%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% 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 : n019.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 06:56:28 AM UTC 2026
% Result : Unsatisfiable 3.73s 2.34s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 262 ( 38 ~; 30 |; 0 &; 194 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(y_decl,type,
y: $i ).
thf(yp_decl,type,
yp: $i ).
thf(trancl_decl,type,
trancl: $i > $i ).
thf(r_decl,type,
r: $i ).
thf(ya_decl,type,
ya: $i ).
thf(combK_decl,type,
combK: $i ).
thf(combS_decl,type,
combS: $i ).
thf(comb_app_decl,type,
comb_app: $i > $i > $i ).
thf(trans_decl,type,
trans: $i > $o ).
thf(diamond_decl,type,
diamond: $i > $o ).
thf(diamond_strip_lemmaD_sk1_decl,type,
diamond_strip_lemmaD_sk1: $i > $i > $i > $i > $i ).
thf(15,axiom,
r @ ( ya @ ( y @ pair ) @ member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h2) ).
thf(52,plain,
r @ ( ya @ ( y @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ ( B @ diamond_strip_lemmaD_sk1 ) ) ) @ ( C @ pair ) @ member ) )
| ~ ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ trancl @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ diamond ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ ( B @ diamond_strip_lemmaD_sk1 ) ) ) @ ( C @ pair ) @ member ) )
| ~ ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ trancl @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ diamond ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
r @ trancl @ ( yp @ ( y @ pair ) @ member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c1) ).
thf(16,plain,
r @ trancl @ ( yp @ ( y @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ trancl @ ( A @ ( D @ ( C @ ( B @ diamond_strip_lemmaD_sk1 ) ) ) @ ( D @ pair ) @ member ) )
| ~ ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ trancl @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ diamond ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ trancl @ ( A @ ( D @ ( C @ ( B @ diamond_strip_lemmaD_sk1 ) ) ) @ ( D @ pair ) @ member ) )
| ~ ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ trancl @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ diamond ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ trancl @ ( B @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r_into_trancl) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ trancl @ ( B @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(25,plain,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app3) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ ( D @ ( C @ pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ trans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transD) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ ( D @ ( C @ pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( r @ trancl @ ( A @ ( yp @ pair ) @ member ) )
| ~ ( r @ trancl @ ( A @ ( ya @ pair ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c2) ).
thf(17,plain,
! [A: $i] :
( ~ ( r @ trancl @ ( A @ ( yp @ pair ) @ member ) )
| ~ ( r @ trancl @ ( A @ ( ya @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(22,plain,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] : ( A @ trancl @ trans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_trancl) ).
thf(44,plain,
! [A: $i] : ( A @ trancl @ trans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
r @ diamond,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h1) ).
thf(51,plain,
r @ diamond,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(19,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[52,49,16,47,42,25,33,28,38,45,17,22,44,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% 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
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 23:14:49 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.85/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.14 % [INFO] Parsing done (175ms).
% 1.25/1.16 % [INFO] Running in sequential loop mode.
% 1.84/1.55 % [INFO] eprover registered as external prover.
% 1.84/1.56 % [INFO] Scanning for conjecture ...
% 2.05/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.05/1.69 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.21/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.73 % [INFO] Type checking passed.
% 2.21/1.73 % [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 ...
% 3.73/2.34 % External prover 'e' found a proof!
% 3.73/2.34 % [INFO] Killing All external provers ...
% 3.73/2.34 % Time passed: 1799ms (effective reasoning time: 1174ms)
% 3.73/2.34 % Axioms used in derivation (13): app_app3, r_into_trancl, diamond_strip_lemmaD2, trans_trancl, diamond_strip_lemmaD1, app_app1, diamond_trancl_1h2, k_app, app_app2, s_app, k_s, diamond_trancl_1h1, transD
% 3.73/2.34 % No. of inferences in proof: 31
% 3.73/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1799 ms resp. 1174 ms w/o parsing
% 3.73/2.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------