%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CSR137^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 07:46:57 AM UTC 2026
% Result : Theorem 105.83s 54.31s
% Output : Refutation 105.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 362 ( 64 ~; 55 |; 9 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 120 ( 0 ^; 111 !; 9 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(num_type,type,
num: $tType ).
thf(lAnna_THFTYPE_i_decl,type,
lAnna_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(parent_THFTYPE_IiioI_decl,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(26,axiom,
~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_025) ).
thf(78,plain,
~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,plain,
~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(31,axiom,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_005) ).
thf(85,plain,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,conjecture,
? [A: $i > $i > $o,B: $i > $i > $o,C: $i] :
( ( B @ C @ lBill_THFTYPE_i )
& ( A @ C @ lAnna_THFTYPE_i )
& ~ ! [D: $i,E: $i] : ( B @ D @ E )
& ~ ! [D: $i,E: $i] : ( A @ D @ E ) ),
file('/export/starexec/sandbox/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 )
& ~ ! [D: $i,E: $i] : ( B @ D @ E )
& ~ ! [D: $i,E: $i] : ( A @ D @ E ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ? [A: $i > $i > $o,B: $i > $i > $o,C: $i] :
( ( B @ C @ lBill_THFTYPE_i )
& ( A @ C @ lAnna_THFTYPE_i )
& ~ ! [D: $i,E: $i] : ( B @ D @ E )
& ~ ! [D: $i,E: $i] : ( A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( B @ C @ lBill_THFTYPE_i )
| ~ ( A @ C @ lAnna_THFTYPE_i )
| ( B @ D @ E )
| ( A @ F @ G ) ),
inference(cnf,[status(esa)],[38]) ).
thf(125,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( B @ C @ lBill_THFTYPE_i )
| ( B @ D @ E )
| ( A @ F @ G )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[39]) ).
thf(188,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( B @ C @ lBill_THFTYPE_i )
| ( B @ D @ E )
| ( A @ F @ G )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(pre_uni,[status(thm)],[125:[]]) ).
thf(189,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ F @ G )
| ( B @ D @ E )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(pre_uni,[status(thm)],[188:[]]) ).
thf(7798,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ F @ G )
| ( B @ D @ E )
| ~ $true
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[85,189]) ).
thf(7799,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ F @ G )
| ( B @ D @ E )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[7798]) ).
thf(8276,plain,
! [D: $i,C: $i,B: $i,A: $i > $i > $o] :
( ( A @ C @ D )
| ( parent_THFTYPE_IiioI @ B @ lAnna_THFTYPE_i )
| ( ( A @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(pre_uni,[status(thm)],[7799:[bind(A,$thf( A )),bind(B,$thf( ^ [H: $i] : ^ [I: $i] : ( parent_THFTYPE_IiioI @ H @ lAnna_THFTYPE_i ) )),bind(C,$thf( lMary_THFTYPE_i )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(8283,plain,
! [B: $i,A: $i] :
( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ B @ lAnna_THFTYPE_i ) ),
inference(pre_uni,[status(thm)],[8276:[bind(A,$thf( ^ [E: $i] : ^ [F: $i] : ( parent_THFTYPE_IiioI @ E @ lAnna_THFTYPE_i ) )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(8825,plain,
! [B: $i,A: $i] :
( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ B @ lAnna_THFTYPE_i ) ),
inference(simp,[status(thm)],[8283]) ).
thf(7732,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( B @ D @ E )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ~ $true
| ( ( A @ F @ G )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[189,79]) ).
thf(7733,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( B @ D @ E )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ( ( A @ F @ G )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[7732]) ).
thf(8109,plain,
! [D: $i,C: $i,B: $i,A: $i > $i > $o] :
( ( A @ C @ D )
| ~ ( A @ B @ lBill_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i )
!= ( A @ B @ lBill_THFTYPE_i ) ) ),
inference(pre_uni,[status(thm)],[7733:[bind(A,$thf( ^ [H: $i] : ^ [I: $i] : ( parent_THFTYPE_IiioI @ I @ lAnna_THFTYPE_i ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( lBob_THFTYPE_i ))]]) ).
thf(8118,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i ) ),
inference(pre_uni,[status(thm)],[8109:[bind(A,$thf( ^ [E: $i] : ^ [F: $i] : ( parent_THFTYPE_IiioI @ E @ lAnna_THFTYPE_i ) )),bind(B,$thf( lAnna_THFTYPE_i )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(9238,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i ) ),
inference(simp,[status(thm)],[8118]) ).
thf(7734,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ F @ G )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ~ $true
| ( ( B @ D @ E )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[189,79]) ).
thf(7735,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ F @ G )
| ~ ( B @ C @ lBill_THFTYPE_i )
| ( ( A @ C @ lAnna_THFTYPE_i )
!= ( B @ C @ lBill_THFTYPE_i ) )
| ( ( B @ D @ E )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[7734]) ).
thf(8217,plain,
! [D: $i,C: $i,B: $i,A: $i > $i > $o] :
( ( A @ C @ D )
| ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i )
| ( ( A @ B @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(pre_uni,[status(thm)],[7735:[bind(A,$thf( A )),bind(B,$thf( ^ [H: $i] : ^ [I: $i] : ( parent_THFTYPE_IiioI @ I @ lAnna_THFTYPE_i ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( lBob_THFTYPE_i )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(8228,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i ) ),
inference(pre_uni,[status(thm)],[8217:[bind(A,$thf( ^ [E: $i] : ^ [F: $i] : ( parent_THFTYPE_IiioI @ E @ lAnna_THFTYPE_i ) )),bind(B,$thf( lBill_THFTYPE_i )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(8788,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i )
| ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i ) ),
inference(simp,[status(thm)],[8228]) ).
thf(33095,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i )
| ~ $true
| ( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[8788,79]) ).
thf(33096,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[33095]) ).
thf(33097,plain,
~ ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ),
inference(pattern_uni,[status(thm)],[33096:[bind(A,$thf( lBob_THFTYPE_i ))]]) ).
thf(90423,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i )
| ~ $true
| ( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[9238,33097]) ).
thf(90424,plain,
! [A: $i] :
( ~ ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lBill_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[90423]) ).
thf(90425,plain,
~ ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i ),
inference(pattern_uni,[status(thm)],[90424:[bind(A,$thf( lBill_THFTYPE_i ))]]) ).
thf(138467,plain,
! [B: $i,A: $i] :
( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
| ~ $true
| ( ( parent_THFTYPE_IiioI @ B @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[8825,90425]) ).
thf(138468,plain,
! [B: $i,A: $i] :
( ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i )
| ( ( parent_THFTYPE_IiioI @ B @ lAnna_THFTYPE_i )
!= ( parent_THFTYPE_IiioI @ lAnna_THFTYPE_i @ lAnna_THFTYPE_i ) ) ),
inference(simp,[status(thm)],[138467]) ).
thf(138469,plain,
! [A: $i] : ( parent_THFTYPE_IiioI @ A @ lAnna_THFTYPE_i ),
inference(pattern_uni,[status(thm)],[138468:[bind(A,$thf( A )),bind(B,$thf( lAnna_THFTYPE_i ))]]) ).
thf(139804,plain,
~ $true,
inference(rewrite,[status(thm)],[79,138469]) ).
thf(139805,plain,
$false,
inference(simp,[status(thm)],[139804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CSR137^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:58:26 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.03 % [INFO] Parsing done (243ms).
% 1.59/1.05 % [INFO] Running in sequential loop mode.
% 2.24/1.45 % [INFO] eprover registered as external prover.
% 2.24/1.46 % [INFO] Scanning for conjecture ...
% 2.44/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 2.62/1.65 % [INFO] Axiom selection finished. Selected 35 axioms (removed 9 axioms).
% 2.62/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 2.62/1.68 % [INFO] Type checking passed.
% 2.62/1.69 % [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 ...
% 105.83/54.30 % [INFO] Killing All external provers ...
% 105.83/54.31 % Time passed: 53970ms (effective reasoning time: 53253ms)
% 105.83/54.31 % 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)>
% 105.83/54.31 % Axioms used in derivation (2): ax_025, ax_005
% 105.83/54.31 % No. of inferences in proof: 38
% 105.83/54.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 53970 ms resp. 53253 ms w/o parsing
% 105.83/54.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.83/54.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------