%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : n020.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 06:54:33 AM UTC 2026
% Result : Unsatisfiable 52.33s 20.40s
% Output : Refutation 52.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 325 ( 11 ~; 6 |; 0 &; 308 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
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(inverse_decl,type,
inverse: $i > $i ).
thf(1,negated_conjecture,
( ( c @ ( b @ ( a @ add ) @ add ) )
!= ( c @ ( b @ add ) @ ( a @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',huntinton_2) ).
thf(3,plain,
( ( c @ ( b @ ( a @ add ) @ add ) )
!= ( c @ ( b @ add ) @ ( a @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,plain,
( ( c @ ( b @ ( a @ add ) @ add ) )
!= ( c @ ( b @ add ) @ ( a @ add ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( c @ ( b @ ( a @ add ) @ add ) )
!= ( c @ ( b @ add ) @ ( a @ add ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ add ) @ inverse @ ( C @ inverse @ add ) @ inverse @ ( A @ add ) @ inverse @ ( C @ ( B @ ( A @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dn1) ).
thf(6,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ add ) @ inverse @ ( C @ inverse @ add ) @ inverse @ ( A @ add ) @ inverse @ ( C @ ( B @ ( A @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ add ) @ inverse @ ( C @ inverse @ add ) @ inverse @ ( A @ add ) @ inverse @ ( C @ ( B @ ( A @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= C ),
inference(lifteq,[status(thm)],[6]) ).
thf(18,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ add ) @ inverse @ ( C @ inverse @ add ) @ inverse @ ( A @ add ) @ inverse @ ( C @ ( B @ ( A @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
!= ( H @ ( G @ add ) @ inverse @ ( G @ inverse @ add ) @ inverse @ ( E @ add ) @ inverse ) )
| ( ( C @ ( G @ ( F @ ( E @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= G ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ ( A @ ( C @ ( B @ ( C @ inverse @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= ( C @ inverse ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( R @ inverse @ inverse )),bind(B,$thf( N )),bind(C,$thf( R )),bind(D,$thf( S )),bind(E,$thf( R @ ( N @ ( R @ inverse @ inverse @ add ) @ inverse @ add ) @ inverse )),bind(F,$thf( F )),bind(G,$thf( R @ inverse )),bind(H,$thf( S @ ( R @ add ) @ inverse ))]]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ inverse @ ( A @ ( C @ ( B @ ( C @ inverse @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
= ( C @ inverse ) ),
inference(simp,[status(thm)],[19]) ).
thf(55,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ add ) @ inverse @ ( C @ inverse @ add ) @ inverse @ ( A @ add ) @ inverse @ ( C @ ( B @ ( A @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse )
!= ( E @ ( G @ ( F @ ( G @ inverse @ inverse @ add ) @ inverse @ add ) @ inverse @ add ) @ inverse ) )
| ( ( G @ ( G @ inverse @ ( C @ add ) @ inverse @ add ) @ inverse )
= ( G @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[7,22]) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ ( A @ add ) @ inverse @ add ) @ inverse )
= ( A @ inverse ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( T @ inverse @ inverse )),bind(B,$thf( B )),bind(C,$thf( T )),bind(D,$thf( U )),bind(E,$thf( U @ ( T @ add ) @ inverse @ ( T @ inverse @ add ) @ inverse @ ( T @ inverse @ inverse @ add ) @ inverse )),bind(F,$thf( B )),bind(G,$thf( T ))]]) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ ( A @ add ) @ inverse @ add ) @ inverse )
= ( A @ inverse ) ),
inference(simp,[status(thm)],[56]) ).
thf(8,plain,
( ( ( c @ ( b @ add ) )
!= c )
| ( ( b @ ( a @ add ) )
!= a ) ),
inference(simp,[status(thm)],[5]) ).
thf(95,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ ( A @ add ) @ inverse @ add ) @ inverse )
!= ( D @ ( C @ ( B @ add ) @ inverse @ add ) @ inverse ) )
| ( ( E @ ( D @ add ) @ inverse @ ( D @ inverse @ add ) @ inverse @ ( B @ add ) @ inverse @ ( A @ inverse @ add ) @ inverse )
= D ) ),
inference(paramod_ordered,[status(thm)],[77,7]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ add ) @ inverse @ ( B @ inverse @ add ) @ inverse @ ( B @ add ) @ inverse @ ( B @ inverse @ add ) @ inverse )
= B ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ inverse )),bind(D,$thf( F ))]]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ add ) @ inverse @ ( B @ inverse @ add ) @ inverse @ ( B @ add ) @ inverse @ ( B @ inverse @ add ) @ inverse )
= B ),
inference(simp,[status(thm)],[96]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ ( A @ add ) @ inverse @ add ) @ inverse )
!= ( B @ inverse @ ( B @ add ) @ inverse ) )
| ( ( B @ ( A @ inverse @ add ) @ inverse )
= ( B @ inverse ) ) ),
inference(paramod_ordered,[status(thm)],[77,77]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ ( A @ add ) @ inverse @ add ) )
!= ( B @ inverse @ ( B @ add ) ) )
| ( ( B @ ( A @ inverse @ add ) @ inverse )
= ( B @ inverse ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(1072,plain,
$false,
inference(e,[status(thm)],[5,6,77,7,3,8,126,22,118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO073-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % 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
% 0.17/0.41 % Computer : n020.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sat Sep 26 22:43:33 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.15 % [INFO] Parsing done (169ms).
% 1.28/1.17 % [INFO] Running in sequential loop mode.
% 1.82/1.56 % [INFO] eprover registered as external prover.
% 1.82/1.57 % [INFO] Scanning for conjecture ...
% 2.03/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.03/1.68 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.03/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/1.70 % [INFO] Type checking passed.
% 2.20/1.70 % [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 ...
% 52.33/20.40 % External prover 'e' found a proof!
% 52.33/20.40 % [INFO] Killing All external provers ...
% 52.33/20.40 % Time passed: 19843ms (effective reasoning time: 19226ms)
% 52.33/20.40 % Axioms used in derivation (1): dn1
% 52.33/20.40 % No. of inferences in proof: 20
% 52.33/20.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 19843 ms resp. 19226 ms w/o parsing
% 52.33/20.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.33/20.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------