%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU150+3 : 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 : n020.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 10:43:05 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 67 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 93 ( 7 ~; 6 |; 0 &; 71 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 ^; 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_SY10,type,
sK3_SY10: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [SY8: $i,SY9: $i] :
( ( ( singleton @ sK1_A )
= ( unordered_pair @ SY8 @ SY9 ) )
=> ( SY8 = SY9 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(11,plain,
( ( ! [SY10: $i] :
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ SY10 ) )
=> ( sK2_SY8 = SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
=> ( sK2_SY8 = sK3_SY10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(14,plain,
( ( sK2_SY8 = sK3_SY10 )
= $false ),
inference(standard_cnf,[status(thm)],[12]) ).
thf(15,plain,
( ( sK2_SY8 != sK3_SY10 )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( sK2_SY8 != sK3_SY10 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( unordered_pair @ SV1 @ SY11 )
= ( unordered_pair @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( sK2_SY8 = sK3_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ( ( singleton @ SV2 )
!= ( unordered_pair @ SY12 @ SY13 ) )
| ( SV2 = SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV3 )
= ( unordered_pair @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY14: $i] :
( ( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SY14 ) )
| ( SV2 = SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SV5 ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SV5 ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ( singleton @ SV2 )
= ( unordered_pair @ SV4 @ SV5 ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,28,24,22]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+3 : 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
% 0.10/0.18 % Computer : n020.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 15:02:51 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.24
% 0.10/0.24 No.of.Axioms: 2
% 0.10/0.24
% 0.10/0.24 Length.of.Defs: 0
% 0.10/0.24
% 0.10/0.24 Contains.Choice.Funs: false
% 0.10/0.24
% 0.10/0.24 ********************************
% 0.10/0.24 * All subproblems solved! *
% 0.10/0.24 ********************************
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.24
% 0.10/0.24 %**** Beginning of derivation protocol ****
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24
% 0.10/0.24 %**** End of derivation protocol ****
% 0.10/0.24 %**** no. of clauses in derivation: 28 ****
% 0.10/0.24 %**** clause counter: 29 ****
% 0.10/0.24
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------