%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n008.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 06:54:29 AM UTC 2026
% Result : Unsatisfiable 3.42s 2.32s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 106 ( 2 ~; 0 |; 0 &; 104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(e_decl,type,
e: $i ).
thf(f_decl,type,
f: $i ).
thf(g_decl,type,
g: $i ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ multiply ) ) @ ( D @ ( C @ ( B @ ( A @ multiply ) ) @ multiply ) ) )
= ( E @ ( D @ ( C @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(10,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ multiply ) ) @ ( D @ ( C @ ( B @ ( A @ multiply ) ) @ multiply ) ) )
= ( E @ ( D @ ( C @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( c @ ( e @ ( f @ ( g @ multiply ) ) @ ( d @ multiply ) ) @ ( g @ ( d @ ( c @ multiply ) ) @ ( f @ ( e @ ( d @ ( c @ multiply ) ) @ multiply ) ) @ inverse @ ( b @ ( a @ inverse @ ( a @ multiply ) ) @ multiply ) ) )
!= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_single_axiom) ).
thf(7,plain,
( ( c @ ( e @ ( f @ ( g @ multiply ) ) @ ( d @ multiply ) ) @ ( g @ ( d @ ( c @ multiply ) ) @ ( f @ ( e @ ( d @ ( c @ multiply ) ) @ multiply ) ) @ inverse @ ( b @ ( a @ inverse @ ( a @ multiply ) ) @ multiply ) ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ inverse @ ( B @ ( A @ multiply ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ inverse @ ( B @ ( A @ multiply ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ inverse @ multiply ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ inverse @ multiply ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.09 % 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 : n008.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 22:38:40 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
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.18 % [INFO] Parsing done (181ms).
% 1.21/1.19 % [INFO] Running in sequential loop mode.
% 1.79/1.59 % [INFO] eprover registered as external prover.
% 1.99/1.60 % [INFO] Scanning for conjecture ...
% 1.99/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.15/1.72 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.15/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.74 % [INFO] Type checking passed.
% 2.15/1.74 % [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 ...
% 3.42/2.31 % External prover 'e' found a proof!
% 3.42/2.31 % [INFO] Killing All external provers ...
% 3.42/2.31 % Time passed: 1759ms (effective reasoning time: 1115ms)
% 3.42/2.32 % Axioms used in derivation (5): associativity, ternary_multiply_1, right_inverse, ternary_multiply_2, left_inverse
% 3.42/2.32 % No. of inferences in proof: 13
% 3.42/2.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1759 ms resp. 1115 ms w/o parsing
% 3.42/2.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.42/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------