%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% 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 : n010.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 07:19:42 AM UTC 2026
% Result : Unsatisfiable 4.61s 7.88s
% Output : Refutation 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 264 ( 2 ~; 0 |; 0 &; 262 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(true_decl,type,
true: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(d_decl,type,
d: $i ).
thf(h_decl,type,
h: $i ).
thf(j_decl,type,
j: $i ).
thf(k_decl,type,
k: $i ).
thf(identity_decl,type,
identity: $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( true @ ( identity @ ( B @ ( A @ product ) ) @ ( true @ ( B @ ( A @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_1) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( true @ ( identity @ ( B @ ( A @ product ) ) @ ( true @ ( B @ ( A @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( true @ ( identity @ ( A @ ( B @ product ) ) @ ( true @ ( B @ ( A @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( true @ ( identity @ ( A @ ( B @ product ) ) @ ( true @ ( B @ ( A @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( C @ ( E @ ( F @ product ) ) @ ( true @ ( A @ ( D @ ( F @ product ) ) @ ifeq ) ) ) @ ( true @ ( E @ ( B @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(48,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( C @ ( E @ ( F @ product ) ) @ ( true @ ( A @ ( D @ ( F @ product ) ) @ ifeq ) ) ) @ ( true @ ( E @ ( B @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( E @ ( B @ ( F @ product ) ) @ ( true @ ( F @ ( A @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( E @ ( C @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(50,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( E @ ( B @ ( F @ product ) ) @ ( true @ ( F @ ( A @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( E @ ( C @ ( D @ product ) ) @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
( ( identity @ ( A @ inverse @ ( A @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(42,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ ( A @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,negated_conjecture,
( ( j @ ( b @ ( h @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
thf(24,plain,
( ( j @ ( b @ ( h @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ ( a @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(20,plain,
( ( c @ ( b @ ( a @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( true @ ( D @ ( B @ ( A @ product ) ) @ ifeq2 ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq2 ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( true @ ( D @ ( B @ ( A @ product ) ) @ ifeq2 ) ) ) @ ( true @ ( C @ ( B @ ( A @ product ) ) @ ifeq2 ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( identity @ ( A @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( identity @ ( A @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( identity @ ( b @ inverse @ ( k @ product ) ) )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
thf(21,plain,
( ( identity @ ( b @ inverse @ ( k @ product ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,negated_conjecture,
( ( d @ ( a @ inverse @ ( c @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
thf(22,plain,
( ( d @ ( a @ inverse @ ( c @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( identity @ ( A @ ( A @ inverse @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(40,plain,
! [A: $i] :
( ( identity @ ( A @ ( A @ inverse @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
( ( h @ ( b @ inverse @ ( d @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
thf(23,plain,
( ( h @ ( b @ inverse @ ( d @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ ( identity @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( A @ ( identity @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ( k @ ( h @ inverse @ ( j @ product ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
thf(19,plain,
( ( k @ ( h @ inverse @ ( j @ product ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(234,plain,
$false,
inference(e,[status(thm)],[52,54,48,50,42,24,20,46,38,21,32,34,22,44,40,23,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.14/5.40 % Computer : n010.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Fri Sep 25 14:15:51 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.17/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/6.20 % [INFO] Parsing done (190ms).
% 1.36/6.21 % [INFO] Running in sequential loop mode.
% 1.93/6.61 % [INFO] eprover registered as external prover.
% 1.93/6.62 % [INFO] Scanning for conjecture ...
% 2.09/6.72 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.09/6.76 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.09/6.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.09/6.79 % [INFO] Type checking passed.
% 2.09/6.79 % [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 ...
% 4.61/7.88 % External prover 'e' found a proof!
% 4.61/7.88 % [INFO] Killing All external provers ...
% 4.61/7.88 % Time passed: 2322ms (effective reasoning time: 1661ms)
% 4.61/7.88 % Axioms used in derivation (12): ifeq_axiom_001, ifeq_axiom, left_identity, x_cubed_is_identity_1, left_inverse, right_identity, right_inverse, associativity1, total_function2, associativity2, x_cubed_is_identity_2, total_function1
% 4.61/7.88 % No. of inferences in proof: 37
% 4.61/7.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2322 ms resp. 1661 ms w/o parsing
% 5.41/7.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.41/7.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------