%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET991+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 : n026.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 08:57:55 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_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_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_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(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
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(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t12_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
file('theBenchmark.p',t12_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(f_1_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_1_2,plain,
! [U_1,U_0] : subset(U_1,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1] : subset(U_1,U_1),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
subset(U_1,U_1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_2_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_3_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_4_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_5_2,plain,
! [U_3] :
? [U_2] : element(U_2,U_3),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_3] : element(sK1(U_3),U_3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1(U_3))],[f_5_2]) ).
cnf(f_5_4,plain,
element(sK1(U_3),U_3),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_6_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_7_2,plain,
! [U_5] : ~ empty(powerset(U_5)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
~ empty(powerset(U_5)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_8_2,plain,
! [U_6] :
( ~ empty(relation_dom(U_6))
| ~ relation(U_6)
| empty(U_6) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ empty(relation_dom(U_6))
| ~ relation(U_6)
| empty(U_6) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_9_2,plain,
! [U_7] :
( ~ empty(relation_rng(U_7))
| ~ relation(U_7)
| empty(U_7) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ empty(relation_rng(U_7))
| ~ relation(U_7)
| empty(U_7) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_10_2,plain,
! [U_8] :
( ( relation(relation_dom(U_8))
& empty(relation_dom(U_8)) )
| ~ empty(U_8) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( empty(relation_dom(U_8))
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( relation(relation_dom(U_8))
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_11_2,plain,
! [U_9] :
( ( relation(relation_rng(U_9))
& empty(relation_rng(U_9)) )
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( empty(relation_rng(U_9))
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( relation(relation_rng(U_9))
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_12_2,plain,
! [U_10] :
( relation(U_10)
| ~ empty(U_10) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( relation(U_10)
| ~ empty(U_10) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_13_2,plain,
! [U_12,U_11] :
( in(U_12,U_11)
| empty(U_11)
| ~ element(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( in(U_12,U_11)
| empty(U_11)
| ~ element(U_12,U_11) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_14,U_13] :
( ( element(U_14,powerset(U_13))
| ~ subset(U_14,U_13) )
& ( subset(U_14,U_13)
| ~ element(U_14,powerset(U_13)) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_18,U_16] :
( element(U_18,powerset(U_16))
| ~ subset(U_18,U_16) )
& ! [U_17,U_15] :
( subset(U_17,U_15)
| ~ element(U_17,powerset(U_15)) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_17,U_15)
| ~ element(U_17,powerset(U_15)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( element(U_18,powerset(U_16))
| ~ subset(U_18,U_16) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_15_2,plain,
! [U_21,U_20,U_19] :
( element(U_21,U_19)
| ~ element(U_20,powerset(U_19))
| ~ in(U_21,U_20) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( element(U_21,U_19)
| ~ element(U_20,powerset(U_19))
| ~ in(U_21,U_20) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_16_2,plain,
! [U_24,U_23,U_22] :
( ~ empty(U_22)
| ~ element(U_23,powerset(U_22))
| ~ in(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_24,U_23] :
( ! [U_22] :
( ~ empty(U_22)
| ~ element(U_23,powerset(U_22)) )
| ~ in(U_24,U_23) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( ~ empty(U_22)
| ~ element(U_23,powerset(U_22))
| ~ in(U_24,U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_17_2,plain,
! [U_25] :
( U_25 = empty_set
| ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_25 = empty_set
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_18_2,plain,
! [U_27,U_26] :
( ~ empty(U_26)
| U_27 = U_26
| ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_27] :
( ! [U_26] :
( ~ empty(U_26)
| U_27 = U_26 )
| ~ empty(U_27) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ empty(U_26)
| U_27 = U_26
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_19_2,plain,
! [U_29,U_28] :
( ~ in(U_28,U_29)
| ~ in(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( ~ in(U_28,U_29)
| ~ in(U_29,U_28) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_20_2,plain,
? [U_30] :
( function(U_30)
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2)],[f_20_2]) ).
cnf(f_20_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_21_2,plain,
! [U_32] :
( ? [U_31] :
( ~ empty(U_31)
& element(U_31,powerset(U_32)) )
| empty(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32] :
( ( ~ empty(sK3(U_32))
& element(sK3(U_32),powerset(U_32)) )
| empty(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_31,sK3(U_32))],[f_21_2]) ).
cnf(f_21_4,plain,
( element(sK3(U_32),powerset(U_32))
| empty(U_32) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( ~ empty(sK3(U_32))
| empty(U_32) ),
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_34] :
? [U_33] :
( empty(U_33)
& element(U_33,powerset(U_34)) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_34] :
( empty(sK4(U_34))
& element(sK4(U_34),powerset(U_34)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_34))],[f_22_2]) ).
cnf(f_22_4,plain,
element(sK4(U_34),powerset(U_34)),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
empty(sK4(U_34)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_23_2,plain,
? [U_35] :
( relation(U_35)
& empty(U_35) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_35,sK5)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_24_2,plain,
? [U_36] :
( relation(U_36)
& ~ empty(U_36) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK6),
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_37] :
( relation_empty_yielding(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation_empty_yielding(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_empty_yielding(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_38] : empty(U_38),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_38,sK8)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_39] : ~ empty(U_39),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_39,sK9)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_28_2,plain,
! [U_41,U_40] :
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(U_41,U_40)
| ~ in(U_41,U_40) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_29_2,plain,
! [U_43,U_42] :
( ~ empty(U_42)
| ~ in(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( ~ empty(U_42)
| ~ in(U_43,U_42) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
inference(negate,[status(cth)],[t12_funct_1]) ).
fof(f_30_2,negated_conjecture,
? [A,B] :
( ~ in(apply(B,A),relation_rng(B))
& in(A,relation_dom(B))
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_30_1]) ).
fof(f_30_3,negated_conjecture,
? [U_45,U_44] :
( ~ in(apply(U_44,U_45),relation_rng(U_44))
& in(U_45,relation_dom(U_44))
& function(U_44)
& relation(U_44) ),
inference(variable_rename,[status(thm)],[f_30_2]) ).
fof(f_30_4,negated_conjecture,
? [U_44] :
( ~ in(apply(U_44,sK10),relation_rng(U_44))
& in(sK10,relation_dom(U_44))
& function(U_44)
& relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_45,sK10)],[f_30_3]) ).
fof(f_30_5,negated_conjecture,
( ~ in(apply(sK11,sK10),relation_rng(sK11))
& in(sK10,relation_dom(sK11))
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_44,sK11)],[f_30_4]) ).
fof(f_30_6,negated_conjecture,
( ~ in(apply(sK11,sK10),relation_rng(sK11))
& in(sK10,relation_dom(sK11))
& function(sK11)
& relation(sK11) ),
inference(definitional_conversion,[status(esa)],[f_30_5]) ).
cnf(f_30_7,negated_conjecture,
relation(sK11),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_8,negated_conjecture,
function(sK11),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_9,negated_conjecture,
in(sK10,relation_dom(sK11)),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_10,negated_conjecture,
~ in(apply(sK11,sK10),relation_rng(sK11)),
inference(clausify,[status(thm)],[f_30_6]) ).
fof(f_31_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_31_2,plain,
! [U_53] :
( ! [U_52] :
( ( U_52 = relation_rng(U_53)
| ? [U_51] :
( ( ~ in(U_51,U_52)
& ? [U_50] :
( U_51 = apply(U_53,U_50)
& in(U_50,relation_dom(U_53)) ) )
| ( ! [U_49] :
( U_51 != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(U_51,U_52) ) ) )
& ( ! [U_48] :
( ( in(U_48,U_52)
| ! [U_47] :
( U_48 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ( ? [U_46] :
( U_48 = apply(U_53,U_46)
& in(U_46,relation_dom(U_53)) )
| ~ in(U_48,U_52) ) )
| U_52 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_53] :
( ( ! [U_59] :
( U_59 = relation_rng(U_53)
| ? [U_57] :
( ~ in(U_57,U_59)
& ? [U_50] :
( U_57 = apply(U_53,U_50)
& in(U_50,relation_dom(U_53)) ) )
| ? [U_56] :
( ! [U_49] :
( U_56 != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(U_56,U_59) ) )
& ! [U_58] :
( ( ! [U_55] :
( in(U_55,U_58)
| ! [U_47] :
( U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ! [U_54] :
( ? [U_46] :
( U_54 = apply(U_53,U_46)
& in(U_46,relation_dom(U_53)) )
| ~ in(U_54,U_58) ) )
| U_58 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_53] :
( ( ! [U_59] :
( U_59 = relation_rng(U_53)
| ? [U_57] :
( ~ in(U_57,U_59)
& ? [U_50] :
( U_57 = apply(U_53,U_50)
& in(U_50,relation_dom(U_53)) ) )
| ? [U_56] :
( ! [U_49] :
( U_56 != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(U_56,U_59) ) )
& ! [U_58] :
( ( ! [U_55] :
( in(U_55,U_58)
| ! [U_47] :
( U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ! [U_54] :
( ( U_54 = apply(U_53,sK12(U_53,U_58,U_54))
& in(sK12(U_53,U_58,U_54),relation_dom(U_53)) )
| ~ in(U_54,U_58) ) )
| U_58 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_46,sK12(U_53,U_58,U_54))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_53] :
( ( ! [U_59] :
( U_59 = relation_rng(U_53)
| ? [U_57] :
( ~ in(U_57,U_59)
& ? [U_50] :
( U_57 = apply(U_53,U_50)
& in(U_50,relation_dom(U_53)) ) )
| ( ! [U_49] :
( sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(sK13(U_53,U_59),U_59) ) )
& ! [U_58] :
( ( ! [U_55] :
( in(U_55,U_58)
| ! [U_47] :
( U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ! [U_54] :
( ( U_54 = apply(U_53,sK12(U_53,U_58,U_54))
& in(sK12(U_53,U_58,U_54),relation_dom(U_53)) )
| ~ in(U_54,U_58) ) )
| U_58 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_56,sK13(U_53,U_59))],[f_31_4]) ).
fof(f_31_6,plain,
! [U_53] :
( ( ! [U_59] :
( U_59 = relation_rng(U_53)
| ( ~ in(sK14(U_53,U_59),U_59)
& ? [U_50] :
( sK14(U_53,U_59) = apply(U_53,U_50)
& in(U_50,relation_dom(U_53)) ) )
| ( ! [U_49] :
( sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(sK13(U_53,U_59),U_59) ) )
& ! [U_58] :
( ( ! [U_55] :
( in(U_55,U_58)
| ! [U_47] :
( U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ! [U_54] :
( ( U_54 = apply(U_53,sK12(U_53,U_58,U_54))
& in(sK12(U_53,U_58,U_54),relation_dom(U_53)) )
| ~ in(U_54,U_58) ) )
| U_58 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_57,sK14(U_53,U_59))],[f_31_5]) ).
fof(f_31_7,plain,
! [U_53] :
( ( ! [U_59] :
( U_59 = relation_rng(U_53)
| ( ~ in(sK14(U_53,U_59),U_59)
& sK14(U_53,U_59) = apply(U_53,sK15(U_53,U_59))
& in(sK15(U_53,U_59),relation_dom(U_53)) )
| ( ! [U_49] :
( sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53)) )
& in(sK13(U_53,U_59),U_59) ) )
& ! [U_58] :
( ( ! [U_55] :
( in(U_55,U_58)
| ! [U_47] :
( U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53)) ) )
& ! [U_54] :
( ( U_54 = apply(U_53,sK12(U_53,U_58,U_54))
& in(sK12(U_53,U_58,U_54),relation_dom(U_53)) )
| ~ in(U_54,U_58) ) )
| U_58 != relation_rng(U_53) ) )
| ~ function(U_53)
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_50,sK15(U_53,U_59))],[f_31_6]) ).
cnf(f_31_8,plain,
( in(sK12(U_53,U_58,U_54),relation_dom(U_53))
| ~ in(U_54,U_58)
| U_58 != relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,plain,
( U_54 = apply(U_53,sK12(U_53,U_58,U_54))
| ~ in(U_54,U_58)
| U_58 != relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,plain,
( in(U_55,U_58)
| U_55 != apply(U_53,U_47)
| ~ in(U_47,relation_dom(U_53))
| U_58 != relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_11,plain,
( in(sK15(U_53,U_59),relation_dom(U_53))
| in(sK13(U_53,U_59),U_59)
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_12,plain,
( sK14(U_53,U_59) = apply(U_53,sK15(U_53,U_59))
| in(sK13(U_53,U_59),U_59)
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_13,plain,
( ~ in(sK14(U_53,U_59),U_59)
| in(sK13(U_53,U_59),U_59)
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_14,plain,
( in(sK15(U_53,U_59),relation_dom(U_53))
| sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53))
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_15,plain,
( sK14(U_53,U_59) = apply(U_53,sK15(U_53,U_59))
| sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53))
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_16,plain,
( ~ in(sK14(U_53,U_59),U_59)
| sK13(U_53,U_59) != apply(U_53,U_49)
| ~ in(U_49,relation_dom(U_53))
| U_59 = relation_rng(U_53)
| ~ function(U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_31_7]) ).
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,
( powerset(Eq_x_0) = powerset(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,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK3(Eq_x_0) = sK3(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,
( 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_12,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(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,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(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,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,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_19,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_20,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET991+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
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 23:12:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
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