%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 06:54:28 AM UTC 2026
% Result : Unsatisfiable 4.17s 2.44s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 206 ( 2 ~; 0 |; 0 &; 204 @)
% ( 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 : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(n1_decl,type,
n1: $i ).
thf(n0_decl,type,
n0: $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ inverse @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ inverse @ add ) @ ( B @ ( A @ add ) @ multiply ) @ ( A @ inverse @ ( A @ add ) @ multiply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1_dual) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ inverse @ add ) @ ( B @ ( A @ add ) @ multiply ) @ ( A @ inverse @ ( A @ add ) @ multiply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
thf(17,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ multiply ) @ ( A @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ multiply ) @ ( A @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( b @ ( b @ ( a @ add ) @ multiply ) )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add) ).
thf(12,plain,
( ( b @ ( b @ ( a @ add ) @ multiply ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ inverse @ add ) @ ( B @ ( A @ add ) @ multiply ) @ ( B @ inverse @ ( A @ add ) @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2_dual) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ inverse @ add ) @ ( B @ ( A @ add ) @ multiply ) @ ( B @ inverse @ ( A @ add ) @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ inverse @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ ( A @ inverse @ ( A @ multiply ) @ add ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ inverse @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ ( A @ inverse @ ( A @ multiply ) @ add ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ add ) )
= ( A @ ( C @ add ) @ ( A @ ( B @ add ) @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( A @ add ) )
= ( A @ ( C @ add ) @ ( A @ ( B @ add ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ multiply ) )
= ( A @ ( C @ multiply ) @ ( A @ ( B @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( A @ multiply ) )
= ( A @ ( C @ multiply ) @ ( A @ ( B @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
thf(21,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ add ) @ ( A @ ( A @ add ) @ multiply ) @ ( B @ inverse @ ( A @ add ) @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3_dual) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ add ) @ ( A @ ( A @ add ) @ multiply ) @ ( B @ inverse @ ( A @ add ) @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n015.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
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 22:40:29 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (182ms).
% 1.42/1.20 % [INFO] Running in sequential loop mode.
% 1.85/1.59 % [INFO] eprover registered as external prover.
% 2.04/1.60 % [INFO] Scanning for conjecture ...
% 2.04/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.23/1.71 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.23/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.75 % [INFO] Type checking passed.
% 2.23/1.75 % [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 ...
% 4.17/2.43 % External prover 'e' found a proof!
% 4.17/2.43 % [INFO] Killing All external provers ...
% 4.17/2.43 % Time passed: 1875ms (effective reasoning time: 1227ms)
% 4.17/2.43 % Axioms used in derivation (10): pixley3, pixley1, pixley2, pixley2_dual, additive_inverse, multiply_add_property, pixley3_dual, pixley1_dual, add_multiply_property, multiplicative_inverse
% 4.17/2.43 % No. of inferences in proof: 23
% 4.17/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1875 ms resp. 1227 ms w/o parsing
% 4.17/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.17/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------