%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% 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 : n003.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 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(gsy_c_HOL_Oundefined_000tc__Com__Ostate,axiom,
is_state(undefined_state(state)),
file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Ostate) ).
fof(fact_0_state__not__singleton__def,axiom,
( hoare_165779456gleton
<=> ? [S,T] :
( S != T
& is_state(T)
& is_state(S) ) ),
file('theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(fact_1_induct__false__def,axiom,
~ induct_false,
file('theBenchmark.p',fact_1_induct__false__def) ).
fof(fact_2_induct__trueI,axiom,
induct_true,
file('theBenchmark.p',fact_2_induct__trueI) ).
fof(fact_3_induct__true__def,axiom,
induct_true,
file('theBenchmark.p',fact_3_induct__true__def) ).
fof(conj_0,hypothesis,
hoare_165779456gleton,
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [T] :
( is_state(T)
=> ~ ! [S] :
( is_state(S)
=> S = T ) ),
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
is_state(undefined_state(state)),
inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Ostate]) ).
cnf(f_1_2,plain,
is_state(undefined_state(state)),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
( ( hoare_165779456gleton
| ! [S,T] :
( S = T
| ~ is_state(T)
| ~ is_state(S) ) )
& ( ? [S,T] :
( S != T
& is_state(T)
& is_state(S) )
| ~ hoare_165779456gleton ) ),
inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def]) ).
fof(f_2_2,plain,
( ( hoare_165779456gleton
| ! [U_3,U_2] :
( U_3 = U_2
| ~ is_state(U_2)
| ~ is_state(U_3) ) )
& ( ? [U_1,U_0] :
( U_1 != U_0
& is_state(U_0)
& is_state(U_1) )
| ~ hoare_165779456gleton ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ( hoare_165779456gleton
| ! [U_3] :
( ! [U_2] :
( U_3 = U_2
| ~ is_state(U_2) )
| ~ is_state(U_3) ) )
& ( ? [U_1] :
( ? [U_0] :
( U_1 != U_0
& is_state(U_0) )
& is_state(U_1) )
| ~ hoare_165779456gleton ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ( hoare_165779456gleton
| ! [U_3] :
( ! [U_2] :
( U_3 = U_2
| ~ is_state(U_2) )
| ~ is_state(U_3) ) )
& ( ( ? [U_0] :
( sK1 != U_0
& is_state(U_0) )
& is_state(sK1) )
| ~ hoare_165779456gleton ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_2_3]) ).
fof(f_2_5,plain,
( ( hoare_165779456gleton
| ! [U_3] :
( ! [U_2] :
( U_3 = U_2
| ~ is_state(U_2) )
| ~ is_state(U_3) ) )
& ( ( sK1 != sK2
& is_state(sK2)
& is_state(sK1) )
| ~ hoare_165779456gleton ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2)],[f_2_4]) ).
cnf(f_2_6,plain,
( is_state(sK1)
| ~ hoare_165779456gleton ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( is_state(sK2)
| ~ hoare_165779456gleton ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( sK1 != sK2
| ~ hoare_165779456gleton ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( hoare_165779456gleton
| U_3 = U_2
| ~ is_state(U_2)
| ~ is_state(U_3) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
~ induct_false,
inference(fof_nnf,[status(thm)],[fact_1_induct__false__def]) ).
cnf(f_3_2,plain,
~ induct_false,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
induct_true,
inference(fof_nnf,[status(thm)],[fact_2_induct__trueI]) ).
cnf(f_4_2,plain,
induct_true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
induct_true,
inference(fof_nnf,[status(thm)],[fact_3_induct__true__def]) ).
cnf(f_5_2,plain,
induct_true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
hoare_165779456gleton,
inference(fof_nnf,[status(thm)],[conj_0]) ).
cnf(f_6_2,plain,
hoare_165779456gleton,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,negated_conjecture,
~ ! [T] :
( is_state(T)
=> ~ ! [S] :
( is_state(S)
=> S = T ) ),
inference(negate,[status(cth)],[conj_1]) ).
fof(f_7_2,negated_conjecture,
? [T] :
( ! [S] :
( S = T
| ~ is_state(S) )
& is_state(T) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_5] :
( ! [U_4] :
( U_4 = U_5
| ~ is_state(U_4) )
& is_state(U_5) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ! [U_4] :
( U_4 = sK3
| ~ is_state(U_4) )
& is_state(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ! [U_4] :
( U_4 = sK3
| ~ is_state(U_4) )
& is_state(sK3) ),
inference(definitional_conversion,[status(esa)],[f_7_4]) ).
cnf(f_7_6,negated_conjecture,
is_state(sK3),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
( U_4 = sK3
| ~ is_state(U_4) ),
inference(clausify,[status(thm)],[f_7_5]) ).
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,
( undefined_state(Eq_x_0) = undefined_state(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( is_state(Eq_y_0)
| ~ is_state(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.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 05:40:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------