%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET940+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:42:37 AM UTC 2026
% Result : Theorem 0.17s 0.29s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 173 ( 79 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 228 ( 24 ~; 12 |; 0 &; 188 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 ^; 76 !; 4 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l52_zfmisc_1) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(9,conjecture,
! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_zfmisc_1) ).
thf(10,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY16: $i] :
( ( union @ ( unordered_pair @ sK1_A @ SY16 ) )
= ( set_union2 @ sK1_A @ SY16 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ( union @ ( unordered_pair @ sK1_A @ sK2_SY16 ) )
= ( set_union2 @ sK1_A @ sK2_SY16 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ( union @ ( unordered_pair @ sK1_A @ sK2_SY16 ) )
!= ( set_union2 @ sK1_A @ sK2_SY16 ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(28,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(33,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(34,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( union @ ( unordered_pair @ A @ B ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(36,plain,
( ( ( union @ ( unordered_pair @ sK1_A @ sK2_SY16 ) )
!= ( set_union2 @ sK1_A @ sK2_SY16 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( empty @ SV1 )
| ! [SY17: $i] :
~ ( empty @ ( set_union2 @ SV1 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
| ! [SY18: $i] :
~ ( empty @ ( set_union2 @ SY18 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( unordered_pair @ SV3 @ SY19 )
= ( unordered_pair @ SY19 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ( set_union2 @ SV4 @ SY20 )
= ( set_union2 @ SY20 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV5: $i] :
( ( ( set_union2 @ SV5 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV6: $i] :
( ( ! [SY21: $i] :
( ( union @ ( unordered_pair @ SV6 @ SY21 ) )
= ( set_union2 @ SV6 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
( ( ( union @ ( unordered_pair @ sK1_A @ sK2_SY16 ) )
= ( set_union2 @ sK1_A @ sK2_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV1: $i] :
( ( ( empty @ SV1 )
= $true )
| ( ( ! [SY17: $i] :
~ ( empty @ ( set_union2 @ SV1 @ SY17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ! [SY18: $i] :
~ ( empty @ ( set_union2 @ SY18 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV7: $i,SV3: $i] :
( ( ( unordered_pair @ SV3 @ SV7 )
= ( unordered_pair @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV8: $i,SV4: $i] :
( ( ( set_union2 @ SV4 @ SV8 )
= ( set_union2 @ SV8 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV9: $i,SV6: $i] :
( ( ( union @ ( unordered_pair @ SV6 @ SV9 ) )
= ( set_union2 @ SV6 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV10: $i,SV1: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV1 @ SV10 ) ) )
= $true )
| ( ( empty @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i,SV11: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV11 @ SV2 ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV10: $i,SV1: $i] :
( ( ( empty @ ( set_union2 @ SV1 @ SV10 ) )
= $false )
| ( ( empty @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV2: $i,SV11: $i] :
( ( ( empty @ ( set_union2 @ SV11 @ SV2 ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,53,52,49,48,47,44,42,41]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET940+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.25 % Computer : n007.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8046.5625MB
% 0.06/0.25 % OS : Linux 6.8.0-71-generic
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Oct 6 14:55:30 UTC 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.29
% 0.17/0.29 No.of.Axioms: 8
% 0.17/0.29
% 0.17/0.29 Length.of.Defs: 0
% 0.17/0.29
% 0.17/0.29 Contains.Choice.Funs: false
% 0.17/0.29 .
% 0.17/0.29
% 0.17/0.29 ********************************
% 0.17/0.29 * All subproblems solved! *
% 0.17/0.29 ********************************
% 0.17/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:54,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.29
% 0.17/0.29 %**** Beginning of derivation protocol ****
% 0.17/0.29 % SZS output start CNFRefutation
% See solution above
% 0.17/0.29
% 0.17/0.29 %**** End of derivation protocol ****
% 0.17/0.29 %**** no. of clauses in derivation: 55 ****
% 0.17/0.29 %**** clause counter: 54 ****
% 0.17/0.29
% 0.17/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:54,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------