%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO249^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n012.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 : Wed Sep 30 08:45:28 AM UTC 2026
% Result : Theorem 3.71s 1.70s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 42 equ; 0 cnn)
% Maximal formula atoms : 65 ( 58 avg)
% Number of connectives : 425 ( 2 ~; 0 |; 90 &; 294 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 72 !; 3 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(cBIGPHI_decl,type,
cBIGPHI: $i > $i ).
thf(cHOM_FROM_HH_1_decl,type,
cHOM_FROM_HH_1: ( $i > $i ) > $o ).
thf(cPHI_2_decl,type,
cPHI_2: $i > $i ).
thf(cHOM_FROM_SS_PRIME_decl,type,
cHOM_FROM_SS_PRIME: ( $i > $i ) > $o ).
thf(cPHI_1_decl,type,
cPHI_1: $i > $i ).
thf(cSS_PRIME_decl,type,
cSS_PRIME: $i > $o ).
thf(el1_decl,type,
el1: $i > ( $i > $o ) > $o ).
thf(cHH_1_decl,type,
cHH_1: $i > $o ).
thf(cBIGHI_decl,type,
cBIGHI: $i > $i ).
thf(cHH_2_decl,type,
cHH_2: $i > $o ).
thf(cTIMES_decl,type,
cTIMES: $i > $i > $i ).
thf(1,conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_2 )
& ( el1 @ B @ cHH_2 )
& ( el1 @ C @ cHH_2 )
& ( el1 @ D @ cHH_2 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cSS_PRIME )
& ( el1 @ B @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cSS_PRIME ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( el1 @ C @ cHH_1 )
& ( el1 @ D @ cHH_1 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i > $i] :
( ( cHOM_FROM_SS_PRIME @ A )
= ( ! [B: $i,C: $i] :
( ( ( el1 @ B @ cSS_PRIME )
& ( el1 @ C @ cSS_PRIME ) )
=> ( ( A @ ( cTIMES @ B @ C ) )
= ( cTIMES @ ( A @ B ) @ ( A @ C ) ) ) ) ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= ( ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ A @ B ) )
= ( cTIMES @ ( cBIGPHI @ A ) @ ( cBIGPHI @ B ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cHH_1 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ A ) @ cHH_1 ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( A = B ) )
=> ( ( cBIGHI @ A )
= ( cBIGPHI @ B ) ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( ( cBIGPHI @ ( cPHI_1 @ A ) )
= ( cPHI_2 @ A ) ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ? [B: $i] :
( ( el1 @ B @ cSS_PRIME )
& ( ( cPHI_1 @ B )
= A ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPROB757) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_2 )
& ( el1 @ B @ cHH_2 )
& ( el1 @ C @ cHH_2 )
& ( el1 @ D @ cHH_2 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cSS_PRIME )
& ( el1 @ B @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cSS_PRIME ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( el1 @ C @ cHH_1 )
& ( el1 @ D @ cHH_1 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i > $i] :
( ( cHOM_FROM_SS_PRIME @ A )
= ( ! [B: $i,C: $i] :
( ( ( el1 @ B @ cSS_PRIME )
& ( el1 @ C @ cSS_PRIME ) )
=> ( ( A @ ( cTIMES @ B @ C ) )
= ( cTIMES @ ( A @ B ) @ ( A @ C ) ) ) ) ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= ( ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ A @ B ) )
= ( cTIMES @ ( cBIGPHI @ A ) @ ( cBIGPHI @ B ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cHH_1 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ A ) @ cHH_1 ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( A = B ) )
=> ( ( cBIGHI @ A )
= ( cBIGPHI @ B ) ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( ( cBIGPHI @ ( cPHI_1 @ A ) )
= ( cPHI_2 @ A ) ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ? [B: $i] :
( ( el1 @ B @ cSS_PRIME )
& ( ( cPHI_1 @ B )
= A ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_2 )
& ( el1 @ B @ cHH_2 )
& ( el1 @ C @ cHH_2 )
& ( el1 @ D @ cHH_2 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cSS_PRIME )
& ( el1 @ B @ cSS_PRIME ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cSS_PRIME ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( el1 @ C @ cHH_1 )
& ( el1 @ D @ cHH_1 )
& ( A = B )
& ( C = D ) )
=> ( ( cTIMES @ A @ C )
= ( cTIMES @ B @ D ) ) )
& ! [A: $i > $i] :
( ( cHOM_FROM_SS_PRIME @ A )
= ( ! [B: $i,C: $i] :
( ( ( el1 @ B @ cSS_PRIME )
& ( el1 @ C @ cSS_PRIME ) )
=> ( ( A @ ( cTIMES @ B @ C ) )
= ( cTIMES @ ( A @ B ) @ ( A @ C ) ) ) ) ) )
& ( ( cHOM_FROM_HH_1 @ cBIGPHI )
= ( ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( ( cBIGPHI @ ( cTIMES @ A @ B ) )
= ( cTIMES @ ( cBIGPHI @ A ) @ ( cBIGPHI @ B ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 ) )
=> ( el1 @ ( cTIMES @ A @ B ) @ cHH_1 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_2 @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ( el1 @ ( cBIGPHI @ A ) @ cHH_2 ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( el1 @ ( cPHI_1 @ A ) @ cHH_1 ) )
& ! [A: $i,B: $i] :
( ( ( el1 @ A @ cHH_1 )
& ( el1 @ B @ cHH_1 )
& ( A = B ) )
=> ( ( cBIGHI @ A )
= ( cBIGPHI @ B ) ) )
& ! [A: $i] :
( ( el1 @ A @ cSS_PRIME )
=> ( ( cBIGPHI @ ( cPHI_1 @ A ) )
= ( cPHI_2 @ A ) ) )
& ! [A: $i] :
( ( el1 @ A @ cHH_1 )
=> ? [B: $i] :
( ( el1 @ B @ cSS_PRIME )
& ( ( cPHI_1 @ B )
= A ) ) )
& ( cHOM_FROM_SS_PRIME @ cPHI_1 )
& ( cHOM_FROM_SS_PRIME @ cPHI_2 ) )
=> ( cHOM_FROM_HH_1 @ cBIGPHI ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO249^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % 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
% 0.06/0.17 % Computer : n012.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 16:40:48 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 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
% 0.79/0.62 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.94/0.76 % [INFO] Parsing done (132ms).
% 0.94/0.77 % [INFO] Running in sequential loop mode.
% 1.41/1.00 % [INFO] eprover registered as external prover.
% 1.41/1.00 % [INFO] Scanning for conjecture ...
% 1.67/1.09 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.67/1.12 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.67/1.12 % [INFO] Problem is higher-order (TPTP THF).
% 1.67/1.12 % [INFO] Type checking passed.
% 1.67/1.13 % [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 ...
% 3.71/1.70 % External prover 'e' found a proof!
% 3.71/1.70 % [INFO] Killing All external provers ...
% 3.71/1.70 % Time passed: 1413ms (effective reasoning time: 931ms)
% 3.71/1.70 % Solved by 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)>
% 3.71/1.70 % Axioms used in derivation (0):
% 3.71/1.70 % No. of inferences in proof: 4
% 3.71/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1413 ms resp. 931 ms w/o parsing
% 3.71/1.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------