%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n013.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 08:57:57 AM UTC 2026
% Result : Theorem 192.25s 192.52s
% Output : Proof 192.84s
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_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(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_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_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_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_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
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(t54_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t60_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C,D] :
( ( in(D,relation_dom(B))
& in(C,relation_dom(A)) )
=> ( apply(A,C) = D
<=> apply(B,D) = C ) )
& relation_rng(A) = relation_dom(B)
& relation_dom(A) = relation_rng(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('theBenchmark.p',t60_funct_1) ).
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(t9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C] :
( in(C,relation_dom(A))
=> apply(A,C) = apply(B,C) )
& relation_dom(A) = relation_dom(B) )
=> A = B ) ) ),
file('theBenchmark.p',t9_funct_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] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_5_2,plain,
! [U_12] :
( ! [U_11] :
( ( U_11 = relation_rng(U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& ? [U_9] :
( U_10 = apply(U_12,U_9)
& in(U_9,relation_dom(U_12)) ) )
| ( ! [U_8] :
( U_10 != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(U_10,U_11) ) ) )
& ( ! [U_7] :
( ( in(U_7,U_11)
| ! [U_6] :
( U_7 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ( ? [U_5] :
( U_7 = apply(U_12,U_5)
& in(U_5,relation_dom(U_12)) )
| ~ in(U_7,U_11) ) )
| U_11 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_rng(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] :
( U_16 = apply(U_12,U_9)
& in(U_9,relation_dom(U_12)) ) )
| ? [U_15] :
( ! [U_8] :
( U_15 != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(U_15,U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] :
( U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ! [U_13] :
( ? [U_5] :
( U_13 = apply(U_12,U_5)
& in(U_5,relation_dom(U_12)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_rng(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] :
( U_16 = apply(U_12,U_9)
& in(U_9,relation_dom(U_12)) ) )
| ? [U_15] :
( ! [U_8] :
( U_15 != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(U_15,U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] :
( U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ! [U_13] :
( ( U_13 = apply(U_12,sK1(U_12,U_17,U_13))
& in(sK1(U_12,U_17,U_13),relation_dom(U_12)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_12,U_17,U_13))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_rng(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] :
( U_16 = apply(U_12,U_9)
& in(U_9,relation_dom(U_12)) ) )
| ( ! [U_8] :
( sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] :
( U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ! [U_13] :
( ( U_13 = apply(U_12,sK1(U_12,U_17,U_13))
& in(sK1(U_12,U_17,U_13),relation_dom(U_12)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_12,U_18))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_rng(U_12)
| ( ~ in(sK3(U_12,U_18),U_18)
& ? [U_9] :
( sK3(U_12,U_18) = apply(U_12,U_9)
& in(U_9,relation_dom(U_12)) ) )
| ( ! [U_8] :
( sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] :
( U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ! [U_13] :
( ( U_13 = apply(U_12,sK1(U_12,U_17,U_13))
& in(sK1(U_12,U_17,U_13),relation_dom(U_12)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_12,U_18))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_rng(U_12)
| ( ~ in(sK3(U_12,U_18),U_18)
& sK3(U_12,U_18) = apply(U_12,sK4(U_12,U_18))
& in(sK4(U_12,U_18),relation_dom(U_12)) )
| ( ! [U_8] :
( sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12)) )
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] :
( U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12)) ) )
& ! [U_13] :
( ( U_13 = apply(U_12,sK1(U_12,U_17,U_13))
& in(sK1(U_12,U_17,U_13),relation_dom(U_12)) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_rng(U_12) ) )
| ~ function(U_12)
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_12,U_18))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(sK1(U_12,U_17,U_13),relation_dom(U_12))
| ~ in(U_13,U_17)
| U_17 != relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( U_13 = apply(U_12,sK1(U_12,U_17,U_13))
| ~ in(U_13,U_17)
| U_17 != relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(U_14,U_17)
| U_14 != apply(U_12,U_6)
| ~ in(U_6,relation_dom(U_12))
| U_17 != relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( in(sK4(U_12,U_18),relation_dom(U_12))
| in(sK2(U_12,U_18),U_18)
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( sK3(U_12,U_18) = apply(U_12,sK4(U_12,U_18))
| in(sK2(U_12,U_18),U_18)
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(sK3(U_12,U_18),U_18)
| in(sK2(U_12,U_18),U_18)
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_14,plain,
( in(sK4(U_12,U_18),relation_dom(U_12))
| sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12))
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_15,plain,
( sK3(U_12,U_18) = apply(U_12,sK4(U_12,U_18))
| sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12))
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_16,plain,
( ~ in(sK3(U_12,U_18),U_18)
| sK2(U_12,U_18) != apply(U_12,U_8)
| ~ in(U_8,relation_dom(U_12))
| U_18 = relation_rng(U_12)
| ~ function(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_6_2,plain,
! [U_19] :
( ( function(function_inverse(U_19))
& relation(function_inverse(U_19)) )
| ~ function(U_19)
| ~ relation(U_19) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(function_inverse(U_19))
| ~ function(U_19)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(function_inverse(U_19))
| ~ function(U_19)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_7_2,plain,
! [U_21] :
? [U_20] : element(U_20,U_21),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_21] : element(sK5(U_21),U_21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5(U_21))],[f_7_2]) ).
cnf(f_7_4,plain,
element(sK5(U_21),U_21),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_8_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_9_2,plain,
! [U_22] : ~ empty(powerset(U_22)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
~ empty(powerset(U_22)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_11_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_12_2,plain,
! [U_23] :
( ~ empty(relation_dom(U_23))
| ~ relation(U_23)
| empty(U_23) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ~ empty(relation_dom(U_23))
| ~ relation(U_23)
| empty(U_23) ),
inference(clausify,[status(thm)],[f_12_2]) ).
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_24] :
( ~ empty(relation_rng(U_24))
| ~ relation(U_24)
| empty(U_24) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ~ empty(relation_rng(U_24))
| ~ relation(U_24)
| empty(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_14_2,plain,
! [U_25] :
( ( relation(relation_dom(U_25))
& empty(relation_dom(U_25)) )
| ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( empty(relation_dom(U_25))
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( relation(relation_dom(U_25))
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_15_2,plain,
! [U_26] :
( ( relation(relation_rng(U_26))
& empty(relation_rng(U_26)) )
| ~ empty(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( empty(relation_rng(U_26))
| ~ empty(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( relation(relation_rng(U_26))
| ~ empty(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_16_2,plain,
? [U_27] :
( function(U_27)
& relation(U_27) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_16_2]) ).
cnf(f_16_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
function(sK6),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_17_2,plain,
? [U_28] :
( relation(U_28)
& empty(U_28) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_28,sK7)],[f_17_2]) ).
cnf(f_17_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_18_2,plain,
! [U_30] :
( ? [U_29] :
( ~ empty(U_29)
& element(U_29,powerset(U_30)) )
| empty(U_30) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_30] :
( ( ~ empty(sK8(U_30))
& element(sK8(U_30),powerset(U_30)) )
| empty(U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_29,sK8(U_30))],[f_18_2]) ).
cnf(f_18_4,plain,
( element(sK8(U_30),powerset(U_30))
| empty(U_30) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ empty(sK8(U_30))
| empty(U_30) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_19_2,plain,
? [U_31] : empty(U_31),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_31,sK9)],[f_19_2]) ).
cnf(f_19_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_20_2,plain,
? [U_32] :
( function(U_32)
& empty(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_32,sK10)],[f_20_2]) ).
cnf(f_20_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
function(sK10),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_21_2,plain,
? [U_33] :
( relation(U_33)
& ~ empty(U_33) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_33,sK11)],[f_21_2]) ).
cnf(f_21_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_22_2,plain,
! [U_35] :
? [U_34] :
( empty(U_34)
& element(U_34,powerset(U_35)) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_35] :
( empty(sK12(U_35))
& element(sK12(U_35),powerset(U_35)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_34,sK12(U_35))],[f_22_2]) ).
cnf(f_22_4,plain,
element(sK12(U_35),powerset(U_35)),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
empty(sK12(U_35)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_23_2,plain,
? [U_36] : ~ empty(U_36),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_36,sK13)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_24_2,plain,
? [U_37] :
( one_to_one(U_37)
& function(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( one_to_one(sK14)
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_37,sK14)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
function(sK14),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
one_to_one(sK14),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_25_2,plain,
? [U_38] :
( relation_empty_yielding(U_38)
& relation(U_38) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation_empty_yielding(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_38,sK15)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_empty_yielding(sK15),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_26_2,plain,
! [U_40,U_39] : subset(U_40,U_40),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_40] : subset(U_40,U_40),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
subset(U_40,U_40),
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_42,U_41] :
( element(U_42,U_41)
| ~ in(U_42,U_41) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_42,U_41)
| ~ in(U_42,U_41) ),
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_44,U_43] :
( in(U_44,U_43)
| empty(U_43)
| ~ element(U_44,U_43) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( in(U_44,U_43)
| empty(U_43)
| ~ element(U_44,U_43) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_46,U_45] :
( ( element(U_46,powerset(U_45))
| ~ subset(U_46,U_45) )
& ( subset(U_46,U_45)
| ~ element(U_46,powerset(U_45)) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_50,U_48] :
( element(U_50,powerset(U_48))
| ~ subset(U_50,U_48) )
& ! [U_49,U_47] :
( subset(U_49,U_47)
| ~ element(U_49,powerset(U_47)) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( subset(U_49,U_47)
| ~ element(U_49,powerset(U_47)) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
( element(U_50,powerset(U_48))
| ~ subset(U_50,U_48) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_30_2,plain,
! [U_53,U_52,U_51] :
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_31_2,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ? [U_57,U_56] :
( ( ( U_56 != apply(U_58,U_57)
| ~ in(U_57,relation_rng(U_59)) )
& U_57 = apply(U_59,U_56)
& in(U_56,relation_dom(U_59)) )
| ( ( U_57 != apply(U_59,U_56)
| ~ in(U_56,relation_dom(U_59)) )
& U_56 = apply(U_58,U_57)
& in(U_57,relation_rng(U_59)) ) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_55,U_54] :
( ( ( U_54 = apply(U_58,U_55)
& in(U_55,relation_rng(U_59)) )
| U_55 != apply(U_59,U_54)
| ~ in(U_54,relation_dom(U_59)) )
& ( ( U_55 = apply(U_59,U_54)
& in(U_54,relation_dom(U_59)) )
| U_54 != apply(U_58,U_55)
| ~ in(U_55,relation_rng(U_59)) ) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ? [U_67,U_65] :
( ( U_65 != apply(U_58,U_67)
| ~ in(U_67,relation_rng(U_59)) )
& U_67 = apply(U_59,U_65)
& in(U_65,relation_dom(U_59)) )
| ? [U_66,U_64] :
( ( U_66 != apply(U_59,U_64)
| ~ in(U_64,relation_dom(U_59)) )
& U_64 = apply(U_58,U_66)
& in(U_66,relation_rng(U_59)) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_63,U_61] :
( ( U_61 = apply(U_58,U_63)
& in(U_63,relation_rng(U_59)) )
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59)) )
& ! [U_62,U_60] :
( ( U_62 = apply(U_59,U_60)
& in(U_60,relation_dom(U_59)) )
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59)) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ? [U_67,U_65] :
( ( U_65 != apply(U_58,U_67)
| ~ in(U_67,relation_rng(U_59)) )
& U_67 = apply(U_59,U_65)
& in(U_65,relation_dom(U_59)) )
| ? [U_64] :
( ( sK16(U_59,U_58) != apply(U_59,U_64)
| ~ in(U_64,relation_dom(U_59)) )
& U_64 = apply(U_58,sK16(U_59,U_58))
& in(sK16(U_59,U_58),relation_rng(U_59)) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_63,U_61] :
( ( U_61 = apply(U_58,U_63)
& in(U_63,relation_rng(U_59)) )
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59)) )
& ! [U_62,U_60] :
( ( U_62 = apply(U_59,U_60)
& in(U_60,relation_dom(U_59)) )
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59)) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16(U_59,U_58))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ? [U_67,U_65] :
( ( U_65 != apply(U_58,U_67)
| ~ in(U_67,relation_rng(U_59)) )
& U_67 = apply(U_59,U_65)
& in(U_65,relation_dom(U_59)) )
| ( ( sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59)) )
& sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
& in(sK16(U_59,U_58),relation_rng(U_59)) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_63,U_61] :
( ( U_61 = apply(U_58,U_63)
& in(U_63,relation_rng(U_59)) )
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59)) )
& ! [U_62,U_60] :
( ( U_62 = apply(U_59,U_60)
& in(U_60,relation_dom(U_59)) )
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59)) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_64,sK17(U_59,U_58))],[f_31_4]) ).
fof(f_31_6,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ? [U_65] :
( ( U_65 != apply(U_58,sK18(U_59,U_58))
| ~ in(sK18(U_59,U_58),relation_rng(U_59)) )
& sK18(U_59,U_58) = apply(U_59,U_65)
& in(U_65,relation_dom(U_59)) )
| ( ( sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59)) )
& sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
& in(sK16(U_59,U_58),relation_rng(U_59)) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_63,U_61] :
( ( U_61 = apply(U_58,U_63)
& in(U_63,relation_rng(U_59)) )
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59)) )
& ! [U_62,U_60] :
( ( U_62 = apply(U_59,U_60)
& in(U_60,relation_dom(U_59)) )
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59)) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_67,sK18(U_59,U_58))],[f_31_5]) ).
fof(f_31_7,plain,
! [U_59] :
( ! [U_58] :
( ( ( U_58 = function_inverse(U_59)
| ( ( sK19(U_59,U_58) != apply(U_58,sK18(U_59,U_58))
| ~ in(sK18(U_59,U_58),relation_rng(U_59)) )
& sK18(U_59,U_58) = apply(U_59,sK19(U_59,U_58))
& in(sK19(U_59,U_58),relation_dom(U_59)) )
| ( ( sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59)) )
& sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
& in(sK16(U_59,U_58),relation_rng(U_59)) )
| relation_dom(U_58) != relation_rng(U_59) )
& ( ( ! [U_63,U_61] :
( ( U_61 = apply(U_58,U_63)
& in(U_63,relation_rng(U_59)) )
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59)) )
& ! [U_62,U_60] :
( ( U_62 = apply(U_59,U_60)
& in(U_60,relation_dom(U_59)) )
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59)) )
& relation_dom(U_58) = relation_rng(U_59) )
| U_58 != function_inverse(U_59) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_65,sK19(U_59,U_58))],[f_31_6]) ).
cnf(f_31_8,plain,
( relation_dom(U_58) = relation_rng(U_59)
| U_58 != function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,plain,
( in(U_60,relation_dom(U_59))
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59))
| U_58 != function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,plain,
( U_62 = apply(U_59,U_60)
| U_60 != apply(U_58,U_62)
| ~ in(U_62,relation_rng(U_59))
| U_58 != function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_11,plain,
( in(U_63,relation_rng(U_59))
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59))
| U_58 != function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_12,plain,
( U_61 = apply(U_58,U_63)
| U_63 != apply(U_59,U_61)
| ~ in(U_61,relation_dom(U_59))
| U_58 != function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_13,plain,
( in(sK19(U_59,U_58),relation_dom(U_59))
| in(sK16(U_59,U_58),relation_rng(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_14,plain,
( sK18(U_59,U_58) = apply(U_59,sK19(U_59,U_58))
| in(sK16(U_59,U_58),relation_rng(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_15,plain,
( in(sK19(U_59,U_58),relation_dom(U_59))
| sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_16,plain,
( sK18(U_59,U_58) = apply(U_59,sK19(U_59,U_58))
| sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_17,plain,
( in(sK16(U_59,U_58),relation_rng(U_59))
| sK19(U_59,U_58) != apply(U_58,sK18(U_59,U_58))
| ~ in(sK18(U_59,U_58),relation_rng(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_18,plain,
( sK17(U_59,U_58) = apply(U_58,sK16(U_59,U_58))
| sK19(U_59,U_58) != apply(U_58,sK18(U_59,U_58))
| ~ in(sK18(U_59,U_58),relation_rng(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_19,plain,
( in(sK19(U_59,U_58),relation_dom(U_59))
| sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_20,plain,
( sK18(U_59,U_58) = apply(U_59,sK19(U_59,U_58))
| sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_21,plain,
( sK19(U_59,U_58) != apply(U_58,sK18(U_59,U_58))
| ~ in(sK18(U_59,U_58),relation_rng(U_59))
| sK16(U_59,U_58) != apply(U_59,sK17(U_59,U_58))
| ~ in(sK17(U_59,U_58),relation_dom(U_59))
| relation_dom(U_58) != relation_rng(U_59)
| U_58 = function_inverse(U_59)
| ~ function(U_58)
| ~ relation(U_58)
| ~ one_to_one(U_59)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_31_7]) ).
fof(f_32_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_32_2,plain,
! [U_70,U_69,U_68] :
( ~ empty(U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_70,U_69] :
( ! [U_68] :
( ~ empty(U_68)
| ~ element(U_69,powerset(U_68)) )
| ~ in(U_70,U_69) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ empty(U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C,D] :
( ( in(D,relation_dom(B))
& in(C,relation_dom(A)) )
=> ( apply(A,C) = D
<=> apply(B,D) = C ) )
& relation_rng(A) = relation_dom(B)
& relation_dom(A) = relation_rng(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
inference(negate,[status(cth)],[t60_funct_1]) ).
fof(f_33_2,negated_conjecture,
? [A] :
( ? [B] :
( B != function_inverse(A)
& ! [C,D] :
( ( ( apply(A,C) = D
| apply(B,D) != C )
& ( apply(B,D) = C
| apply(A,C) != D ) )
| ~ in(D,relation_dom(B))
| ~ in(C,relation_dom(A)) )
& relation_rng(A) = relation_dom(B)
& relation_dom(A) = relation_rng(B)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_74] :
( ? [U_73] :
( U_73 != function_inverse(U_74)
& ! [U_72,U_71] :
( ( ( apply(U_74,U_72) = U_71
| apply(U_73,U_71) != U_72 )
& ( apply(U_73,U_71) = U_72
| apply(U_74,U_72) != U_71 ) )
| ~ in(U_71,relation_dom(U_73))
| ~ in(U_72,relation_dom(U_74)) )
& relation_rng(U_74) = relation_dom(U_73)
& relation_dom(U_74) = relation_rng(U_73)
& one_to_one(U_74)
& function(U_73)
& relation(U_73) )
& function(U_74)
& relation(U_74) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
( ? [U_73] :
( U_73 != function_inverse(sK20)
& ! [U_72,U_71] :
( ( ( apply(sK20,U_72) = U_71
| apply(U_73,U_71) != U_72 )
& ( apply(U_73,U_71) = U_72
| apply(sK20,U_72) != U_71 ) )
| ~ in(U_71,relation_dom(U_73))
| ~ in(U_72,relation_dom(sK20)) )
& relation_rng(sK20) = relation_dom(U_73)
& relation_dom(sK20) = relation_rng(U_73)
& one_to_one(sK20)
& function(U_73)
& relation(U_73) )
& function(sK20)
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_74,sK20)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( sK21 != function_inverse(sK20)
& ! [U_72,U_71] :
( ( ( apply(sK20,U_72) = U_71
| apply(sK21,U_71) != U_72 )
& ( apply(sK21,U_71) = U_72
| apply(sK20,U_72) != U_71 ) )
| ~ in(U_71,relation_dom(sK21))
| ~ in(U_72,relation_dom(sK20)) )
& relation_rng(sK20) = relation_dom(sK21)
& relation_dom(sK20) = relation_rng(sK21)
& one_to_one(sK20)
& function(sK21)
& relation(sK21)
& function(sK20)
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_73,sK21)],[f_33_4]) ).
cnf(f_33_6,negated_conjecture,
relation(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
function(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,negated_conjecture,
relation(sK21),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_9,negated_conjecture,
function(sK21),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_10,negated_conjecture,
one_to_one(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_11,negated_conjecture,
relation_dom(sK20) = relation_rng(sK21),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_12,negated_conjecture,
relation_rng(sK20) = relation_dom(sK21),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_13,negated_conjecture,
( apply(sK21,U_71) = U_72
| apply(sK20,U_72) != U_71
| ~ in(U_71,relation_dom(sK21))
| ~ in(U_72,relation_dom(sK20)) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_14,negated_conjecture,
( apply(sK20,U_72) = U_71
| apply(sK21,U_71) != U_72
| ~ in(U_71,relation_dom(sK21))
| ~ in(U_72,relation_dom(sK20)) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_15,negated_conjecture,
sK21 != function_inverse(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_75] :
( U_75 = empty_set
| ~ empty(U_75) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_75 = empty_set
| ~ empty(U_75) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_77,U_76] :
( ~ empty(U_76)
| ~ in(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_76)
| ~ in(U_77,U_76) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_79,U_78] :
( ~ empty(U_78)
| U_79 = U_78
| ~ empty(U_79) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_79] :
( ! [U_78] :
( ~ empty(U_78)
| U_79 = U_78 )
| ~ empty(U_79) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_78)
| U_79 = U_78
| ~ empty(U_79) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
( ! [B] :
( A = B
| ? [C] :
( apply(A,C) != apply(B,C)
& in(C,relation_dom(A)) )
| relation_dom(A) != relation_dom(B)
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t9_funct_1]) ).
fof(f_37_2,plain,
! [U_82] :
( ! [U_81] :
( U_82 = U_81
| ? [U_80] :
( apply(U_82,U_80) != apply(U_81,U_80)
& in(U_80,relation_dom(U_82)) )
| relation_dom(U_82) != relation_dom(U_81)
| ~ function(U_81)
| ~ relation(U_81) )
| ~ function(U_82)
| ~ relation(U_82) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_82] :
( ! [U_81] :
( U_82 = U_81
| ( apply(U_82,sK22(U_82,U_81)) != apply(U_81,sK22(U_82,U_81))
& in(sK22(U_82,U_81),relation_dom(U_82)) )
| relation_dom(U_82) != relation_dom(U_81)
| ~ function(U_81)
| ~ relation(U_81) )
| ~ function(U_82)
| ~ relation(U_82) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_80,sK22(U_82,U_81))],[f_37_2]) ).
cnf(f_37_4,plain,
( in(sK22(U_82,U_81),relation_dom(U_82))
| relation_dom(U_82) != relation_dom(U_81)
| U_82 = U_81
| ~ function(U_81)
| ~ relation(U_81)
| ~ function(U_82)
| ~ relation(U_82) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( apply(U_82,sK22(U_82,U_81)) != apply(U_81,sK22(U_82,U_81))
| relation_dom(U_82) != relation_dom(U_81)
| U_82 = U_81
| ~ function(U_81)
| ~ relation(U_81)
| ~ function(U_82)
| ~ relation(U_82) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
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(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(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,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(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,
( sK17(Eq_x_0,Eq_x_1) = sK17(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,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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(equality_27,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 23:13:06 UTC 2026
% 0.07/0.34 % CPUTime :
% 192.25/192.52 % SZS status Theorem for theBenchmark
% 192.25/192.52 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------