%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 07:43:11 AM UTC 2026
% Result : Unsatisfiable 23.93s 6.84s
% Output : Refutation 23.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 51 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 50 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 272 ( 2 ~; 0 |; 0 &; 270 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(sK2_goals_X0_decl,type,
sK2_goals_X0: $i ).
thf(sK1_goals_X1_decl,type,
sK1_goals_X1: $i ).
thf(antidomain_decl,type,
antidomain: $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(zero_decl,type,
zero: $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $i ).
thf(true_decl,type,
true: $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(22,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(69,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ leq ) @ ( B @ ( B @ ( A @ addition ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ leq ) @ ( B @ ( B @ ( A @ addition ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(65,plain,
! [B: $i,A: $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)],[20]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
thf(53,plain,
! [B: $i,A: $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)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(41,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(73,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(45,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(39,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(35,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(63,plain,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(59,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
( ( sK2_goals_X0 @ antidomain @ ( sK1_goals_X1 @ antidomain @ addition ) )
!= ( sK2_goals_X0 @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_1) ).
thf(27,plain,
( ( sK2_goals_X0 @ antidomain @ ( sK1_goals_X1 @ antidomain @ addition ) )
!= ( sK2_goals_X0 @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ addition ) @ ( true @ ( B @ ( A @ leq ) @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ addition ) @ ( true @ ( B @ ( A @ leq ) @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( sK1_goals_X1 @ ( sK2_goals_X0 @ addition ) )
= sK1_goals_X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(26,plain,
( ( sK1_goals_X1 @ ( sK2_goals_X0 @ addition ) )
= sK1_goals_X1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(55,plain,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2517,plain,
$false,
inference(e,[status(thm)],[69,37,57,61,33,65,53,41,73,45,39,35,63,43,75,51,47,59,27,71,49,67,31,26,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/0.51 % Computer : n002.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 19:23:22 UTC 2026
% 0.25/0.52 % CPUTime :
% 0.25/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.41/1.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.96/1.64 % [INFO] Parsing done (276ms).
% 1.96/1.66 % [INFO] Running in sequential loop mode.
% 3.02/2.27 % [INFO] eprover registered as external prover.
% 3.02/2.28 % [INFO] Scanning for conjecture ...
% 3.42/2.42 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 3.58/2.51 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 3.58/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.58/2.57 % [INFO] Type checking passed.
% 3.58/2.58 % [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 ...
% 23.93/6.84 % External prover 'e' found a proof!
% 23.93/6.84 % [INFO] Killing All external provers ...
% 23.93/6.84 % Time passed: 6115ms (effective reasoning time: 5168ms)
% 23.93/6.84 % Axioms used in derivation (23): additive_identity, codomain4, ifeq_axiom, domain3, multiplicative_right_identity, codomain2, order_1, right_annihilation, domain1, ifeq_axiom_001, domain4, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_left_identity, codomain3, multiplicative_associativity, left_distributivity
% 23.93/6.84 % No. of inferences in proof: 51
% 23.93/6.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6115 ms resp. 5168 ms w/o parsing
% 23.93/6.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.93/6.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------