%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO009-1 : 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 : n007.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 06:54:24 AM UTC 2026
% Result : Unsatisfiable 3.70s 2.48s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 528 ( 78 ~; 76 |; 0 &; 374 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 164 ( 0 ^; 164 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(x_decl,type,
x: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(y_decl,type,
y: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ sum ) ) )
| ~ ( G @ ( E @ ( C @ product ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
thf(56,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ sum ) ) )
| ~ ( G @ ( E @ ( C @ product ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
~ ( x @ ( y @ ( x @ add ) @ ( x @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).
thf(24,plain,
~ ( x @ ( y @ ( x @ add ) @ ( x @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(60,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(53,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ product ) ) )
| ~ ( G @ ( F @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
thf(41,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ product ) ) )
| ~ ( G @ ( F @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
thf(48,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(50,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(58,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(46,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] : ( multiplicative_identity @ ( A @ inverse @ ( A @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
thf(29,plain,
! [A: $i] : ( multiplicative_identity @ ( A @ inverse @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ sum ) ) )
| ~ ( G @ ( E @ ( C @ product ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
thf(38,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ sum ) ) )
| ~ ( G @ ( E @ ( C @ product ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] : ( multiplicative_identity @ ( A @ ( A @ inverse @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(33,plain,
! [A: $i] : ( multiplicative_identity @ ( A @ ( A @ inverse @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(34,plain,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] : ( additive_identity @ ( A @ inverse @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(45,plain,
! [A: $i] : ( additive_identity @ ( A @ inverse @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: $i] : ( A @ ( A @ ( multiplicative_identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(59,plain,
! [A: $i] : ( A @ ( A @ ( multiplicative_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(40,plain,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(26,plain,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( A @ inverse @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(55,plain,
! [A: $i] : ( additive_identity @ ( A @ ( A @ inverse @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ product ) ) )
| ~ ( G @ ( B @ ( F @ sum ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
thf(51,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ product ) ) )
| ~ ( G @ ( B @ ( F @ sum ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(66,plain,
$false,
inference(e,[status(thm)],[56,24,60,53,41,35,48,50,43,58,46,29,38,33,34,45,59,27,40,26,55,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 22:32:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.84/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.14 % [INFO] Parsing done (184ms).
% 1.24/1.16 % [INFO] Running in sequential loop mode.
% 1.83/1.55 % [INFO] eprover registered as external prover.
% 1.83/1.56 % [INFO] Scanning for conjecture ...
% 2.02/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.17/1.71 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.17/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.17/1.76 % [INFO] Type checking passed.
% 2.17/1.76 % [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 ...
% 3.70/2.48 % External prover 'e' found a proof!
% 3.70/2.48 % [INFO] Killing All external provers ...
% 3.70/2.48 % Time passed: 1950ms (effective reasoning time: 1314ms)
% 3.70/2.48 % Axioms used in derivation (22): distributivity8, distributivity6, addition_is_well_defined, commutativity_of_multiplication, additive_inverse2, commutativity_of_addition, additive_identity2, distributivity2, multiplication_is_well_defined, multiplicative_identity1, multiplicative_identity2, multiplicative_inverse1, distributivity7, distributivity4, closure_of_addition, distributivity3, multiplicative_inverse2, additive_identity1, additive_inverse1, distributivity1, closure_of_multiplication, distributivity5
% 3.70/2.48 % No. of inferences in proof: 47
% 3.70/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1950 ms resp. 1314 ms w/o parsing
% 4.15/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.15/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------