%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n019.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 08:59:04 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.13s
% 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_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(d8_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('theBenchmark.p',d8_lattice3) ).
fof(d9_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('theBenchmark.p',d9_lattice3) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_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(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_yellow_0,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('theBenchmark.p',t6_yellow_0) ).
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] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_2_2,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( finite(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ! [B,C] :
( ( ( relstr_element_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d8_lattice3]) ).
fof(f_3_2,plain,
! [U_7] :
( ! [U_6,U_5] :
( ( ( relstr_element_smaller(U_7,U_6,U_5)
| ? [U_4] :
( ~ related(U_7,U_5,U_4)
& in(U_4,U_6)
& element(U_4,the_carrier(U_7)) ) )
& ( ! [U_3] :
( related(U_7,U_5,U_3)
| ~ in(U_3,U_6)
| ~ element(U_3,the_carrier(U_7)) )
| ~ relstr_element_smaller(U_7,U_6,U_5) ) )
| ~ element(U_5,the_carrier(U_7)) )
| ~ rel_str(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_7] :
( ! [U_6,U_5] :
( ( ( relstr_element_smaller(U_7,U_6,U_5)
| ( ~ related(U_7,U_5,sK1(U_7,U_6,U_5))
& in(sK1(U_7,U_6,U_5),U_6)
& element(sK1(U_7,U_6,U_5),the_carrier(U_7)) ) )
& ( ! [U_3] :
( related(U_7,U_5,U_3)
| ~ in(U_3,U_6)
| ~ element(U_3,the_carrier(U_7)) )
| ~ relstr_element_smaller(U_7,U_6,U_5) ) )
| ~ element(U_5,the_carrier(U_7)) )
| ~ rel_str(U_7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1(U_7,U_6,U_5))],[f_3_2]) ).
cnf(f_3_4,plain,
( related(U_7,U_5,U_3)
| ~ in(U_3,U_6)
| ~ element(U_3,the_carrier(U_7))
| ~ relstr_element_smaller(U_7,U_6,U_5)
| ~ element(U_5,the_carrier(U_7))
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( element(sK1(U_7,U_6,U_5),the_carrier(U_7))
| relstr_element_smaller(U_7,U_6,U_5)
| ~ element(U_5,the_carrier(U_7))
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( in(sK1(U_7,U_6,U_5),U_6)
| relstr_element_smaller(U_7,U_6,U_5)
| ~ element(U_5,the_carrier(U_7))
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( ~ related(U_7,U_5,sK1(U_7,U_6,U_5))
| relstr_element_smaller(U_7,U_6,U_5)
| ~ element(U_5,the_carrier(U_7))
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ! [B,C] :
( ( ( relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_lattice3]) ).
fof(f_4_2,plain,
! [U_12] :
( ! [U_11,U_10] :
( ( ( relstr_set_smaller(U_12,U_11,U_10)
| ? [U_9] :
( ~ related(U_12,U_9,U_10)
& in(U_9,U_11)
& element(U_9,the_carrier(U_12)) ) )
& ( ! [U_8] :
( related(U_12,U_8,U_10)
| ~ in(U_8,U_11)
| ~ element(U_8,the_carrier(U_12)) )
| ~ relstr_set_smaller(U_12,U_11,U_10) ) )
| ~ element(U_10,the_carrier(U_12)) )
| ~ rel_str(U_12) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_12] :
( ! [U_11,U_10] :
( ( ( relstr_set_smaller(U_12,U_11,U_10)
| ( ~ related(U_12,sK2(U_12,U_11,U_10),U_10)
& in(sK2(U_12,U_11,U_10),U_11)
& element(sK2(U_12,U_11,U_10),the_carrier(U_12)) ) )
& ( ! [U_8] :
( related(U_12,U_8,U_10)
| ~ in(U_8,U_11)
| ~ element(U_8,the_carrier(U_12)) )
| ~ relstr_set_smaller(U_12,U_11,U_10) ) )
| ~ element(U_10,the_carrier(U_12)) )
| ~ rel_str(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_12,U_11,U_10))],[f_4_2]) ).
cnf(f_4_4,plain,
( related(U_12,U_8,U_10)
| ~ in(U_8,U_11)
| ~ element(U_8,the_carrier(U_12))
| ~ relstr_set_smaller(U_12,U_11,U_10)
| ~ element(U_10,the_carrier(U_12))
| ~ rel_str(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( element(sK2(U_12,U_11,U_10),the_carrier(U_12))
| relstr_set_smaller(U_12,U_11,U_10)
| ~ element(U_10,the_carrier(U_12))
| ~ rel_str(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( in(sK2(U_12,U_11,U_10),U_11)
| relstr_set_smaller(U_12,U_11,U_10)
| ~ element(U_10,the_carrier(U_12))
| ~ rel_str(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( ~ related(U_12,sK2(U_12,U_11,U_10),U_10)
| relstr_set_smaller(U_12,U_11,U_10)
| ~ element(U_10,the_carrier(U_12))
| ~ rel_str(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_6_2,plain,
! [U_13] :
( one_sorted_str(U_13)
| ~ rel_str(U_13) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( one_sorted_str(U_13)
| ~ rel_str(U_13) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_10_2,plain,
? [U_14] : rel_str(U_14),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
rel_str(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_14,sK3)],[f_10_2]) ).
cnf(f_10_4,plain,
rel_str(sK3),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_11_2,plain,
? [U_15] : one_sorted_str(U_15),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
one_sorted_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4)],[f_11_2]) ).
cnf(f_11_4,plain,
one_sorted_str(sK4),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_12_2,plain,
! [U_17] :
? [U_16] : element(U_16,U_17),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_17] : element(sK5(U_17),U_17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_16,sK5(U_17))],[f_12_2]) ).
cnf(f_12_4,plain,
element(sK5(U_17),U_17),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_14_2,plain,
? [U_18] :
( finite(U_18)
& ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( finite(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_18,sK6)],[f_14_2]) ).
cnf(f_14_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
finite(sK6),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_15_2,plain,
? [U_19] : empty(U_19),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_19,sK7)],[f_15_2]) ).
cnf(f_15_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_16_2,plain,
? [U_20] : ~ empty(U_20),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_20,sK8)],[f_16_2]) ).
cnf(f_16_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_17_2,plain,
! [U_22,U_21] :
( element(U_22,U_21)
| ~ in(U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( element(U_22,U_21)
| ~ in(U_22,U_21) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_18_2,plain,
! [U_24,U_23] :
( in(U_24,U_23)
| empty(U_23)
| ~ element(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( in(U_24,U_23)
| empty(U_23)
| ~ element(U_24,U_23) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_19_2,plain,
! [U_25] :
( U_25 = empty_set
| ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( U_25 = empty_set
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(negate,[status(cth)],[t6_yellow_0]) ).
fof(f_20_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ~ relstr_element_smaller(A,empty_set,B)
| ~ relstr_set_smaller(A,empty_set,B) )
& element(B,the_carrier(A)) )
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[f_20_1]) ).
fof(f_20_3,negated_conjecture,
? [U_27] :
( ? [U_26] :
( ( ~ relstr_element_smaller(U_27,empty_set,U_26)
| ~ relstr_set_smaller(U_27,empty_set,U_26) )
& element(U_26,the_carrier(U_27)) )
& rel_str(U_27) ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( ? [U_26] :
( ( ~ relstr_element_smaller(sK9,empty_set,U_26)
| ~ relstr_set_smaller(sK9,empty_set,U_26) )
& element(U_26,the_carrier(sK9)) )
& rel_str(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9)],[f_20_3]) ).
fof(f_20_5,negated_conjecture,
( ( ~ relstr_element_smaller(sK9,empty_set,sK10)
| ~ relstr_set_smaller(sK9,empty_set,sK10) )
& element(sK10,the_carrier(sK9))
& rel_str(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_26,sK10)],[f_20_4]) ).
fof(f_20_6,negated_conjecture,
( ( ~ relstr_element_smaller(sK9,empty_set,sK10)
| ~ relstr_set_smaller(sK9,empty_set,sK10) )
& element(sK10,the_carrier(sK9))
& rel_str(sK9) ),
inference(definitional_conversion,[status(esa)],[f_20_5]) ).
cnf(f_20_7,negated_conjecture,
rel_str(sK9),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,negated_conjecture,
element(sK10,the_carrier(sK9)),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_9,negated_conjecture,
( ~ relstr_element_smaller(sK9,empty_set,sK10)
| ~ relstr_set_smaller(sK9,empty_set,sK10) ),
inference(clausify,[status(thm)],[f_20_6]) ).
fof(f_21_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_21_2,plain,
! [U_29,U_28] :
( ~ empty(U_28)
| ~ in(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ empty(U_28)
| ~ in(U_29,U_28) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_22_2,plain,
! [U_31,U_30] :
( ~ empty(U_30)
| U_31 = U_30
| ~ empty(U_31) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_31] :
( ! [U_30] :
( ~ empty(U_30)
| U_31 = U_30 )
| ~ empty(U_31) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( ~ empty(U_30)
| U_31 = U_30
| ~ empty(U_31) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(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,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,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_13,axiom,
( relstr_element_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_element_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( related(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ related(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( relstr_set_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_set_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| 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 : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 00:02:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------