%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n012.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 08:57:58 AM UTC 2026
% Result : Theorem 120.54s 120.82s
% Output : Proof 121.45s
% 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(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_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(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_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_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
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(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
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_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
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(t68_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t71_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t71_funct_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(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] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_5_2,plain,
! [U_6,U_5] : set_intersection2(U_6,U_5) = set_intersection2(U_5,U_6),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_intersection2(U_6,U_5) = set_intersection2(U_5,U_6),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_6_2,plain,
! [U_8,U_7] :
( relation(relation_dom_restriction(U_8,U_7))
| ~ relation(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_8] :
( ! [U_7] : relation(relation_dom_restriction(U_8,U_7))
| ~ relation(U_8) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( relation(relation_dom_restriction(U_8,U_7))
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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_10] :
? [U_9] : element(U_9,U_10),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_10] : element(sK1(U_10),U_10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_10))],[f_7_2]) ).
cnf(f_7_4,plain,
element(sK1(U_10),U_10),
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,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_9_2,plain,
! [U_12,U_11] :
( ( relation_empty_yielding(relation_dom_restriction(U_12,U_11))
& relation(relation_dom_restriction(U_12,U_11)) )
| ~ relation_empty_yielding(U_12)
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_12] :
( ( ! [U_14] : relation_empty_yielding(relation_dom_restriction(U_12,U_14))
& ! [U_13] : relation(relation_dom_restriction(U_12,U_13)) )
| ~ relation_empty_yielding(U_12)
| ~ relation(U_12) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( relation(relation_dom_restriction(U_12,U_13))
| ~ relation_empty_yielding(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_12,U_14))
| ~ relation_empty_yielding(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_10_2,plain,
! [U_16,U_15] :
( relation(set_intersection2(U_16,U_15))
| ~ relation(U_15)
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( relation(set_intersection2(U_16,U_15))
| ~ relation(U_15)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_11_2,plain,
! [U_17] : ~ empty(powerset(U_17)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ empty(powerset(U_17)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_12_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_13_2,plain,
! [U_19,U_18] :
( ( function(relation_dom_restriction(U_19,U_18))
& relation(relation_dom_restriction(U_19,U_18)) )
| ~ function(U_19)
| ~ relation(U_19) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_19] :
( ( ! [U_21] : function(relation_dom_restriction(U_19,U_21))
& ! [U_20] : relation(relation_dom_restriction(U_19,U_20)) )
| ~ function(U_19)
| ~ relation(U_19) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( relation(relation_dom_restriction(U_19,U_20))
| ~ function(U_19)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( function(relation_dom_restriction(U_19,U_21))
| ~ function(U_19)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_15_2,plain,
! [U_22] :
( ~ empty(relation_dom(U_22))
| ~ relation(U_22)
| empty(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ empty(relation_dom(U_22))
| ~ relation(U_22)
| empty(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_16_2,plain,
! [U_23] :
( ( relation(relation_dom(U_23))
& empty(relation_dom(U_23)) )
| ~ empty(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( empty(relation_dom(U_23))
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(relation_dom(U_23))
| ~ empty(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_17_2,plain,
! [U_25,U_24] : set_intersection2(U_25,U_25) = U_25,
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_25] : set_intersection2(U_25,U_25) = U_25,
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
set_intersection2(U_25,U_25) = U_25,
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_18_2,plain,
? [U_26] :
( function(U_26)
& relation(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_18_2]) ).
cnf(f_18_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_19_2,plain,
? [U_27] :
( relation(U_27)
& empty(U_27) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_27,sK3)],[f_19_2]) ).
cnf(f_19_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_20_2,plain,
! [U_29] :
( ? [U_28] :
( ~ empty(U_28)
& element(U_28,powerset(U_29)) )
| empty(U_29) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_29] :
( ( ~ empty(sK4(U_29))
& element(sK4(U_29),powerset(U_29)) )
| empty(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4(U_29))],[f_20_2]) ).
cnf(f_20_4,plain,
( element(sK4(U_29),powerset(U_29))
| empty(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ~ empty(sK4(U_29))
| empty(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_21_2,plain,
? [U_30] : empty(U_30),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_30,sK5)],[f_21_2]) ).
cnf(f_21_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_22_2,plain,
? [U_31] :
( function(U_31)
& empty(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( function(sK6)
& empty(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_23_2,plain,
? [U_32] :
( relation(U_32)
& ~ empty(U_32) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_32,sK7)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_24_2,plain,
! [U_34] :
? [U_33] :
( empty(U_33)
& element(U_33,powerset(U_34)) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_34] :
( empty(sK8(U_34))
& element(sK8(U_34),powerset(U_34)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_33,sK8(U_34))],[f_24_2]) ).
cnf(f_24_4,plain,
element(sK8(U_34),powerset(U_34)),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
empty(sK8(U_34)),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_25_2,plain,
? [U_35] : ~ empty(U_35),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_35,sK9)],[f_25_2]) ).
cnf(f_25_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_26_2,plain,
? [U_36] :
( one_to_one(U_36)
& function(U_36)
& relation(U_36) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_36,sK10)],[f_26_2]) ).
cnf(f_26_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_27_2,plain,
? [U_37] :
( relation_empty_yielding(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_37,sK11)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_28_2,plain,
! [U_39,U_38] : subset(U_39,U_39),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_39] : subset(U_39,U_39),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
subset(U_39,U_39),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_29_2,plain,
! [U_41,U_40] :
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_30_2,plain,
! [U_42] : set_intersection2(U_42,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
set_intersection2(U_42,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_31_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_31_1]) ).
cnf(f_31_3,plain,
( in(U_44,U_43)
| empty(U_43)
| ~ element(U_44,U_43) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_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_32_1]) ).
fof(f_32_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_32_2]) ).
cnf(f_32_4,plain,
( subset(U_49,U_47)
| ~ element(U_49,powerset(U_47)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( element(U_50,powerset(U_48))
| ~ subset(U_50,U_48) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_33_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_33_1]) ).
cnf(f_33_3,plain,
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_34_2,plain,
! [U_56,U_55,U_54] :
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54))
| ~ in(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_56,U_55] :
( ! [U_54] :
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54)) )
| ~ in(U_56,U_55) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54))
| ~ in(U_56,U_55) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_35_2,plain,
! [U_61,U_60] :
( ! [U_59] :
( ( ( U_60 = relation_dom_restriction(U_59,U_61)
| ? [U_58] :
( apply(U_60,U_58) != apply(U_59,U_58)
& in(U_58,relation_dom(U_60)) )
| relation_dom(U_60) != set_intersection2(relation_dom(U_59),U_61) )
& ( ( ! [U_57] :
( apply(U_60,U_57) = apply(U_59,U_57)
| ~ in(U_57,relation_dom(U_60)) )
& relation_dom(U_60) = set_intersection2(relation_dom(U_59),U_61) )
| U_60 != relation_dom_restriction(U_59,U_61) ) )
| ~ function(U_59)
| ~ relation(U_59) )
| ~ function(U_60)
| ~ relation(U_60) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_61,U_60] :
( ! [U_59] :
( ( ( U_60 = relation_dom_restriction(U_59,U_61)
| ( apply(U_60,sK12(U_61,U_60,U_59)) != apply(U_59,sK12(U_61,U_60,U_59))
& in(sK12(U_61,U_60,U_59),relation_dom(U_60)) )
| relation_dom(U_60) != set_intersection2(relation_dom(U_59),U_61) )
& ( ( ! [U_57] :
( apply(U_60,U_57) = apply(U_59,U_57)
| ~ in(U_57,relation_dom(U_60)) )
& relation_dom(U_60) = set_intersection2(relation_dom(U_59),U_61) )
| U_60 != relation_dom_restriction(U_59,U_61) ) )
| ~ function(U_59)
| ~ relation(U_59) )
| ~ function(U_60)
| ~ relation(U_60) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12(U_61,U_60,U_59))],[f_35_2]) ).
cnf(f_35_4,plain,
( relation_dom(U_60) = set_intersection2(relation_dom(U_59),U_61)
| U_60 != relation_dom_restriction(U_59,U_61)
| ~ function(U_59)
| ~ relation(U_59)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( apply(U_60,U_57) = apply(U_59,U_57)
| ~ in(U_57,relation_dom(U_60))
| U_60 != relation_dom_restriction(U_59,U_61)
| ~ function(U_59)
| ~ relation(U_59)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( in(sK12(U_61,U_60,U_59),relation_dom(U_60))
| relation_dom(U_60) != set_intersection2(relation_dom(U_59),U_61)
| U_60 = relation_dom_restriction(U_59,U_61)
| ~ function(U_59)
| ~ relation(U_59)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( apply(U_60,sK12(U_61,U_60,U_59)) != apply(U_59,sK12(U_61,U_60,U_59))
| relation_dom(U_60) != set_intersection2(relation_dom(U_59),U_61)
| U_60 = relation_dom_restriction(U_59,U_61)
| ~ function(U_59)
| ~ relation(U_59)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_36_2,plain,
! [U_62] :
( U_62 = empty_set
| ~ empty(U_62) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( U_62 = empty_set
| ~ empty(U_62) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negate,[status(cth)],[t71_funct_1]) ).
fof(f_37_2,negated_conjecture,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,set_intersection2(relation_dom(C),A))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_65,U_64,U_63] :
( apply(relation_dom_restriction(U_63,U_65),U_64) != apply(U_63,U_64)
& in(U_64,set_intersection2(relation_dom(U_63),U_65))
& function(U_63)
& relation(U_63) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
? [U_64,U_63] :
( apply(relation_dom_restriction(U_63,sK13),U_64) != apply(U_63,U_64)
& in(U_64,set_intersection2(relation_dom(U_63),sK13))
& function(U_63)
& relation(U_63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_65,sK13)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
? [U_63] :
( apply(relation_dom_restriction(U_63,sK13),sK14) != apply(U_63,sK14)
& in(sK14,set_intersection2(relation_dom(U_63),sK13))
& function(U_63)
& relation(U_63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_64,sK14)],[f_37_4]) ).
fof(f_37_6,negated_conjecture,
( apply(relation_dom_restriction(sK15,sK13),sK14) != apply(sK15,sK14)
& in(sK14,set_intersection2(relation_dom(sK15),sK13))
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_63,sK15)],[f_37_5]) ).
fof(f_37_7,negated_conjecture,
( apply(relation_dom_restriction(sK15,sK13),sK14) != apply(sK15,sK14)
& in(sK14,set_intersection2(relation_dom(sK15),sK13))
& function(sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_37_6]) ).
cnf(f_37_8,negated_conjecture,
relation(sK15),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_9,negated_conjecture,
function(sK15),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_10,negated_conjecture,
in(sK14,set_intersection2(relation_dom(sK15),sK13)),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_11,negated_conjecture,
apply(relation_dom_restriction(sK15,sK13),sK14) != apply(sK15,sK14),
inference(clausify,[status(thm)],[f_37_7]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_67,U_66] :
( ~ empty(U_66)
| ~ in(U_67,U_66) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( ~ empty(U_66)
| ~ in(U_67,U_66) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_69,U_68] :
( ~ empty(U_68)
| U_69 = U_68
| ~ empty(U_69) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_69] :
( ! [U_68] :
( ~ empty(U_68)
| U_69 = U_68 )
| ~ empty(U_69) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ empty(U_68)
| U_69 = U_68
| ~ empty(U_69) ),
inference(clausify,[status(thm)],[f_39_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,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(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,
( 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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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_19,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_20,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
% 0.00/0.01 % Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 19 23:13:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 120.54/120.82 % SZS status Theorem for theBenchmark
% 120.54/120.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------