%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% 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 07:21:56 AM UTC 2026
% Result : Unsatisfiable 46.43s 11.03s
% Output : Refutation 47.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 302 ( 2 ~; 0 |; 0 &; 300 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(t_decl,type,
t: $i > $i > $i ).
thf(eta_decl,type,
eta: $i > $i ).
thf(x0_decl,type,
x0: $i ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(x1_decl,type,
x1: $i ).
thf(x2_decl,type,
x2: $i ).
thf(j_decl,type,
j: $i > $i ).
thf(quotient_decl,type,
quotient: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(i_decl,type,
i: $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ quotient ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( A @ i @ product ) )
= ( A @ j @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ i @ product ) )
= ( A @ j @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( one @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(46,plain,
! [A: $i] :
( ( one @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ eta )
= ( A @ ( A @ i @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
thf(60,plain,
! [A: $i] :
( ( A @ eta )
= ( A @ ( A @ i @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( A @ product ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) @ ( A @ difference ) )
= ( A @ ( A @ ( C @ product ) @ ( B @ product ) @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) @ ( A @ difference ) )
= ( A @ ( A @ ( C @ product ) @ ( B @ product ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ product ) @ ( A @ ( A @ j @ quotient ) @ product ) @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( A @ ( A @ product ) @ ( A @ ( A @ j @ quotient ) @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ product ) @ ( A @ ( A @ j @ quotient ) @ product ) @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( A @ ( A @ product ) @ ( A @ ( A @ j @ quotient ) @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ eta @ product ) @ ( A @ product ) )
= ( B @ ( A @ j @ j @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ eta @ product ) @ ( A @ product ) )
= ( B @ ( A @ j @ j @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ product ) @ ( A @ difference ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( one @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ j )
= ( A @ ( one @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
thf(24,plain,
! [A: $i] :
( ( A @ j )
= ( A @ ( one @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( x2 @ ( x1 @ product ) @ ( x0 @ eta @ t ) )
!= ( x2 @ ( x0 @ eta @ t ) @ ( x1 @ ( x0 @ eta @ t ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(21,plain,
( ( x2 @ ( x1 @ product ) @ ( x0 @ eta @ t ) )
!= ( x2 @ ( x0 @ eta @ t ) @ ( x1 @ ( x0 @ eta @ t ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ product ) )
= ( C @ ( B @ ( A @ eta @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ eta @ product ) )
= ( C @ ( B @ ( A @ eta @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ j @ quotient ) )
= ( A @ i @ ( A @ j @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( A @ j @ quotient ) )
= ( A @ i @ ( A @ j @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ t ) )
= ( A @ ( B @ ( A @ product ) @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ t ) )
= ( A @ ( B @ ( A @ product ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) )
= ( A @ ( B @ ( B @ ( A @ product ) @ ( C @ product ) @ quotient ) @ quotient ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ product ) @ ( A @ product ) @ ( B @ ( A @ product ) @ difference ) )
= ( A @ ( B @ ( B @ ( A @ product ) @ ( C @ product ) @ quotient ) @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ eta @ ( B @ product ) @ ( A @ product ) )
= ( A @ eta @ ( B @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A @ eta @ ( B @ product ) @ ( A @ product ) )
= ( A @ eta @ ( B @ ( A @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ i )
= ( one @ ( A @ difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(26,plain,
! [A: $i] :
( ( A @ i )
= ( one @ ( A @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ quotient ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ i @ i @ product ) )
= ( B @ ( A @ product ) @ ( A @ eta @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ i @ i @ product ) )
= ( B @ ( A @ product ) @ ( A @ eta @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15426,plain,
$false,
inference(e,[status(thm)],[56,52,46,60,44,54,48,50,58,42,24,21,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.09 % 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
% 0.20/0.46 % Computer : n007.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 15:43:23 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 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
% 0.99/1.08 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.28 % [INFO] Parsing done (196ms).
% 1.27/1.30 % [INFO] Running in sequential loop mode.
% 2.06/1.70 % [INFO] eprover registered as external prover.
% 2.06/1.71 % [INFO] Scanning for conjecture ...
% 2.24/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.24/1.87 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.24/1.90 % [INFO] Problem is propositional (TPTP CNF).
% 2.42/1.91 % [INFO] Type checking passed.
% 2.42/1.91 % [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 ...
% 46.43/11.03 % External prover 'e' found a proof!
% 46.43/11.03 % [INFO] Killing All external provers ...
% 46.43/11.03 % Time passed: 10384ms (effective reasoning time: 9725ms)
% 46.43/11.03 % Axioms used in derivation (19): sos14, sos06, sos13, sos10, sos09, sos02, sos11, sos19, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 46.43/11.03 % No. of inferences in proof: 41
% 46.43/11.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10384 ms resp. 9725 ms w/o parsing
% 47.04/11.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.04/11.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------