%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/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 : Wed Oct 7 11:09:37 AM UTC 2026
% Result : Theorem 0.10s 0.21s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 85 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 513 ( 131 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1090 ( 252 ~; 133 |; 15 &; 672 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 253 ( 0 ^; 247 !; 6 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_group_isomorphism_from_to,type,
a_group_isomorphism_from_to: $i > $i > $i > $o ).
thf(tp_a_member_of,type,
a_member_of: $i > $i > $o ).
thf(tp_a_path_from_to_in,type,
a_path_from_to_in: $i > $i > $i > $i > $o ).
thf(tp_alpha_hat,type,
alpha_hat: $i > $i ).
thf(tp_first_homotop_grp,type,
first_homotop_grp: $i > $i > $i ).
thf(tp_isomorphic_groups,type,
isomorphic_groups: $i > $i > $o ).
thf(tp_path_connected,type,
path_connected: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i > $i > $i ).
thf(tp_sK5_SY35,type,
sK5_SY35: $i > $i > $i > $i ).
thf(1,axiom,
! [A: $i,X0: $i,X1: $i,X: $i] :
( ( a_path_from_to_in @ A @ X0 @ X1 @ X )
=> ( a_group_isomorphism_from_to @ ( alpha_hat @ A ) @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_1) ).
thf(2,axiom,
! [X: $i,X0: $i,X1: $i] :
( ( path_connected @ X )
<=> ( ( ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ? [P: $i] : ( a_path_from_to_in @ P @ X0 @ X1 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_connected_defn) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( isomorphic_groups @ A @ B )
<=> ? [F: $i] : ( a_group_isomorphism_from_to @ F @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
thf(4,conjecture,
! [X: $i,X0: $i,X1: $i] :
( ( ( path_connected @ X )
& ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_2) ).
thf(5,negated_conjecture,
( ( ! [X: $i,X0: $i,X1: $i] :
( ( ( path_connected @ X )
& ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X: $i,X0: $i,X1: $i] :
( ( ( path_connected @ X )
& ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [A: $i,X0: $i,X1: $i,X: $i] :
( ( a_path_from_to_in @ A @ X0 @ X1 @ X )
=> ( a_group_isomorphism_from_to @ ( alpha_hat @ A ) @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [X: $i,X0: $i,X1: $i] :
( ( path_connected @ X )
<=> ( ( ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ? [P: $i] : ( a_path_from_to_in @ P @ X0 @ X1 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( isomorphic_groups @ A @ B )
<=> ? [F: $i] : ( a_group_isomorphism_from_to @ F @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY14: $i,SY15: $i] :
( ( ( path_connected @ sK1_X )
& ( a_member_of @ SY14 @ sK1_X )
& ( a_member_of @ SY15 @ sK1_X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ SY14 ) @ ( first_homotop_grp @ sK1_X @ SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY16: $i] :
( ( ( path_connected @ sK1_X )
& ( a_member_of @ sK2_SY14 @ sK1_X )
& ( a_member_of @ SY16 @ sK1_X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ( path_connected @ sK1_X )
& ( a_member_of @ sK2_SY14 @ sK1_X )
& ( a_member_of @ sK3_SY16 @ sK1_X ) )
=> ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ sK3_SY16 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( path_connected @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(14,plain,
( ( a_member_of @ sK2_SY14 @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(15,plain,
( ( a_member_of @ sK3_SY16 @ sK1_X )
= $true ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(16,plain,
( ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ sK3_SY16 ) )
= $false ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ sK3_SY16 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( isomorphic_groups @ A @ B )
<=> ? [F: $i] : ( a_group_isomorphism_from_to @ F @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [X: $i,X0: $i,X1: $i] :
( ( path_connected @ X )
<=> ( ( ( a_member_of @ X0 @ X )
& ( a_member_of @ X1 @ X ) )
=> ? [P: $i] : ( a_path_from_to_in @ P @ X0 @ X1 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [A: $i,X0: $i,X1: $i,X: $i] :
( ( a_path_from_to_in @ A @ X0 @ X1 @ X )
=> ( a_group_isomorphism_from_to @ ( alpha_hat @ A ) @ ( first_homotop_grp @ X @ X0 ) @ ( first_homotop_grp @ X @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(21,plain,
( ( a_member_of @ sK3_SY16 @ sK1_X )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( a_member_of @ sK2_SY14 @ sK1_X )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
( ( path_connected @ sK1_X )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,plain,
( ( ~ ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ sK3_SY16 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( a_path_from_to_in @ SX0 @ SX1 @ SX2 @ SX3 )
| ( a_group_isomorphism_from_to @ ( alpha_hat @ SX0 ) @ ( first_homotop_grp @ SX3 @ SX1 ) @ ( first_homotop_grp @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( path_connected @ SX0 )
| ~ ~ ( ~ ( a_member_of @ SX1 @ SX0 )
| ~ ( a_member_of @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
~ ( a_path_from_to_in @ SX3 @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SX1 @ SX0 )
| ~ ( a_member_of @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
~ ( a_path_from_to_in @ SX3 @ SX1 @ SX2 @ SX0 ) )
| ( path_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( isomorphic_groups @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( a_group_isomorphism_from_to @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( a_group_isomorphism_from_to @ SX2 @ SX0 @ SX1 )
| ( isomorphic_groups @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(28,plain,
( ( isomorphic_groups @ ( first_homotop_grp @ sK1_X @ sK2_SY14 ) @ ( first_homotop_grp @ sK1_X @ sK3_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ~ ( a_path_from_to_in @ SV1 @ SY17 @ SY18 @ SY19 )
| ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SY19 @ SY17 ) @ ( first_homotop_grp @ SY19 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY20: $i,SY21: $i] :
~ ( ~ ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SY20 @ SV2 )
| ~ ( a_member_of @ SY21 @ SV2 ) )
| ~ ! [SY22: $i] :
~ ( a_path_from_to_in @ SY22 @ SY20 @ SY21 @ SV2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SY20 @ SV2 )
| ~ ( a_member_of @ SY21 @ SV2 ) )
| ~ ! [SY23: $i] :
~ ( a_path_from_to_in @ SY23 @ SY20 @ SY21 @ SV2 ) )
| ( path_connected @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
~ ( ~ ( ~ ( isomorphic_groups @ SV3 @ SY24 )
| ~ ! [SY25: $i] :
~ ( a_group_isomorphism_from_to @ SY25 @ SV3 @ SY24 ) )
| ~ ( ~ ~ ! [SY26: $i] :
~ ( a_group_isomorphism_from_to @ SY26 @ SV3 @ SY24 )
| ( isomorphic_groups @ SV3 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( a_path_from_to_in @ SV1 @ SV4 @ SY27 @ SY28 )
| ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SY28 @ SV4 ) @ ( first_homotop_grp @ SY28 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY29: $i] :
~ ( ~ ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SY29 @ SV2 ) )
| ~ ! [SY30: $i] :
~ ( a_path_from_to_in @ SY30 @ SV5 @ SY29 @ SV2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SY29 @ SV2 ) )
| ~ ! [SY31: $i] :
~ ( a_path_from_to_in @ SY31 @ SV5 @ SY29 @ SV2 ) )
| ( path_connected @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( isomorphic_groups @ SV3 @ SV6 )
| ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
| ~ ( ~ ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 )
| ( isomorphic_groups @ SV3 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ! [SY34: $i] :
( ~ ( a_path_from_to_in @ SV1 @ SV4 @ SV7 @ SY34 )
| ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SY34 @ SV4 ) @ ( first_homotop_grp @ SY34 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
| ( path_connected @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( isomorphic_groups @ SV3 @ SV6 )
| ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
| ~ ( ~ ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 )
| ( isomorphic_groups @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( a_path_from_to_in @ SV1 @ SV4 @ SV7 @ SV9 )
| ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SV9 @ SV4 ) @ ( first_homotop_grp @ SV9 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
| ( path_connected @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( isomorphic_groups @ SV3 @ SV6 )
| ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 )
| ( isomorphic_groups @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( a_path_from_to_in @ SV1 @ SV4 @ SV7 @ SV9 ) )
= $true )
| ( ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SV9 @ SV4 ) @ ( first_homotop_grp @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
| ( path_connected @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( isomorphic_groups @ SV3 @ SV6 )
| ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 )
| ( isomorphic_groups @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( a_path_from_to_in @ SV1 @ SV4 @ SV7 @ SV9 )
= $false )
| ( ( a_group_isomorphism_from_to @ ( alpha_hat @ SV1 ) @ ( first_homotop_grp @ SV9 @ SV4 ) @ ( first_homotop_grp @ SV9 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( path_connected @ SV2 )
| ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
| ( path_connected @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( isomorphic_groups @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 ) )
= $true )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( path_connected @ SV2 ) )
= $true )
| ( ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) ) )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV3: $i] :
( ( ( isomorphic_groups @ SV3 @ SV6 )
= $false )
| ( ( ~ ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 ) )
= $false )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ( path_connected @ SV2 )
= $false )
| ( ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
| ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY32: $i] :
~ ( a_group_isomorphism_from_to @ SY32 @ SV3 @ SV6 ) )
= $false )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY33: $i] :
~ ( a_group_isomorphism_from_to @ SY33 @ SV3 @ SV6 ) )
= $true )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV2: $i,SV8: $i,SV5: $i] :
( ( ( ~ ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( a_group_isomorphism_from_to @ ( sK4_SY32 @ SV6 @ SV3 ) @ SV3 @ SV6 ) )
= $false )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(64,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( a_group_isomorphism_from_to @ SV10 @ SV3 @ SV6 ) )
= $true )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) ) )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV2: $i,SV8: $i,SV5: $i] :
( ( ( ! [SY36: $i] :
~ ( a_path_from_to_in @ SY36 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV3: $i,SV6: $i] :
( ( ( a_group_isomorphism_from_to @ ( sK4_SY32 @ SV6 @ SV3 ) @ SV3 @ SV6 )
= $true )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( a_group_isomorphism_from_to @ SV10 @ SV3 @ SV6 )
= $false )
| ( ( isomorphic_groups @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( a_member_of @ SV5 @ SV2 )
| ~ ( a_member_of @ SV8 @ SV2 ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( a_path_from_to_in @ SV11 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( a_member_of @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( a_member_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( a_member_of @ SV5 @ SV2 ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(75,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( a_member_of @ SV8 @ SV2 ) )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV11: $i] :
( ( ( a_path_from_to_in @ SV11 @ SV5 @ SV8 @ SV2 )
= $false )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV8: $i,SV2: $i,SV5: $i] :
( ( ( a_member_of @ SV5 @ SV2 )
= $false )
| ( ( ~ ( a_member_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i,SV5: $i] :
( ( ( a_member_of @ SV5 @ SV2 )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV2: $i,SV8: $i] :
( ( ( a_member_of @ SV8 @ SV2 )
= $true )
| ( ( path_connected @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( a_member_of @ SV8 @ SV2 )
= $false )
| ( ( a_member_of @ SV5 @ SV2 )
= $false )
| ( ( ~ ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $true )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV2: $i,SV8: $i,SV5: $i] :
( ( ( ! [SY35: $i] :
~ ( a_path_from_to_in @ SY35 @ SV5 @ SV8 @ SV2 ) )
= $false )
| ( ( a_member_of @ SV5 @ SV2 )
= $false )
| ( ( a_member_of @ SV8 @ SV2 )
= $false )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(82,plain,
! [SV5: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( a_path_from_to_in @ ( sK5_SY35 @ SV2 @ SV8 @ SV5 ) @ SV5 @ SV8 @ SV2 ) )
= $false )
| ( ( a_member_of @ SV5 @ SV2 )
= $false )
| ( ( a_member_of @ SV8 @ SV2 )
= $false )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(83,plain,
! [SV5: $i,SV8: $i,SV2: $i] :
( ( ( a_path_from_to_in @ ( sK5_SY35 @ SV2 @ SV8 @ SV5 ) @ SV5 @ SV8 @ SV2 )
= $true )
| ( ( a_member_of @ SV5 @ SV2 )
= $false )
| ( ( a_member_of @ SV8 @ SV2 )
= $false )
| ( ( path_connected @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(84,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,83,79,78,76,69,68,47,28,23,22]) ).
thf(85,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 17:55:31 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.21
% 0.10/0.21 No.of.Axioms: 3
% 0.10/0.21
% 0.10/0.21 Length.of.Defs: 0
% 0.10/0.21
% 0.10/0.21 Contains.Choice.Funs: false
% 0.10/0.21 ..
% 0.10/0.21
% 0.10/0.21 ********************************
% 0.10/0.21 * All subproblems solved! *
% 0.10/0.21 ********************************
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:84,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.21
% 0.10/0.21 %**** Beginning of derivation protocol ****
% 0.10/0.21 % SZS output start CNFRefutation
% See solution above
% 0.10/0.21
% 0.10/0.21 %**** End of derivation protocol ****
% 0.10/0.21 %**** no. of clauses in derivation: 85 ****
% 0.10/0.21 %**** clause counter: 84 ****
% 0.10/0.21
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:84,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------