%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% 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 : 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 07:19:47 AM UTC 2026
% Result : Unsatisfiable 2.82s 1.57s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 18 ~; 16 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(not_identity_decl,type,
not_identity: $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(left_solution_decl,type,
left_solution: $i > $i > $i ).
thf(right_solution_decl,type,
right_solution: $i > $i > $i ).
thf(2,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
thf(10,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(14,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ left_solution ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_soln) ).
thf(18,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ left_solution ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(16,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(11,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)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ not_identity @ ( A @ ( A @ not_identity @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
thf(8,plain,
! [A: $i] :
~ ( A @ not_identity @ ( A @ ( A @ not_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ right_solution ) @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_soln) ).
thf(19,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ right_solution ) @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[10,14,18,16,11,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % 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
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 14:15:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.68/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.89 % [INFO] Parsing done (103ms).
% 0.88/0.89 % [INFO] Running in sequential loop mode.
% 1.66/1.18 % [INFO] eprover registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.83/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.83/1.25 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.83/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.26 % [INFO] Type checking passed.
% 1.83/1.26 % [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 ...
% 2.82/1.57 % External prover 'e' found a proof!
% 2.82/1.57 % [INFO] Killing All external provers ...
% 2.82/1.57 % Time passed: 1029ms (effective reasoning time: 673ms)
% 2.82/1.57 % Axioms used in derivation (6): total_function1, right_soln, associativity1, left_soln, total_function2, associativity2
% 2.82/1.57 % No. of inferences in proof: 15
% 2.82/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1029 ms resp. 673 ms w/o parsing
% 2.82/1.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.82/1.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------