%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PLA005-2 : TPTP v9.3.1. Released v1.1.0.
% 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 : 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 : Sun Sep 27 08:19:53 AM UTC 2026
% Result : Unsatisfiable 6.52s 3.61s
% Output : Refutation 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 460 ( 46 ~; 44 |; 0 &; 370 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(holds_decl,type,
holds: $i > $i > $o ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(on_decl,type,
on: $i > $i > $i ).
thf(d_decl,type,
d: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(a_decl,type,
a: $i ).
thf(differ_decl,type,
differ: $i > $i > $o ).
thf(clear_decl,type,
clear: $i > $i ).
thf(do_decl,type,
do: $i > $i > $i ).
thf(putdown_decl,type,
putdown: $i > $i > $i ).
thf(holding_decl,type,
holding: $i > $i ).
thf(table_decl,type,
table: $i ).
thf(empty_decl,type,
empty: $i ).
thf(s0_decl,type,
s0: $i ).
thf(pickup_decl,type,
pickup: $i > $i ).
thf(19,axiom,
s0 @ ( a @ clear @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state5) ).
thf(56,plain,
s0 @ ( a @ clear @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
s0 @ ( empty @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state8) ).
thf(42,plain,
s0 @ ( empty @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ holds ) )
| ~ ( C @ ( A @ holds ) )
| ( C @ ( B @ ( A @ and ) @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ holds ) )
| ~ ( C @ ( A @ holds ) )
| ( C @ ( B @ ( A @ and ) @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
s0 @ ( table @ ( a @ on ) @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state1) ).
thf(65,plain,
s0 @ ( table @ ( a @ on ) @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ on ) @ holds ) )
| ( E @ ( D @ ( C @ putdown ) @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_4) ).
thf(53,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ on ) @ holds ) )
| ( E @ ( D @ ( C @ putdown ) @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
d @ ( c @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_c_d) ).
thf(41,plain,
d @ ( c @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( table @ ( A @ differ ) )
| ~ ( B @ ( A @ clear @ holds ) )
| ~ ( B @ ( empty @ holds ) )
| ( B @ ( A @ pickup @ do ) @ ( A @ holding @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_1) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( table @ ( A @ differ ) )
| ~ ( B @ ( A @ clear @ holds ) )
| ~ ( B @ ( empty @ holds ) )
| ( B @ ( A @ pickup @ do ) @ ( A @ holding @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( empty @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_1) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( empty @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
c @ ( b @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_b_c) ).
thf(39,plain,
c @ ( b @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
table @ ( d @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_d_table) ).
thf(66,plain,
table @ ( d @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( table @ clear @ holds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clear_table) ).
thf(43,plain,
! [A: $i] : ( A @ ( table @ clear @ holds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
d @ ( a @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_d) ).
thf(58,plain,
d @ ( a @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
d @ ( b @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_b_d) ).
thf(46,plain,
d @ ( b @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
s0 @ ( c @ clear @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state7) ).
thf(57,plain,
s0 @ ( c @ clear @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
table @ ( b @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_b_table) ).
thf(38,plain,
table @ ( b @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,axiom,
c @ ( a @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_c) ).
thf(70,plain,
c @ ( a @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
s0 @ ( table @ ( b @ on ) @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state2) ).
thf(45,plain,
s0 @ ( table @ ( b @ on ) @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ ( a @ ( c @ on ) @ ( b @ ( d @ on ) @ and ) @ holds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_DB_AC) ).
thf(32,plain,
! [A: $i] :
~ ( A @ ( a @ ( c @ on ) @ ( b @ ( d @ on ) @ and ) @ holds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ differ ) )
| ( B @ ( A @ differ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_differ) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ differ ) )
| ( B @ ( A @ differ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
s0 @ ( table @ ( d @ on ) @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state4) ).
thf(44,plain,
s0 @ ( table @ ( d @ on ) @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ differ ) )
| ~ ( C @ ( A @ clear @ holds ) )
| ( C @ ( B @ pickup @ do ) @ ( A @ clear @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_4) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ differ ) )
| ~ ( C @ ( A @ clear @ holds ) )
| ( C @ ( B @ pickup @ do ) @ ( A @ clear @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_2) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ differ ) )
| ~ ( D @ ( B @ ( A @ on ) @ holds ) )
| ( D @ ( C @ pickup @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_3) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ differ ) )
| ~ ( D @ ( B @ ( A @ on ) @ holds ) )
| ( D @ ( C @ pickup @ do ) @ ( B @ ( A @ on ) @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
s0 @ ( d @ ( c @ on ) @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state3) ).
thf(50,plain,
s0 @ ( d @ ( c @ on ) @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
s0 @ ( b @ clear @ holds ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state6) ).
thf(67,plain,
s0 @ ( b @ clear @ holds ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,axiom,
b @ ( a @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_b) ).
thf(40,plain,
b @ ( a @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
table @ ( c @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_c_table) ).
thf(55,plain,
table @ ( c @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( A @ clear @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_3) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ holding @ holds ) )
| ( C @ ( B @ ( A @ putdown ) @ do ) @ ( A @ clear @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( empty @ holds ) )
| ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ ( B @ on ) @ holds ) )
| ( C @ ( B @ pickup @ do ) @ ( A @ clear @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_2) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( empty @ holds ) )
| ~ ( C @ ( B @ clear @ holds ) )
| ~ ( C @ ( A @ ( B @ on ) @ holds ) )
| ( C @ ( B @ pickup @ do ) @ ( A @ clear @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
table @ ( a @ differ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_table) ).
thf(47,plain,
table @ ( a @ differ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ differ ) )
| ~ ( D @ ( A @ clear @ holds ) )
| ( D @ ( C @ ( B @ putdown ) @ do ) @ ( A @ clear @ holds ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_5) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ differ ) )
| ~ ( D @ ( A @ clear @ holds ) )
| ( D @ ( C @ ( B @ putdown ) @ do ) @ ( A @ clear @ holds ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[56,42,61,65,53,41,73,71,39,66,43,58,46,57,38,70,45,32,34,44,59,48,63,50,67,40,55,36,51,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA005-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % 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
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:43:35 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 1.32/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.55 % [INFO] Parsing done (310ms).
% 1.85/1.57 % [INFO] Running in sequential loop mode.
% 3.14/2.22 % [INFO] eprover registered as external prover.
% 3.14/2.23 % [INFO] Scanning for conjecture ...
% 3.34/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 3.76/2.50 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 3.76/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.76/2.56 % [INFO] Type checking passed.
% 3.76/2.57 % [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 ...
% 6.52/3.60 % External prover 'e' found a proof!
% 6.52/3.60 % [INFO] Killing All external provers ...
% 6.52/3.60 % Time passed: 2993ms (effective reasoning time: 2019ms)
% 6.52/3.61 % Axioms used in derivation (30): differ_a_table, initial_state7, differ_b_table, initial_state4, pickup_4, putdown_2, initial_state5, clear_table, initial_state6, differ_a_b, differ_c_table, initial_state2, putdown_4, initial_state8, pickup_1, initial_state3, putdown_3, differ_b_c, differ_b_d, and_definition, initial_state1, differ_a_c, pickup_3, differ_d_table, differ_a_d, putdown_5, putdown_1, symmetry_of_differ, differ_c_d, pickup_2
% 6.52/3.61 % No. of inferences in proof: 63
% 6.52/3.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2993 ms resp. 2019 ms w/o parsing
% 6.81/3.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.81/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------