%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n015.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 07:44:30 AM UTC 2026
% Result : Unsatisfiable 6.42s 3.85s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 560 ( 102 ~; 128 |; 0 &; 330 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 17 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(e_decl,type,
e: $i > $o ).
thf(exist_decl,type,
exist: $i ).
thf(f_decl,type,
f: $i > $o ).
thf(r_decl,type,
r: $i > $i > $o ).
thf(u2r2_decl,type,
u2r2: $i > $i ).
thf(r3least_decl,type,
r3least: $i > $o ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(u2r3_decl,type,
u2r3: $i > $i ).
thf(u2r1_decl,type,
u2r1: $i > $i ).
thf(a_decl,type,
a: $i > $o ).
thf(d_decl,type,
d: $i > $o ).
thf(c_decl,type,
c: $i > $o ).
thf(u3r2_decl,type,
u3r2: $i > $i ).
thf(u3r1_decl,type,
u3r1: $i > $i ).
thf(u1r1_decl,type,
u1r1: $i > $i ).
thf(u1r3_decl,type,
u1r3: $i > $i ).
thf(u1r2_decl,type,
u1r2: $i > $i ).
thf(20,axiom,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r1 @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(69,plain,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r1 @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( A @ u2r1 @ ( A @ u2r3 @ equalish ) )
| ~ ( A @ r3least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ u2r1 @ ( A @ u2r3 @ equalish ) )
| ~ ( A @ r3least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ u3r1 @ ( A @ u3r2 @ equalish ) )
| ~ ( A @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ u3r1 @ ( A @ u3r2 @ equalish ) )
| ~ ( A @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r2 @ c )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(85,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r2 @ c )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2,negated_conjecture,
~ ( exist @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(33,plain,
~ ( exist @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( A @ u1r2 @ ( A @ u1r3 @ equalish ) )
| ~ ( A @ r3least )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(65,plain,
! [A: $i] :
( ~ ( A @ u1r2 @ ( A @ u1r3 @ equalish ) )
| ~ ( A @ r3least )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ c )
| ( A @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(53,plain,
! [A: $i] :
( ~ ( A @ c )
| ( A @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r ) )
| ~ ( B @ e )
| ( A @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r ) )
| ~ ( B @ e )
| ( A @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ d )
| ( A @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(41,plain,
! [A: $i] :
( ~ ( A @ d )
| ( A @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r2 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(73,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r2 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r3 @ ( A @ r ) )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(59,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r3 @ ( A @ r ) )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( A @ e )
| ( A @ r3least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(91,plain,
! [A: $i] :
( ~ ( A @ e )
| ( A @ r3least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r2 @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(35,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r2 @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r2 @ ( A @ r ) )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(63,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r2 @ ( A @ r ) )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ d )
| ~ ( B @ d )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( C @ ( B @ equalish ) )
| ( A @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ d )
| ~ ( B @ d )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( C @ ( B @ equalish ) )
| ( A @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ u2r2 @ ( A @ u2r3 @ equalish ) )
| ~ ( A @ r3least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(43,plain,
! [A: $i] :
( ~ ( A @ u2r2 @ ( A @ u2r3 @ equalish ) )
| ~ ( A @ r3least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r2 @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(87,plain,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r2 @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c )
| ~ ( A @ c )
| ~ ( B @ ( C @ r ) )
| ~ ( A @ ( C @ r ) )
| ~ ( C @ e )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c )
| ~ ( A @ c )
| ~ ( B @ ( C @ r ) )
| ~ ( A @ ( C @ r ) )
| ~ ( C @ e )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r1 @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
thf(75,plain,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r1 @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r3 @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(51,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r3 @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ u1r2 @ ( A @ u1r3 @ equalish ) )
| ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ u1r2 @ ( A @ u1r3 @ equalish ) )
| ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( D @ ( C @ equalish ) )
| ( D @ ( B @ equalish ) )
| ( C @ ( B @ equalish ) )
| ( A @ r3least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ r ) )
| ~ ( C @ ( A @ r ) )
| ~ ( B @ ( A @ r ) )
| ( D @ ( C @ equalish ) )
| ( D @ ( B @ equalish ) )
| ( C @ ( B @ equalish ) )
| ( A @ r3least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r2 @ c )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(83,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r2 @ c )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r3 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(61,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r3 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r3 @ c )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(89,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ~ ( A @ u1r1 @ a )
| ( A @ u1r3 @ c )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,negated_conjecture,
exist @ e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(32,plain,
exist @ e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ u2r1 @ ( A @ u2r2 @ equalish ) )
| ~ ( A @ r3least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(45,plain,
! [A: $i] :
( ~ ( A @ u2r1 @ ( A @ u2r2 @ equalish ) )
| ~ ( A @ r3least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r2 @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(71,plain,
! [A: $i] :
( ~ ( A @ f )
| ( A @ u3r2 @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ a )
| ( A @ d )
| ( A @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ a )
| ( A @ d )
| ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r3 @ c )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u1r3 @ c )
| ( A @ u1r1 @ ( A @ r ) )
| ( A @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r1 @ ( A @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(39,plain,
! [A: $i] :
( ~ ( A @ r3least )
| ( A @ u2r1 @ ( A @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[69,37,57,85,33,65,53,77,41,73,59,91,35,63,67,43,87,55,75,51,79,47,83,61,89,32,45,71,49,81,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.12 % 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
% 0.25/0.51 % Computer : n015.cluster.edu
% 0.25/0.51 % Model : x86_64 x86_64
% 0.25/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.51 % Memory : 8046.5625MB
% 0.25/0.51 % OS : Linux 6.8.0-71-generic
% 0.25/0.51 % CPULimit : 300
% 0.25/0.51 % WCLimit : 300
% 0.25/0.51 % DateTime : Fri Sep 25 19:35:43 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 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
% 1.53/1.42 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.02/1.74 % [INFO] Parsing done (312ms).
% 2.02/1.76 % [INFO] Running in sequential loop mode.
% 3.19/2.40 % [INFO] eprover registered as external prover.
% 3.19/2.41 % [INFO] Scanning for conjecture ...
% 3.38/2.56 % [INFO] Found a conjecture (or negated_conjecture) and 29 axioms. Running axiom selection ...
% 3.53/2.66 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 3.72/2.74 % [INFO] Problem is propositional (TPTP CNF).
% 3.72/2.75 % [INFO] Type checking passed.
% 3.72/2.76 % [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 ...
% 6.42/3.85 % External prover 'e' found a proof!
% 6.42/3.85 % [INFO] Killing All external provers ...
% 6.42/3.85 % Time passed: 3110ms (effective reasoning time: 2074ms)
% 6.42/3.85 % Axioms used in derivation (29): clause_5, clause_23, clause_16, clause_26, clause_9, clause_25, clause_21, clause_4, clause_13, clause_6, clause_17, clause_30, clause_27, clause_8, clause_15, clause_20, clause_19, clause_14, clause_31, clause_7, clause_10, clause_18, clause_29, clause_11, clause_24, clause_22, clause_3, clause_12, clause_28
% 6.42/3.85 % No. of inferences in proof: 63
% 6.42/3.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3110 ms resp. 2074 ms w/o parsing
% 6.67/3.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.67/3.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------