%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n015.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 10:40:35 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 159 ( 99 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 194 ( 10 ~; 0 |; 4 &; 180 @)
% ( 0 <=>; 0 =>; 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 : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_symmetric_difference,type,
symmetric_difference: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(8,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(9,axiom,
! [B: $i] :
( ( difference @ empty_set @ B )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
thf(10,axiom,
! [B: $i] :
( ( difference @ B @ empty_set )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
thf(11,axiom,
! [B: $i] :
( ( union @ B @ empty_set )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
thf(12,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(13,conjecture,
! [B: $i] :
( ( ( symmetric_difference @ B @ empty_set )
= B )
& ( ( symmetric_difference @ empty_set @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
thf(14,negated_conjecture,
( ( ! [B: $i] :
( ( ( symmetric_difference @ B @ empty_set )
= B )
& ( ( symmetric_difference @ empty_set @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [B: $i] :
( ( ( symmetric_difference @ B @ empty_set )
= B )
& ( ( symmetric_difference @ empty_set @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( ! [B: $i] :
( ( difference @ empty_set @ B )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [B: $i] :
( ( difference @ B @ empty_set )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [B: $i] :
( ( union @ B @ empty_set )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(22,plain,
( ( ( ( symmetric_difference @ sK1_B @ empty_set )
= sK1_B )
& ( ( symmetric_difference @ empty_set @ sK1_B )
= sK1_B ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(23,plain,
( ( ( symmetric_difference @ sK1_B @ empty_set )
= sK1_B )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[22]) ).
thf(24,plain,
( ( ( symmetric_difference @ empty_set @ sK1_B )
= sK1_B )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[22]) ).
thf(25,plain,
( ( ( symmetric_difference @ sK1_B @ empty_set )
!= sK1_B )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(26,plain,
( ( ( symmetric_difference @ empty_set @ sK1_B )
!= sK1_B )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [B: $i] :
( ( union @ B @ empty_set )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [B: $i] :
( ( difference @ B @ empty_set )
= B ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [B: $i] :
( ( difference @ empty_set @ B )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ( symmetric_difference @ sK1_B @ empty_set )
!= sK1_B )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY9: $i] :
( ( symmetric_difference @ SV1 @ SY9 )
= ( union @ ( difference @ SV1 @ SY9 ) @ ( difference @ SY9 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( union @ SV2 @ empty_set )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV3: $i] :
( ( ( difference @ SV3 @ empty_set )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( difference @ empty_set @ SV4 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV5: $i] :
( ( ~ ( member @ SV5 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY10: $i] :
( ( symmetric_difference @ SV6 @ SY10 )
= ( symmetric_difference @ SY10 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
( ( ( symmetric_difference @ sK1_B @ empty_set )
= sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV7: $i,SV1: $i] :
( ( ( symmetric_difference @ SV1 @ SV7 )
= ( union @ ( difference @ SV1 @ SV7 ) @ ( difference @ SV7 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV5: $i] :
( ( member @ SV5 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV8: $i,SV6: $i] :
( ( ( symmetric_difference @ SV6 @ SV8 )
= ( symmetric_difference @ SV8 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,43,42,41,40,37,36]) ).
thf(45,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(46,plain,
( ( ! [B: $i] :
( ( union @ B @ empty_set )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [B: $i] :
( ( difference @ B @ empty_set )
= B ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [B: $i] :
( ( difference @ empty_set @ B )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(49,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(50,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(51,plain,
( ( ( symmetric_difference @ empty_set @ sK1_B )
!= sK1_B )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(52,plain,
! [SV9: $i] :
( ( ! [SY11: $i] :
( ( symmetric_difference @ SV9 @ SY11 )
= ( union @ ( difference @ SV9 @ SY11 ) @ ( difference @ SY11 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV10: $i] :
( ( ( union @ SV10 @ empty_set )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV11: $i] :
( ( ( difference @ SV11 @ empty_set )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV12: $i] :
( ( ( difference @ empty_set @ SV12 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV13: $i] :
( ( ~ ( member @ SV13 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV14: $i] :
( ( ! [SY12: $i] :
( ( symmetric_difference @ SV14 @ SY12 )
= ( symmetric_difference @ SY12 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(58,plain,
( ( ( symmetric_difference @ empty_set @ sK1_B )
= sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV15: $i,SV9: $i] :
( ( ( symmetric_difference @ SV9 @ SV15 )
= ( union @ ( difference @ SV9 @ SV15 ) @ ( difference @ SV15 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV13: $i] :
( ( member @ SV13 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV16: $i,SV14: $i] :
( ( ( symmetric_difference @ SV14 @ SV16 )
= ( symmetric_difference @ SV16 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,61,60,59,58,55,54]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:50:43 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 6
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % 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:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 57 ****
% 0.09/0.23 %**** clause counter: 62 ****
% 0.09/0.23
% 0.09/0.23 % 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:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------