%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CSR138^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 Sep 30 07:46:58 AM UTC 2026
% Result : Theorem 9.79s 3.25s
% Output : Refutation 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 68 ( 48 unt; 0 typ; 8 def)
% Number of atoms : 134 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 253 ( 47 ~; 17 |; 9 &; 172 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 16 con; 0-2 aty)
% Number of variables : 112 ( 34 ^; 45 !; 25 ?; 112 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(num_type,type,
num: $tType ).
thf(believes_THFTYPE_IiooI_decl,type,
believes_THFTYPE_IiooI: $i > $o > $o ).
thf(knows_THFTYPE_IiooI_decl,type,
knows_THFTYPE_IiooI: $i > $o > $o ).
thf(lAnna_THFTYPE_i_decl,type,
lAnna_THFTYPE_i: $i ).
thf(lBen_THFTYPE_i_decl,type,
lBen_THFTYPE_i: $i ).
thf(lBill_THFTYPE_i_decl,type,
lBill_THFTYPE_i: $i ).
thf(lBob_THFTYPE_i_decl,type,
lBob_THFTYPE_i: $i ).
thf(lMary_THFTYPE_i_decl,type,
lMary_THFTYPE_i: $i ).
thf(lSue_THFTYPE_i_decl,type,
lSue_THFTYPE_i: $i ).
thf(likes_THFTYPE_IiioI_decl,type,
likes_THFTYPE_IiioI: $i > $i > $o ).
thf(parent_THFTYPE_IiioI_decl,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(property_THFTYPE_IiioI_decl,type,
property_THFTYPE_IiioI: $i > $i > $o ).
thf(subrelation_THFTYPE_IIoooIIiioIoI_decl,type,
subrelation_THFTYPE_IIoooIIiioIoI: ( $o > $o > $o ) > ( $i > $i > $o ) > $o ).
thf(truth_THFTYPE_IoooI_decl,type,
truth_THFTYPE_IoooI: $o > $o > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] : ( likes_THFTYPE_IiioI @ A @ B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( likes_THFTYPE_IiioI @ sk1 @ A ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] : ( likes_THFTYPE_IiioI @ A @ B ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( likes_THFTYPE_IiioI @ sk3 @ A ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] : ( parent_THFTYPE_IiioI @ A @ B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( parent_THFTYPE_IiioI @ sk5 @ A ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] : ( parent_THFTYPE_IiioI @ A @ B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( parent_THFTYPE_IiioI @ sk7 @ A ) ) ) ).
thf(22,axiom,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_051) ).
thf(69,plain,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_001) ).
thf(56,plain,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
subrelation_THFTYPE_IIoooIIiioIoI @ truth_THFTYPE_IoooI @ property_THFTYPE_IiioI,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_210) ).
thf(52,plain,
subrelation_THFTYPE_IIoooIIiioIoI @ truth_THFTYPE_IoooI @ property_THFTYPE_IiioI,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_085) ).
thf(53,plain,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
? [A: $i,B: $i] :
~ ( parent_THFTYPE_IiioI @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_027) ).
thf(41,plain,
? [A: $i,B: $i] :
~ ( parent_THFTYPE_IiioI @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
? [A: $i,B: $i] :
~ ( likes_THFTYPE_IiioI @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_004) ).
thf(34,plain,
? [A: $i,B: $i] :
~ ( likes_THFTYPE_IiioI @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_073) ).
thf(54,plain,
likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
? [A: $i,B: $i] :
~ ( likes_THFTYPE_IiioI @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_005) ).
thf(37,plain,
? [A: $i,B: $i] :
~ ( likes_THFTYPE_IiioI @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
~ ! [A: $i,B: $i] : ( likes_THFTYPE_IiioI @ A @ B ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
~ ( likes_THFTYPE_IiioI @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[38]) ).
thf(20,axiom,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_050) ).
thf(67,plain,
parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_060) ).
thf(58,plain,
likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
? [A: $i > $i > $o,B: $i > $i > $o,C: $i] :
( ( B @ C @ lBill_THFTYPE_i )
& ( A @ C @ lAnna_THFTYPE_i )
& ( B
!= ( ^ [D: $i,E: $i] : $true ) )
& ( A
!= ( ^ [D: $i,E: $i] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ? [A: $i > $i > $o,B: $i > $i > $o,C: $i] :
( ( B @ C @ lBill_THFTYPE_i )
& ( A @ C @ lAnna_THFTYPE_i )
& ( B
!= ( ^ [D: $i,E: $i] : $true ) )
& ( A
!= ( ^ [D: $i,E: $i] : $true ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ? [A: $i > $i > $o,B: $i > $i > $o,C: $i] :
( ( B @ C @ lBill_THFTYPE_i )
& ( A @ C @ lAnna_THFTYPE_i )
& ( B
!= ( ^ [D: $i,E: $i] : $true ) )
& ( A
!= ( ^ [D: $i,E: $i] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( B @ C @ lBill_THFTYPE_i )
| ~ ( A @ C @ lAnna_THFTYPE_i )
| ( B
= ( ^ [D: $i,E: $i] : $true ) )
| ( A
= ( ^ [D: $i,E: $i] : $true ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( B
= ( ^ [D: $i,E: $i] : $true ) )
| ( A
= ( ^ [D: $i,E: $i] : $true ) )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ~ ( A @ C @ lAnna_THFTYPE_i ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(9,axiom,
? [A: $i,B: $i] :
~ ( parent_THFTYPE_IiioI @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_029) ).
thf(44,plain,
? [A: $i,B: $i] :
~ ( parent_THFTYPE_IiioI @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
~ ! [A: $i,B: $i] : ( parent_THFTYPE_IiioI @ A @ B ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
~ ( parent_THFTYPE_IiioI @ sk7 @ sk8 ),
inference(cnf,[status(esa)],[45]) ).
thf(16,axiom,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax) ).
thf(57,plain,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
! [A: $o,B: $i] :
( ( knows_THFTYPE_IiooI @ B @ A )
=> ( truth_THFTYPE_IoooI @ A @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_018) ).
thf(60,plain,
! [A: $o,B: $i] :
( ( knows_THFTYPE_IiooI @ B @ A )
=> ( truth_THFTYPE_IoooI @ A @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_006) ).
thf(40,plain,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,plain,
! [C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( B
= ( ^ [D: $i,E: $i] : $true ) )
| ( A
= ( ^ [D: $i,E: $i] : $true ) )
| ~ $true
| ~ ( A @ C @ lAnna_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[40,25]) ).
thf(95,plain,
! [C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( B
= ( ^ [D: $i,E: $i] : $true ) )
| ( A
= ( ^ [D: $i,E: $i] : $true ) )
| ~ ( A @ C @ lAnna_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(270,plain,
! [A: $i > $i > $o] :
( ( ( ^ [B: $i,C: $i] : ( parent_THFTYPE_IiioI @ B @ lBen_THFTYPE_i ) )
= ( ^ [B: $i,C: $i] : $true ) )
| ( A
= ( ^ [B: $i,C: $i] : $true ) )
| ~ ( A @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) ),
inference(pre_uni,[status(thm)],[95:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ^ [E: $i] : ( parent_THFTYPE_IiioI @ D @ lBen_THFTYPE_i ) )),bind(C,$thf( lMary_THFTYPE_i ))]]) ).
thf(18,axiom,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_034) ).
thf(59,plain,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(42,plain,
~ ! [A: $i,B: $i] : ( parent_THFTYPE_IiioI @ A @ B ),
inference(miniscope,[status(thm)],[41]) ).
thf(43,plain,
~ ( parent_THFTYPE_IiioI @ sk5 @ sk6 ),
inference(cnf,[status(esa)],[42]) ).
thf(70,plain,
( ~ $true
| ( ( parent_THFTYPE_IiioI @ sk5 @ sk6 )
!= ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[40,43]) ).
thf(71,plain,
( ( parent_THFTYPE_IiioI @ sk5 @ sk6 )
!= ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
( ( sk5 != lMary_THFTYPE_i )
| ( sk6 != lBen_THFTYPE_i ) ),
inference(simp,[status(thm)],[71]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ! [C: $i] :
( ( property_THFTYPE_IiioI @ C @ B )
= ( property_THFTYPE_IiioI @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_071) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ! [C: $i] :
( ( property_THFTYPE_IiioI @ C @ B )
= ( property_THFTYPE_IiioI @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_035) ).
thf(55,plain,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,plain,
~ ! [A: $i,B: $i] : ( likes_THFTYPE_IiioI @ A @ B ),
inference(miniscope,[status(thm)],[34]) ).
thf(36,plain,
~ ( likes_THFTYPE_IiioI @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[35]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ! [C: $i] :
( ( property_THFTYPE_IiioI @ B @ C )
= ( property_THFTYPE_IiioI @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_024) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ! [C: $i] :
( ( property_THFTYPE_IiioI @ B @ C )
= ( property_THFTYPE_IiioI @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $o,B: $i] :
( ( knows_THFTYPE_IiooI @ B @ A )
=> ( believes_THFTYPE_IiooI @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_054) ).
thf(47,plain,
! [A: $o,B: $i] :
( ( knows_THFTYPE_IiooI @ B @ A )
=> ( believes_THFTYPE_IiooI @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_072) ).
thf(68,plain,
likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(736,plain,
$false,
inference(e,[status(thm)],[69,56,52,53,41,34,54,39,67,58,37,25,46,57,60,270,44,59,72,43,40,26,55,23,36,30,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR138^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.22 % Computer : n014.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 17:56:00 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.17/1.18 % [INFO] Parsing done (379ms).
% 2.17/1.20 % [INFO] Running in sequential loop mode.
% 3.48/1.64 % [INFO] eprover registered as external prover.
% 3.48/1.64 % [INFO] Scanning for conjecture ...
% 3.96/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 214 axioms. Running axiom selection ...
% 4.17/1.90 % [INFO] Axiom selection finished. Selected 20 axioms (removed 194 axioms).
% 4.17/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 4.17/1.93 % [INFO] Type checking passed.
% 4.17/1.93 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.79/3.25 % External prover 'e' found a proof!
% 9.79/3.25 % [INFO] Killing All external provers ...
% 9.79/3.25 % Time passed: 2884ms (effective reasoning time: 2051ms)
% 9.79/3.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.79/3.25 % Axioms used in derivation (20): ax_051, ax_085, ax_050, ax_073, ax_054, ax_024, ax_060, ax_005, ax_034, ax_072, ax, ax_004, ax_071, ax_006, ax_001, ax_027, ax_210, ax_035, ax_029, ax_018
% 9.79/3.25 % No. of inferences in proof: 60
% 9.79/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2884 ms resp. 2051 ms w/o parsing
% 9.79/3.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.79/3.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------