=> ? [S,T] : ti(state,S) != ti(state,T) ),
file('theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(conj_0,hypothesis,
hBOOL(hoare_1883395792gleton),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [T] :
~ ! [S] : ti(state,S) = ti(state,T),
file('theBenchmark.p',conj_1) ).
fof(f_18_1,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [S,T] : ti(state,S) = ti(state,T) )
& ( ? [S,T] : ti(state,S) != ti(state,T)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def]) ).
fof(f_18_2,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [U_29,U_28] : ti(state,U_29) = ti(state,U_28) )
& ( ? [U_27,U_26] : ti(state,U_27) != ti(state,U_26)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [U_29,U_28] : ti(state,U_29) = ti(state,U_28) )
& ( ? [U_26] : ti(state,sK1) != ti(state,U_26)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_27,sK1)],[f_18_2]) ).
fof(f_18_4,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [U_29,U_28] : ti(state,U_29) = ti(state,U_28) )
& ( ti(state,sK1) != ti(state,sK2)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_18_3]) ).
cnf(f_18_5,plain,
( ti(state,sK1) != ti(state,sK2)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_62_1,plain,
hBOOL(hoare_1883395792gleton),
inference(fof_nnf,[status(thm)],[conj_0]) ).
cnf(f_62_2,plain,
hBOOL(hoare_1883395792gleton),
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_63_1,negated_conjecture,
~ ! [T] :
~ ! [S] : ti(state,S) = ti(state,T),
inference(negate,[status(cth)],[conj_1]) ).
fof(f_63_2,negated_conjecture,
? [T] :
! [S] : ti(state,S) = ti(state,T),
inference(fof_nnf,[status(thm)],[f_63_1]) ).
fof(f_63_3,negated_conjecture,
? [U_188] :
! [U_187] : ti(state,U_187) = ti(state,U_188),
inference(variable_rename,[status(thm)],[f_63_2]) ).
fof(f_63_4,negated_conjecture,
! [U_187] : ti(state,U_187) = ti(state,sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_188,sK12)],[f_63_3]) ).
fof(f_63_5,negated_conjecture,
! [U_187] : ti(state,U_187) = ti(state,sK12),
inference(definitional_conversion,[status(esa)],[f_63_4]) ).
cnf(f_63_6,negated_conjecture,
ti(state,U_187) = ti(state,sK12),
inference(clausify,[status(thm)],[f_63_5]) ).
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(t1,plain,
( ti(state,sK1) != ti(state,sK2)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(start,[status(thm),parent(0:0)],[f_18_5]) ).
cnf(t2,plain,
hBOOL(hoare_1883395792gleton),
inference(extension,[status(thm),parent(t1:1)],[f_62_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ti(state,sK12) != ti(state,sK2)
| ti(state,sK1) != ti(state,sK12)
| ti(state,sK1) = ti(state,sK2) ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
ti(state,sK1) = ti(state,sK12),
inference(extension,[status(thm),parent(t4:2)],[f_63_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ti(state,sK2) != ti(state,sK12)
| ti(state,sK12) = ti(state,sK2) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
ti(state,sK2) = ti(state,sK12),
inference(extension,[status(thm),parent(t8:2)],[f_63_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 05:38:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.94/1.20 % SZS status Theorem for theBenchmark
% 0.94/1.20 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------