%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n016.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 07:43:14 AM UTC 2026
% Result : Theorem 11.53s 9.97s
% Output : Refutation 11.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 405 ( 2 ~; 0 |; 1 &; 391 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(divergence_decl,type,
divergence: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(forward_diamond_decl,type,
forward_diamond: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(coantidomain_decl,type,
coantidomain: $i > $i ).
thf(backward_box_decl,type,
backward_box: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(backward_diamond_decl,type,
backward_diamond: $i > $i > $i ).
thf(domain_difference_decl,type,
domain_difference: $i > $i > $i ).
thf(antidomain_decl,type,
antidomain: $i > $i ).
thf(forward_box_decl,type,
forward_box: $i > $i > $i ).
thf(star_decl,type,
star: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_diamond ) )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_diamond ) )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(42,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ c )
= ( A @ domain @ antidomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
thf(105,plain,
! [A: $i] :
( ( A @ c )
= ( A @ domain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_diamond ) )
= ( A @ ( B @ codomain @ multiplication ) @ codomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_diamond) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_diamond ) )
= ( A @ ( B @ codomain @ multiplication ) @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ! [B: $i] :
( ( ( B @ domain @ ( A @ forward_diamond ) @ ( B @ domain @ addition ) )
= ( B @ domain @ ( A @ forward_diamond ) ) )
=> ( ( B @ domain )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ! [B: $i] :
( ( ( B @ domain @ ( A @ forward_diamond ) @ ( B @ domain @ addition ) )
= ( B @ domain @ ( A @ forward_diamond ) ) )
=> ( ( B @ domain )
= zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ! [B: $i] :
( ( ( B @ domain @ ( A @ forward_diamond ) @ ( B @ domain @ addition ) )
= ( B @ domain @ ( A @ forward_diamond ) ) )
=> ( ( B @ domain )
= zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(72,plain,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_box) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
thf(93,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ domain_difference ) )
= ( B @ antidomain @ ( A @ domain @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_difference) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ domain_difference ) )
= ( B @ antidomain @ ( A @ domain @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(102,plain,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(60,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(81,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_box ) )
= ( B @ c @ ( A @ forward_diamond ) @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_box) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_box ) )
= ( B @ c @ ( A @ forward_diamond ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(108,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
thf(48,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) ) )
=> ( ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divergence2) ).
thf(99,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) ) )
=> ( ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
thf(90,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ divergence @ ( A @ forward_diamond ) )
= ( A @ divergence ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divergence1) ).
thf(111,plain,
! [A: $i] :
( ( A @ divergence @ ( A @ forward_diamond ) )
= ( A @ divergence ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(745,plain,
$false,
inference(e,[status(thm)],[69,120,42,84,96,105,45,54,31,72,114,75,51,93,57,78,102,60,117,81,39,66,108,48,63,99,87,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.25/5.52 % Computer : n016.cluster.edu
% 0.25/5.52 % Model : x86_64 x86_64
% 0.25/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.52 % Memory : 8046.5625MB
% 0.25/5.52 % OS : Linux 6.8.0-71-generic
% 0.25/5.52 % CPULimit : 300
% 0.25/5.52 % WCLimit : 300
% 0.25/5.52 % DateTime : Fri Sep 25 19:30:05 UTC 2026
% 0.25/5.52 % CPUTime :
% 0.25/5.52 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
% 1.39/6.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.28/6.71 % [INFO] Parsing done (338ms).
% 2.28/6.73 % [INFO] Running in sequential loop mode.
% 3.34/7.35 % [INFO] eprover registered as external prover.
% 3.34/7.36 % [INFO] Scanning for conjecture ...
% 3.55/7.49 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 3.94/7.61 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 3.94/7.69 % [INFO] Problem is first-order (TPTP FOF).
% 4.19/7.71 % [INFO] Type checking passed.
% 4.19/7.71 % [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 ...
% 11.53/9.96 % External prover 'e' found a proof!
% 11.53/9.96 % [INFO] Killing All external provers ...
% 11.53/9.96 % Time passed: 4232ms (effective reasoning time: 3222ms)
% 11.53/9.96 % Solved by 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)>
% 11.53/9.96 % Axioms used in derivation (28): forward_box, additive_identity, domain4, backward_box, domain3, codomain2, complement, right_annihilation, backward_diamond, forward_diamond, codomain4, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, divergence2, multiplicative_right_identity, order, additive_commutativity, domain_difference, multiplicative_left_identity, codomain3, domain1, divergence1, multiplicative_associativity, left_distributivity
% 11.53/9.96 % No. of inferences in proof: 60
% 11.53/9.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4232 ms resp. 3222 ms w/o parsing
% 11.53/10.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.53/10.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------