%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ030-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n017.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 08:21:08 AM UTC 2026
% Result : Unsatisfiable 6.14s 3.49s
% Output : Refutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 43
% Syntax : Number of formulae : 87 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 448 ( 110 ~; 126 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(neither_decl,type,
neither: $i > $o ).
thf(cole_decl,type,
cole: $i ).
thf(dix_decl,type,
dix: $i ).
thf(both_decl,type,
both: $i > $o ).
thf(barry_decl,type,
barry: $i ).
thf(oneof_decl,type,
oneof: $i > $o ).
thf(lang_decl,type,
lang: $i ).
thf(salt_decl,type,
salt: $i > $o ).
thf(mill_decl,type,
mill: $i ).
thf(mustard_decl,type,
mustard: $i > $o ).
thf(23,axiom,
( ( barry @ mustard )
| ~ ( mill @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_3) ).
thf(88,plain,
( ( barry @ mustard )
| ~ ( mill @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,axiom,
( ( barry @ mustard )
| ~ ( dix @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_2) ).
thf(120,plain,
( ( barry @ mustard )
| ~ ( dix @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(7,axiom,
( ( mill @ both )
| ( dix @ neither )
| ~ ( barry @ mustard ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2_1) ).
thf(56,plain,
( ( mill @ both )
| ( dix @ neither )
| ~ ( barry @ mustard ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ mustard )
| ( A @ salt )
| ~ ( A @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof1) ).
thf(70,plain,
! [A: $i] :
( ( A @ mustard )
| ( A @ salt )
| ~ ( A @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
( ( mill @ mustard )
| ~ ( lang @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_3) ).
thf(92,plain,
( ( mill @ mustard )
| ~ ( lang @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(43,axiom,
( ( dix @ salt )
| ~ ( cole @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_3) ).
thf(128,plain,
( ( dix @ salt )
| ~ ( cole @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
( ( mill @ mustard )
| ~ ( cole @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_2) ).
thf(64,plain,
( ( mill @ mustard )
| ~ ( cole @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ mustard )
| ~ ( A @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both2) ).
thf(80,plain,
! [A: $i] :
( ( A @ mustard )
| ~ ( A @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( A @ both )
| ~ ( A @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof2) ).
thf(112,plain,
! [A: $i] :
( ~ ( A @ both )
| ~ ( A @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
( ( lang @ both )
| ( barry @ both )
| ~ ( mill @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_1) ).
thf(48,plain,
( ( lang @ both )
| ( barry @ both )
| ~ ( mill @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( ( cole @ mustard )
| ~ ( lang @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_3) ).
thf(50,plain,
( ( cole @ mustard )
| ~ ( lang @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ both )
| ~ ( A @ mustard )
| ~ ( A @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both3) ).
thf(72,plain,
! [A: $i] :
( ( A @ both )
| ~ ( A @ mustard )
| ~ ( A @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( A @ neither )
| ~ ( A @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither1) ).
thf(104,plain,
! [A: $i] :
( ~ ( A @ neither )
| ~ ( A @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,axiom,
( ( lang @ mustard )
| ~ ( cole @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_2) ).
thf(114,plain,
( ( lang @ mustard )
| ~ ( cole @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(5,axiom,
( ( mill @ neither )
| ( lang @ neither )
| ~ ( dix @ mustard ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_1) ).
thf(52,plain,
( ( mill @ neither )
| ( lang @ neither )
| ~ ( dix @ mustard ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ oneof )
| ( A @ neither )
| ( A @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_condition_holds1) ).
thf(110,plain,
! [A: $i] :
( ( A @ oneof )
| ( A @ neither )
| ( A @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(2,axiom,
( ( lang @ salt )
| ~ ( barry @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_2) ).
thf(46,plain,
( ( lang @ salt )
| ~ ( barry @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
( ( lang @ oneof )
| ( cole @ oneof )
| ~ ( barry @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_1) ).
thf(78,plain,
( ( lang @ oneof )
| ( cole @ oneof )
| ~ ( barry @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
( ( cole @ salt )
| ~ ( barry @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_2) ).
thf(106,plain,
( ( cole @ salt )
| ~ ( barry @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(21,axiom,
( ( mill @ salt )
| ~ ( barry @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9_2) ).
thf(84,plain,
( ( mill @ salt )
| ~ ( barry @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
( ( barry @ salt )
| ~ ( lang @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_3) ).
thf(116,plain,
( ( barry @ salt )
| ~ ( lang @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ neither )
| ~ ( A @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof3) ).
thf(74,plain,
! [A: $i] :
( ~ ( A @ neither )
| ~ ( A @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
( ( barry @ salt )
| ~ ( cole @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1_2) ).
thf(60,plain,
( ( barry @ salt )
| ~ ( cole @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
( ( dix @ oneof )
| ( cole @ oneof )
| ~ ( mill @ mustard ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_1) ).
thf(102,plain,
( ( dix @ oneof )
| ( cole @ oneof )
| ~ ( mill @ mustard ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
( ( cole @ salt )
| ~ ( mill @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_3) ).
thf(124,plain,
( ( cole @ salt )
| ~ ( mill @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( A @ mustard )
| ~ ( A @ salt )
| ~ ( A @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneof4) ).
thf(96,plain,
! [A: $i] :
( ~ ( A @ mustard )
| ~ ( A @ salt )
| ~ ( A @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1,negated_conjecture,
( ~ ( mill @ oneof )
| ~ ( lang @ mustard )
| ~ ( mill @ salt )
| ~ ( lang @ oneof )
| ~ ( barry @ both )
| ~ ( dix @ neither )
| ~ ( cole @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_who_takes_what) ).
thf(44,plain,
( ~ ( mill @ oneof )
| ~ ( lang @ mustard )
| ~ ( mill @ salt )
| ~ ( lang @ oneof )
| ~ ( barry @ both )
| ~ ( dix @ neither )
| ~ ( cole @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(38,axiom,
( ( lang @ both )
| ( dix @ both )
| ~ ( cole @ mustard ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_1) ).
thf(118,plain,
( ( lang @ both )
| ( dix @ both )
| ~ ( cole @ mustard ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ salt )
| ~ ( A @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both1) ).
thf(54,plain,
! [A: $i] :
( ( A @ salt )
| ~ ( A @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( A @ mustard )
| ~ ( A @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither3) ).
thf(86,plain,
! [A: $i] :
( ~ ( A @ mustard )
| ~ ( A @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
( ( lang @ salt )
| ~ ( dix @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_3) ).
thf(76,plain,
( ( lang @ salt )
| ~ ( dix @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
( ( dix @ mustard )
| ~ ( lang @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_2) ).
thf(98,plain,
( ( dix @ mustard )
| ~ ( lang @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
( ( dix @ oneof )
| ( barry @ oneof )
| ~ ( lang @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7_1) ).
thf(66,plain,
( ( dix @ oneof )
| ( barry @ oneof )
| ~ ( lang @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
( ( mill @ mustard )
| ~ ( dix @ oneof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10_3) ).
thf(108,plain,
( ( mill @ mustard )
| ~ ( dix @ oneof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
( ( lang @ mustard )
| ~ ( mill @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_3) ).
thf(58,plain,
( ( lang @ mustard )
| ~ ( mill @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ neither )
| ( A @ mustard )
| ( A @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither4) ).
thf(82,plain,
! [A: $i] :
( ( A @ neither )
| ( A @ mustard )
| ( A @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(42,axiom,
( ( cole @ mustard )
| ~ ( dix @ both ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4_2) ).
thf(126,plain,
( ( cole @ mustard )
| ~ ( dix @ both ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(26,axiom,
( ( cole @ both )
| ( barry @ neither )
| ~ ( dix @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_1) ).
thf(94,plain,
( ( cole @ both )
| ( barry @ neither )
| ~ ( dix @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
( ( dix @ mustard )
| ~ ( mill @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6_3) ).
thf(68,plain,
( ( dix @ mustard )
| ~ ( mill @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
( ( mill @ neither )
| ( cole @ neither )
| ~ ( lang @ mustard ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8_1) ).
thf(62,plain,
( ( mill @ neither )
| ( cole @ neither )
| ~ ( lang @ mustard ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(24,axiom,
( ( mill @ neither )
| ( barry @ oneof )
| ~ ( cole @ salt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3_1) ).
thf(90,plain,
( ( mill @ neither )
| ( barry @ oneof )
| ~ ( cole @ salt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
( ( dix @ salt )
| ~ ( barry @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5_2) ).
thf(122,plain,
( ( dix @ salt )
| ~ ( barry @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( A @ salt )
| ~ ( A @ neither ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neither2) ).
thf(100,plain,
! [A: $i] :
( ~ ( A @ salt )
| ~ ( A @ neither ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(136,plain,
$false,
inference(e,[status(thm)],[88,120,56,70,92,128,64,80,112,48,50,72,104,114,52,110,46,78,106,84,116,74,60,102,124,96,44,118,54,86,76,98,66,108,58,82,126,94,68,62,90,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ030-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.40 % Computer : n017.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 05:01:34 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.22/1.15 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.66/1.46 % [INFO] Parsing done (296ms).
% 1.66/1.48 % [INFO] Running in sequential loop mode.
% 2.94/2.07 % [INFO] eprover registered as external prover.
% 2.94/2.08 % [INFO] Scanning for conjecture ...
% 3.18/2.23 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 3.33/2.34 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 3.33/2.39 % [INFO] Problem is propositional (TPTP CNF).
% 3.33/2.40 % [INFO] Type checking passed.
% 3.56/2.40 % [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 ...
% 6.14/3.48 % External prover 'e' found a proof!
% 6.14/3.48 % [INFO] Killing All external provers ...
% 6.14/3.48 % Time passed: 2873ms (effective reasoning time: 1995ms)
% 6.14/3.49 % Axioms used in derivation (42): rule2_3, rule10_2, rule4_1, rule3_3, rule10_1, rule5_1, neither1, rule3_2, rule6_1, rule9_3, both3, rule3_1, oneof4, rule9_1, both2, rule9_2, oneof2, rule1_1, rule8_1, rule5_3, rule6_3, rule2_2, rule5_2, oneof3, rule7_1, rule8_2, rule7_2, rule8_3, rule4_3, both1, neither2, rule10_3, neither3, rule4_2, rule7_3, rule1_3, rule6_2, rule1_2, oneof1, rule2_1, neither4, one_condition_holds1
% 6.14/3.49 % No. of inferences in proof: 87
% 6.14/3.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2873 ms resp. 1995 ms w/o parsing
% 6.36/3.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.36/3.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------