%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU195+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 : n006.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 08:58:26 AM UTC 2026
% Result : Theorem 0.14s 6.98s
% Output : Proof 0.14s
% 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(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_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(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_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_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
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(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t74_relat_1,axiom,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
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(t94_relat_1,conjecture,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
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] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_4,U_3] : unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_4_2,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ? [U_8,U_7] :
( ( ~ in(ordered_pair(U_8,U_7),U_9)
& in(ordered_pair(U_8,U_7),U_11)
& in(U_8,U_10) )
| ( ( ~ in(ordered_pair(U_8,U_7),U_11)
| ~ in(U_8,U_10) )
& in(ordered_pair(U_8,U_7),U_9) ) ) )
& ( ! [U_6,U_5] :
( ( in(ordered_pair(U_6,U_5),U_9)
| ~ in(ordered_pair(U_6,U_5),U_11)
| ~ in(U_6,U_10) )
& ( ( in(ordered_pair(U_6,U_5),U_11)
& in(U_6,U_10) )
| ~ in(ordered_pair(U_6,U_5),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ? [U_19,U_17] :
( ~ in(ordered_pair(U_19,U_17),U_9)
& in(ordered_pair(U_19,U_17),U_11)
& in(U_19,U_10) )
| ? [U_18,U_16] :
( ( ~ in(ordered_pair(U_18,U_16),U_11)
| ~ in(U_18,U_10) )
& in(ordered_pair(U_18,U_16),U_9) ) )
& ( ( ! [U_15,U_13] :
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10) )
& ! [U_14,U_12] :
( ( in(ordered_pair(U_14,U_12),U_11)
& in(U_14,U_10) )
| ~ in(ordered_pair(U_14,U_12),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ? [U_19,U_17] :
( ~ in(ordered_pair(U_19,U_17),U_9)
& in(ordered_pair(U_19,U_17),U_11)
& in(U_19,U_10) )
| ? [U_16] :
( ( ~ in(ordered_pair(sK1(U_11,U_10,U_9),U_16),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_11,U_10,U_9),U_16),U_9) ) )
& ( ( ! [U_15,U_13] :
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10) )
& ! [U_14,U_12] :
( ( in(ordered_pair(U_14,U_12),U_11)
& in(U_14,U_10) )
| ~ in(ordered_pair(U_14,U_12),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_18,sK1(U_11,U_10,U_9))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ? [U_19,U_17] :
( ~ in(ordered_pair(U_19,U_17),U_9)
& in(ordered_pair(U_19,U_17),U_11)
& in(U_19,U_10) )
| ( ( ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9) ) )
& ( ( ! [U_15,U_13] :
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10) )
& ! [U_14,U_12] :
( ( in(ordered_pair(U_14,U_12),U_11)
& in(U_14,U_10) )
| ~ in(ordered_pair(U_14,U_12),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_11,U_10,U_9))],[f_4_4]) ).
fof(f_4_6,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ? [U_17] :
( ~ in(ordered_pair(sK3(U_11,U_10,U_9),U_17),U_9)
& in(ordered_pair(sK3(U_11,U_10,U_9),U_17),U_11)
& in(sK3(U_11,U_10,U_9),U_10) )
| ( ( ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9) ) )
& ( ( ! [U_15,U_13] :
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10) )
& ! [U_14,U_12] :
( ( in(ordered_pair(U_14,U_12),U_11)
& in(U_14,U_10) )
| ~ in(ordered_pair(U_14,U_12),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_11,U_10,U_9))],[f_4_5]) ).
fof(f_4_7,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( U_9 = relation_dom_restriction(U_11,U_10)
| ( ~ in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_9)
& in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_11)
& in(sK3(U_11,U_10,U_9),U_10) )
| ( ( ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9) ) )
& ( ( ! [U_15,U_13] :
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10) )
& ! [U_14,U_12] :
( ( in(ordered_pair(U_14,U_12),U_11)
& in(U_14,U_10) )
| ~ in(ordered_pair(U_14,U_12),U_9) ) )
| U_9 != relation_dom_restriction(U_11,U_10) ) )
| ~ relation(U_9) )
| ~ relation(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_17,sK4(U_11,U_10,U_9))],[f_4_6]) ).
cnf(f_4_8,plain,
( in(U_14,U_10)
| ~ in(ordered_pair(U_14,U_12),U_9)
| U_9 != relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( in(ordered_pair(U_14,U_12),U_11)
| ~ in(ordered_pair(U_14,U_12),U_9)
| U_9 != relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( in(ordered_pair(U_15,U_13),U_9)
| ~ in(ordered_pair(U_15,U_13),U_11)
| ~ in(U_15,U_10)
| U_9 != relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( in(sK3(U_11,U_10,U_9),U_10)
| in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_11)
| in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_9)
| in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_9)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_14,plain,
( in(sK3(U_11,U_10,U_9),U_10)
| ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_15,plain,
( in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_11)
| ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_16,plain,
( ~ in(ordered_pair(sK3(U_11,U_10,U_9),sK4(U_11,U_10,U_9)),U_9)
| ~ in(ordered_pair(sK1(U_11,U_10,U_9),sK2(U_11,U_10,U_9)),U_11)
| ~ in(sK1(U_11,U_10,U_9),U_10)
| U_9 = relation_dom_restriction(U_11,U_10)
| ~ relation(U_9)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_5_2,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ? [U_23,U_22] :
( ( ~ in(ordered_pair(U_23,U_22),U_25)
& in(ordered_pair(U_23,U_22),U_24) )
| ( ~ in(ordered_pair(U_23,U_22),U_24)
& in(ordered_pair(U_23,U_22),U_25) ) ) )
& ( ! [U_21,U_20] :
( ( in(ordered_pair(U_21,U_20),U_25)
| ~ in(ordered_pair(U_21,U_20),U_24) )
& ( in(ordered_pair(U_21,U_20),U_24)
| ~ in(ordered_pair(U_21,U_20),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ? [U_33,U_31] :
( ~ in(ordered_pair(U_33,U_31),U_25)
& in(ordered_pair(U_33,U_31),U_24) )
| ? [U_32,U_30] :
( ~ in(ordered_pair(U_32,U_30),U_24)
& in(ordered_pair(U_32,U_30),U_25) ) )
& ( ( ! [U_29,U_27] :
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24) )
& ! [U_28,U_26] :
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ? [U_33,U_31] :
( ~ in(ordered_pair(U_33,U_31),U_25)
& in(ordered_pair(U_33,U_31),U_24) )
| ? [U_30] :
( ~ in(ordered_pair(sK5(U_25,U_24),U_30),U_24)
& in(ordered_pair(sK5(U_25,U_24),U_30),U_25) ) )
& ( ( ! [U_29,U_27] :
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24) )
& ! [U_28,U_26] :
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_32,sK5(U_25,U_24))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ? [U_33,U_31] :
( ~ in(ordered_pair(U_33,U_31),U_25)
& in(ordered_pair(U_33,U_31),U_24) )
| ( ~ in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_24)
& in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_25) ) )
& ( ( ! [U_29,U_27] :
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24) )
& ! [U_28,U_26] :
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6(U_25,U_24))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ? [U_31] :
( ~ in(ordered_pair(sK7(U_25,U_24),U_31),U_25)
& in(ordered_pair(sK7(U_25,U_24),U_31),U_24) )
| ( ~ in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_24)
& in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_25) ) )
& ( ( ! [U_29,U_27] :
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24) )
& ! [U_28,U_26] :
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7(U_25,U_24))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_25] :
( ! [U_24] :
( ( ( U_25 = U_24
| ( ~ in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_25)
& in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_24) )
| ( ~ in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_24)
& in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_25) ) )
& ( ( ! [U_29,U_27] :
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24) )
& ! [U_28,U_26] :
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25) ) )
| U_25 != U_24 ) )
| ~ relation(U_24) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_31,sK8(U_25,U_24))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(ordered_pair(U_28,U_26),U_24)
| ~ in(ordered_pair(U_28,U_26),U_25)
| U_25 != U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(ordered_pair(U_29,U_27),U_25)
| ~ in(ordered_pair(U_29,U_27),U_24)
| U_25 != U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_24)
| in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_25)
| U_25 = U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( ~ in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_25)
| in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_25)
| U_25 = U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_24)
| ~ in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_24)
| U_25 = U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(ordered_pair(sK7(U_25,U_24),sK8(U_25,U_24)),U_25)
| ~ in(ordered_pair(sK5(U_25,U_24),sK6(U_25,U_24)),U_24)
| U_25 = U_24
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_6_2,plain,
! [U_35,U_34] : ordered_pair(U_35,U_34) = unordered_pair(unordered_pair(U_35,U_34),singleton(U_35)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
ordered_pair(U_35,U_34) = unordered_pair(unordered_pair(U_35,U_34),singleton(U_35)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_11_2,plain,
! [U_37,U_36] :
( relation(relation_composition(U_37,U_36))
| ~ relation(U_36)
| ~ relation(U_37) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(relation_composition(U_37,U_36))
| ~ relation(U_36)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_12_2,plain,
! [U_38] : relation(identity_relation(U_38)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
relation(identity_relation(U_38)),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_13_2,plain,
! [U_40,U_39] :
( relation(relation_dom_restriction(U_40,U_39))
| ~ relation(U_40) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_40] :
( ! [U_39] : relation(relation_dom_restriction(U_40,U_39))
| ~ relation(U_40) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( relation(relation_dom_restriction(U_40,U_39))
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_15_2,plain,
! [U_42] :
? [U_41] : element(U_41,U_42),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_42] : element(sK9(U_42),U_42),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_41,sK9(U_42))],[f_15_2]) ).
cnf(f_15_4,plain,
element(sK9(U_42),U_42),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_16_2,plain,
! [U_44,U_43] :
( ( relation(relation_composition(U_43,U_44))
& empty(relation_composition(U_43,U_44)) )
| ~ relation(U_43)
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( empty(relation_composition(U_43,U_44))
| ~ relation(U_43)
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(relation_composition(U_43,U_44))
| ~ relation(U_43)
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_18_2,plain,
! [U_46,U_45] : ~ empty(ordered_pair(U_46,U_45)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ empty(ordered_pair(U_46,U_45)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_19_2,plain,
! [U_47] : ~ empty(singleton(U_47)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
~ empty(singleton(U_47)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_20_2,plain,
! [U_49,U_48] : ~ empty(unordered_pair(U_49,U_48)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
~ empty(unordered_pair(U_49,U_48)),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_21_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_22_2,plain,
! [U_51,U_50] :
( ( relation(relation_composition(U_51,U_50))
& empty(relation_composition(U_51,U_50)) )
| ~ relation(U_50)
| ~ empty(U_51) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( empty(relation_composition(U_51,U_50))
| ~ relation(U_50)
| ~ empty(U_51) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( relation(relation_composition(U_51,U_50))
| ~ relation(U_50)
| ~ empty(U_51) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_23_2,plain,
? [U_52] :
( relation(U_52)
& empty(U_52) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_52,sK10)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_24_2,plain,
? [U_53] : empty(U_53),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_53,sK11)],[f_24_2]) ).
cnf(f_24_4,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_25_2,plain,
? [U_54] :
( relation(U_54)
& ~ empty(U_54) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_54,sK12)],[f_25_2]) ).
cnf(f_25_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_26_2,plain,
? [U_55] : ~ empty(U_55),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_55,sK13)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_27_2,plain,
! [U_57,U_56] :
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_28_2,plain,
! [U_59,U_58] :
( in(U_59,U_58)
| empty(U_58)
| ~ element(U_59,U_58) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( in(U_59,U_58)
| empty(U_58)
| ~ element(U_59,U_58) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_29_2,plain,
! [U_60] :
( U_60 = empty_set
| ~ empty(U_60) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( U_60 = empty_set
| ~ empty(U_60) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B,C,D] :
( ( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
| ~ in(ordered_pair(A,B),D)
| ~ in(A,C) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(fof_nnf,[status(thm)],[t74_relat_1]) ).
fof(f_30_2,plain,
! [U_64,U_63,U_62,U_61] :
( ( ( in(ordered_pair(U_64,U_63),relation_composition(identity_relation(U_62),U_61))
| ~ in(ordered_pair(U_64,U_63),U_61)
| ~ in(U_64,U_62) )
& ( ( in(ordered_pair(U_64,U_63),U_61)
& in(U_64,U_62) )
| ~ in(ordered_pair(U_64,U_63),relation_composition(identity_relation(U_62),U_61)) ) )
| ~ relation(U_61) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( in(U_64,U_62)
| ~ in(ordered_pair(U_64,U_63),relation_composition(identity_relation(U_62),U_61))
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( in(ordered_pair(U_64,U_63),U_61)
| ~ in(ordered_pair(U_64,U_63),relation_composition(identity_relation(U_62),U_61))
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_5,plain,
( in(ordered_pair(U_64,U_63),relation_composition(identity_relation(U_62),U_61))
| ~ in(ordered_pair(U_64,U_63),U_61)
| ~ in(U_64,U_62)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_31_2,plain,
! [U_66,U_65] :
( ~ empty(U_65)
| ~ in(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ~ empty(U_65)
| ~ in(U_66,U_65) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_32_2,plain,
! [U_68,U_67] :
( ~ empty(U_67)
| U_68 = U_67
| ~ empty(U_68) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_68] :
( ! [U_67] :
( ~ empty(U_67)
| U_68 = U_67 )
| ~ empty(U_68) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ empty(U_67)
| U_68 = U_67
| ~ empty(U_68) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
inference(negate,[status(cth)],[t94_relat_1]) ).
fof(f_33_2,negated_conjecture,
? [A,B] :
( relation_dom_restriction(B,A) != relation_composition(identity_relation(A),B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_70,U_69] :
( relation_dom_restriction(U_69,U_70) != relation_composition(identity_relation(U_70),U_69)
& relation(U_69) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
? [U_69] :
( relation_dom_restriction(U_69,sK14) != relation_composition(identity_relation(sK14),U_69)
& relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_70,sK14)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( relation_dom_restriction(sK15,sK14) != relation_composition(identity_relation(sK14),sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_69,sK15)],[f_33_4]) ).
fof(f_33_6,negated_conjecture,
( relation_dom_restriction(sK15,sK14) != relation_composition(identity_relation(sK14),sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
relation(sK15),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,negated_conjecture,
relation_dom_restriction(sK15,sK14) != relation_composition(identity_relation(sK14),sK15),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_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,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_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_6,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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
% 0.00/0.02 % Problem : SEU195+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/6.61 % Computer : n006.cluster.edu
% 0.11/6.61 % Model : x86_64 x86_64
% 0.11/6.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/6.61 % Memory : 8046.5625MB
% 0.11/6.61 % OS : Linux 6.8.0-71-generic
% 0.11/6.61 % CPULimit : 300
% 0.11/6.61 % WCLimit : 300
% 0.11/6.61 % DateTime : Sat Sep 19 23:29:09 UTC 2026
% 0.11/6.62 % CPUTime :
% 0.14/6.98 % SZS status Theorem for theBenchmark
% 0.14/6.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------