%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG002-1 : 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 : n006.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 06:45:52 AM UTC 2026
% Result : Unsatisfiable 2.72s 1.41s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 206 ( 30 ~; 28 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_than_0_decl,type,
greater_than_0: $i > $o ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ additive_inverse @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_inverse) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ additive_inverse @ ( B @ additive_inverse @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ additive_inverse @ ( A @ additive_inverse @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses1) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ additive_inverse @ ( A @ additive_inverse @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ additive_inverse @ ( A @ additive_inverse @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses2) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ additive_inverse @ ( A @ additive_inverse @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
~ ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).
thf(18,plain,
~ ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( a @ multiplicative_inverse @ greater_than_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
thf(15,plain,
~ ( a @ multiplicative_inverse @ greater_than_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ additive_inverse @ greater_than_0 )
| ~ ( A @ greater_than_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).
thf(28,plain,
! [A: $i] :
( ~ ( A @ additive_inverse @ greater_than_0 )
| ~ ( A @ greater_than_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ greater_than_0 )
| ~ ( B @ greater_than_0 )
| ~ ( A @ greater_than_0 )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ greater_than_0 )
| ~ ( B @ greater_than_0 )
| ~ ( A @ greater_than_0 )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(17,plain,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ additive_inverse @ greater_than_0 )
| ( additive_identity @ ( A @ ( A @ product ) ) )
| ( A @ greater_than_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).
thf(34,plain,
! [A: $i] :
( ( A @ additive_inverse @ greater_than_0 )
| ( additive_identity @ ( A @ ( A @ product ) ) )
| ( A @ greater_than_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
a @ greater_than_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).
thf(40,plain,
a @ greater_than_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ product ) ) )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).
thf(26,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ product ) ) )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( additive_identity @ ( C @ ( C @ product ) ) )
| ~ ( additive_identity @ ( A @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_to_0) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( additive_identity @ ( C @ ( C @ product ) ) )
| ~ ( additive_identity @ ( A @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( additive_identity @ ( A @ ( A @ product ) ) )
| ~ ( A @ greater_than_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).
thf(30,plain,
! [A: $i] :
( ~ ( additive_identity @ ( A @ ( A @ product ) ) )
| ~ ( A @ greater_than_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[24,20,22,18,15,28,38,17,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n006.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 20:56:55 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.59/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.79 % [INFO] Parsing done (90ms).
% 0.71/0.79 % [INFO] Running in sequential loop mode.
% 1.18/0.97 % [INFO] eprover registered as external prover.
% 1.18/0.98 % [INFO] Scanning for conjecture ...
% 1.18/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 1.49/1.03 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.49/1.05 % [INFO] Problem is propositional (TPTP CNF).
% 1.49/1.05 % [INFO] Type checking passed.
% 1.49/1.05 % [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 ...
% 2.72/1.41 % External prover 'e' found a proof!
% 2.72/1.41 % [INFO] Killing All external provers ...
% 2.72/1.41 % Time passed: 910ms (effective reasoning time: 610ms)
% 2.72/1.41 % Axioms used in derivation (13): greater_than_0_square, product_of_inverses1, product_to_inverse, product_of_inverses2, a_greater_than_0, right_identity, product_and_inverse, product_and_greater_than_0, inverse_and_identity, square_to_0, inverse_greater_than_0, commutativity_of_product, not_abelian
% 2.72/1.41 % No. of inferences in proof: 29
% 2.72/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 910 ms resp. 610 ms w/o parsing
% 2.72/1.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.72/1.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------