%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO024-1 : 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 : n014.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 3.65s 7.35s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 92 ( 2 ~; 0 |; 0 &; 90 @)
% ( 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; 4 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $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(pixley_decl,type,
pixley: $i > $i > $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ pixley ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ pixley ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,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(14,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)],[3]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ pixley ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ pixley ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( b @ ( b @ ( a @ multiply ) @ add ) )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_add_multiply) ).
thf(9,plain,
( ( b @ ( b @ ( a @ multiply ) @ add ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ pixley ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ pixley ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ add ) @ multiply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ add ) @ multiply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ pixley ) ) )
= ( C @ ( B @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley_defn) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ pixley ) ) )
= ( C @ ( B @ inverse @ multiply ) @ ( C @ ( A @ multiply ) @ add ) @ ( B @ inverse @ ( A @ multiply ) @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
thf(16,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ add ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,22,12,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.09 % 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
% 0.16/5.43 % Computer : n014.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sat Sep 26 22:37:22 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 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
% 0.21/6.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/6.19 % [INFO] Parsing done (178ms).
% 1.40/6.20 % [INFO] Running in sequential loop mode.
% 2.03/6.61 % [INFO] eprover registered as external prover.
% 2.03/6.62 % [INFO] Scanning for conjecture ...
% 2.21/6.70 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.21/6.74 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.21/6.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/6.76 % [INFO] Type checking passed.
% 2.21/6.76 % [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 ...
% 3.65/7.35 % External prover 'e' found a proof!
% 3.65/7.35 % [INFO] Killing All external provers ...
% 3.65/7.35 % Time passed: 1776ms (effective reasoning time: 1145ms)
% 3.65/7.35 % Axioms used in derivation (7): multiply_add, pixley3, pixley_defn, pixley1, pixley2, additive_inverse, multiply_add_property
% 3.65/7.35 % No. of inferences in proof: 17
% 3.65/7.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1776 ms resp. 1145 ms w/o parsing
% 3.65/7.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/7.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------