%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n006.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 : Sun Sep 27 08:28:46 AM UTC 2026
% Result : Unsatisfiable 3.66s 7.32s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 258 ( 28 ~; 36 |; 0 &; 194 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_decl,type,
intersection: $i > $i > $i > $o ).
thf(aIb_decl,type,
aIb: $i ).
thf(c_decl,type,
c: $i ).
thf(aIbIc_decl,type,
aIbIc: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(member_of_1_not_of_2_decl,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(bIc_decl,type,
bIc: $i ).
thf(h_decl,type,
h: $i > $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
~ ( aIbIc @ ( c @ ( aIb @ intersection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
thf(14,plain,
~ ( aIbIc @ ( c @ ( aIb @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ intersection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
aIb @ ( b @ ( a @ intersection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
thf(30,plain,
aIb @ ( b @ ( a @ intersection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
bIc @ ( c @ ( b @ intersection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_intersection_c) ).
thf(29,plain,
bIc @ ( c @ ( b @ intersection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
aIbIc @ ( bIc @ ( a @ intersection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bIc) ).
thf(22,plain,
aIbIc @ ( bIc @ ( a @ intersection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) ) )
| ~ ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom3) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ intersection ) ) )
| ~ ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( B @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ~ ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( B @ ( A @ member_of_1_not_of_2 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom1) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ h ) ) @ member ) )
| ( C @ ( B @ ( A @ intersection ) ) )
| ( C @ ( C @ ( B @ ( A @ h ) ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[25,14,33,35,18,23,30,20,29,22,27,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.12/5.40 % Computer : n006.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Sat Sep 26 06:48:15 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 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
% 0.17/5.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/6.18 % [INFO] Parsing done (195ms).
% 1.42/6.20 % [INFO] Running in sequential loop mode.
% 1.92/6.58 % [INFO] eprover registered as external prover.
% 1.92/6.59 % [INFO] Scanning for conjecture ...
% 2.11/6.67 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.25/6.73 % [INFO] Axiom selection finished. Selected 12 axioms (removed 3 axioms).
% 2.25/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.25/6.76 % [INFO] Type checking passed.
% 2.25/6.76 % [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 ...
% 3.66/7.32 % External prover 'e' found a proof!
% 3.66/7.32 % [INFO] Killing All external provers ...
% 3.66/7.32 % Time passed: 1772ms (effective reasoning time: 1113ms)
% 3.66/7.32 % Axioms used in derivation (12): member_of_intersection_is_member_of_set2, subsets_axiom2, member_of_both_is_member_of_intersection, member_of_intersection_is_member_of_set1, a_intersection_b, a_intersection_bIc, intersection_axiom3, intersection_axiom2, intersection_axiom1, b_intersection_c, membership_in_subsets, subsets_axiom1
% 3.66/7.32 % No. of inferences in proof: 27
% 3.66/7.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1772 ms resp. 1113 ms w/o parsing
% 3.66/7.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.66/7.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------