%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM001-1 : 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 : n003.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 08:08:04 AM UTC 2026
% Result : Unsatisfiable 4.52s 2.53s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 254 ( 22 ~; 20 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(subtract_decl,type,
subtract: $i > $i > $i ).
thf(1,negated_conjecture,
~ ( c @ ( b @ add ) @ ( a @ add ) @ ( c @ ( b @ ( a @ add ) @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(14,plain,
~ ( c @ ( b @ add ) @ ( a @ add ) @ ( c @ ( b @ ( a @ add ) @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_inverts_subtraction1) ).
thf(21,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ add ) @ subtract ) @ ( C @ ( B @ ( A @ subtract ) @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ add ) @ subtract ) @ ( C @ ( B @ ( A @ subtract ) @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(19,plain,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity2) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ subtract ) @ add ) @ ( C @ ( B @ ( A @ add ) @ subtract ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ add ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution1) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ add ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ subtract ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_substitution1) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ subtract ) @ ( C @ equalish ) )
| ~ ( D @ ( A @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_inverts_subtraction2) ).
thf(22,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ subtract ) @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution2) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ add ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(16,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_substitution2) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( A @ ( D @ subtract ) @ ( C @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(76,plain,
$false,
inference(e,[status(thm)],[14,21,17,23,19,24,25,20,29,22,27,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : 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
% 0.16/0.41 % Computer : n003.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 01:53:38 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.18 % [INFO] Parsing done (193ms).
% 1.26/1.19 % [INFO] Running in sequential loop mode.
% 1.92/1.59 % [INFO] eprover registered as external prover.
% 2.11/1.60 % [INFO] Scanning for conjecture ...
% 2.11/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.29/1.72 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.29/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.29/1.74 % [INFO] Type checking passed.
% 2.29/1.75 % [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 ...
% 4.52/2.53 % External prover 'e' found a proof!
% 4.52/2.53 % [INFO] Killing All external provers ...
% 4.52/2.53 % Time passed: 1982ms (effective reasoning time: 1334ms)
% 4.52/2.53 % Axioms used in derivation (12): addition_inverts_subtraction1, addition_inverts_subtraction2, subtract_substitution1, reflexivity, transitivity, add_substitution2, commutativity1, associativity_of_addition, commutativity_of_addition, commutativity2, add_substitution1, subtract_substitution2
% 4.52/2.53 % No. of inferences in proof: 27
% 4.52/2.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1982 ms resp. 1334 ms w/o parsing
% 4.52/2.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.52/2.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------