%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n002.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 08:58:27 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t115_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_2_2,plain,
! [U_2] :
( relation(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_3_2,plain,
! [U_6,U_5] :
( ( subset(U_6,U_5)
| ? [U_4] :
( ~ in(U_4,U_5)
& in(U_4,U_6) ) )
& ( ! [U_3] :
( in(U_3,U_5)
| ~ in(U_3,U_6) )
| ~ subset(U_6,U_5) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_10,U_8] :
( subset(U_10,U_8)
| ? [U_4] :
( ~ in(U_4,U_8)
& in(U_4,U_10) ) )
& ! [U_9,U_7] :
( ! [U_3] :
( in(U_3,U_7)
| ~ in(U_3,U_9) )
| ~ subset(U_9,U_7) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_10,U_8] :
( subset(U_10,U_8)
| ( ~ in(sK1(U_10,U_8),U_8)
& in(sK1(U_10,U_8),U_10) ) )
& ! [U_9,U_7] :
( ! [U_3] :
( in(U_3,U_7)
| ~ in(U_3,U_9) )
| ~ subset(U_9,U_7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1(U_10,U_8))],[f_3_3]) ).
cnf(f_3_5,plain,
( in(U_3,U_7)
| ~ in(U_3,U_9)
| ~ subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( in(sK1(U_10,U_8),U_10)
| subset(U_10,U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( ~ in(sK1(U_10,U_8),U_8)
| subset(U_10,U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_7_2,plain,
! [U_12,U_11] :
( relation(relation_rng_restriction(U_12,U_11))
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( relation(relation_rng_restriction(U_12,U_11))
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_9_2,plain,
! [U_14] :
? [U_13] : element(U_13,U_14),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_14] : element(sK2(U_14),U_14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2(U_14))],[f_9_2]) ).
cnf(f_9_4,plain,
element(sK2(U_14),U_14),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_10_2,plain,
! [U_15] : ~ empty(powerset(U_15)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ empty(powerset(U_15)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_11_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_12_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_13_2,plain,
! [U_16] :
( ~ empty(relation_rng(U_16))
| ~ relation(U_16)
| empty(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ~ empty(relation_rng(U_16))
| ~ relation(U_16)
| empty(U_16) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_14_2,plain,
! [U_17] :
( ( relation(relation_rng(U_17))
& empty(relation_rng(U_17)) )
| ~ empty(U_17) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( empty(relation_rng(U_17))
| ~ empty(U_17) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( relation(relation_rng(U_17))
| ~ empty(U_17) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_15_2,plain,
? [U_18] :
( relation(U_18)
& empty(U_18) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3)],[f_15_2]) ).
cnf(f_15_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_16_2,plain,
! [U_20] :
( ? [U_19] :
( ~ empty(U_19)
& element(U_19,powerset(U_20)) )
| empty(U_20) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_20] :
( ( ~ empty(sK4(U_20))
& element(sK4(U_20),powerset(U_20)) )
| empty(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_19,sK4(U_20))],[f_16_2]) ).
cnf(f_16_4,plain,
( element(sK4(U_20),powerset(U_20))
| empty(U_20) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ empty(sK4(U_20))
| empty(U_20) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_17_2,plain,
? [U_21] : empty(U_21),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_21,sK5)],[f_17_2]) ).
cnf(f_17_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_18_2,plain,
? [U_22] :
( relation(U_22)
& ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_18_2]) ).
cnf(f_18_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_19_2,plain,
! [U_24] :
? [U_23] :
( empty(U_23)
& element(U_23,powerset(U_24)) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_24] :
( empty(sK7(U_24))
& element(sK7(U_24),powerset(U_24)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7(U_24))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK7(U_24),powerset(U_24)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK7(U_24)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_20_2,plain,
? [U_25] : ~ empty(U_25),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8)],[f_20_2]) ).
cnf(f_20_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_21_2,plain,
! [U_27,U_26] : subset(U_27,U_27),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_27] : subset(U_27,U_27),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
subset(U_27,U_27),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B,C] :
( ( ( in(A,relation_rng(relation_rng_restriction(B,C)))
| ~ in(A,relation_rng(C))
| ~ in(A,B) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t115_relat_1]) ).
fof(f_22_2,plain,
! [U_30,U_29,U_28] :
( ( ( in(U_30,relation_rng(relation_rng_restriction(U_29,U_28)))
| ~ in(U_30,relation_rng(U_28))
| ~ in(U_30,U_29) )
& ( ( in(U_30,relation_rng(U_28))
& in(U_30,U_29) )
| ~ in(U_30,relation_rng(relation_rng_restriction(U_29,U_28))) ) )
| ~ relation(U_28) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( in(U_30,U_29)
| ~ in(U_30,relation_rng(relation_rng_restriction(U_29,U_28)))
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( in(U_30,relation_rng(U_28))
| ~ in(U_30,relation_rng(relation_rng_restriction(U_29,U_28)))
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_5,plain,
( in(U_30,relation_rng(relation_rng_restriction(U_29,U_28)))
| ~ in(U_30,relation_rng(U_28))
| ~ in(U_30,U_29)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
inference(negate,[status(cth)],[t116_relat_1]) ).
fof(f_23_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_32,U_31] :
( ~ subset(relation_rng(relation_rng_restriction(U_32,U_31)),U_32)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
? [U_31] :
( ~ subset(relation_rng(relation_rng_restriction(sK9,U_31)),sK9)
& relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_32,sK9)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
( ~ subset(relation_rng(relation_rng_restriction(sK9,sK10)),sK9)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_31,sK10)],[f_23_4]) ).
fof(f_23_6,negated_conjecture,
( ~ subset(relation_rng(relation_rng_restriction(sK9,sK10)),sK9)
& relation(sK10) ),
inference(definitional_conversion,[status(esa)],[f_23_5]) ).
cnf(f_23_7,negated_conjecture,
relation(sK10),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_8,negated_conjecture,
~ subset(relation_rng(relation_rng_restriction(sK9,sK10)),sK9),
inference(clausify,[status(thm)],[f_23_6]) ).
fof(f_24_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_24_2,plain,
! [U_34,U_33] :
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( element(U_34,U_33)
| ~ in(U_34,U_33) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_25_2,plain,
! [U_36,U_35] :
( in(U_36,U_35)
| empty(U_35)
| ~ element(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( in(U_36,U_35)
| empty(U_35)
| ~ element(U_36,U_35) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_26_2,plain,
! [U_38,U_37] :
( ( element(U_38,powerset(U_37))
| ~ subset(U_38,U_37) )
& ( subset(U_38,U_37)
| ~ element(U_38,powerset(U_37)) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_42,U_40] :
( element(U_42,powerset(U_40))
| ~ subset(U_42,U_40) )
& ! [U_41,U_39] :
( subset(U_41,U_39)
| ~ element(U_41,powerset(U_39)) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( subset(U_41,U_39)
| ~ element(U_41,powerset(U_39)) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( element(U_42,powerset(U_40))
| ~ subset(U_42,U_40) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_27_2,plain,
! [U_45,U_44,U_43] :
( element(U_45,U_43)
| ~ element(U_44,powerset(U_43))
| ~ in(U_45,U_44) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_45,U_43)
| ~ element(U_44,powerset(U_43))
| ~ in(U_45,U_44) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_28_2,plain,
! [U_48,U_47,U_46] :
( ~ empty(U_46)
| ~ element(U_47,powerset(U_46))
| ~ in(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_48,U_47] :
( ! [U_46] :
( ~ empty(U_46)
| ~ element(U_47,powerset(U_46)) )
| ~ in(U_48,U_47) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ empty(U_46)
| ~ element(U_47,powerset(U_46))
| ~ in(U_48,U_47) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_29_2,plain,
! [U_49] :
( U_49 = empty_set
| ~ empty(U_49) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( U_49 = empty_set
| ~ empty(U_49) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_30_2,plain,
! [U_51,U_50] :
( ~ empty(U_50)
| ~ in(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ~ empty(U_50)
| ~ in(U_51,U_50) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_31_2,plain,
! [U_53,U_52] :
( ~ empty(U_52)
| U_53 = U_52
| ~ empty(U_53) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_53] :
( ! [U_52] :
( ~ empty(U_52)
| U_53 = U_52 )
| ~ empty(U_53) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( ~ empty(U_52)
| U_53 = U_52
| ~ empty(U_53) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
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,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:32:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------