%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:20:03 AM UTC 2026
% Result : Unsatisfiable 5.43s 3.28s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 360 ( 56 ~; 60 |; 0 &; 244 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(product1_decl,type,
product1: $i > $i > $i > $o ).
thf(product2_decl,type,
product2: $i > $i > $i > $o ).
thf(group_element_decl,type,
group_element: $i > $o ).
thf(e_1_decl,type,
e_1: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(e_3_decl,type,
e_3: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(e_2_decl,type,
e_2: $i ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( e_3 @ ( B @ ( A @ product1 ) ) )
| ( e_2 @ ( B @ ( A @ product1 ) ) )
| ( e_1 @ ( B @ ( A @ product1 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( e_3 @ ( B @ ( A @ product1 ) ) )
| ( e_2 @ ( B @ ( A @ product1 ) ) )
| ( e_1 @ ( B @ ( A @ product1 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
~ ( e_2 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(41,plain,
~ ( e_2 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function2) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
~ ( e_3 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(39,plain,
~ ( e_3 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
~ ( e_3 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(35,plain,
~ ( e_3 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ ( A @ product1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
~ ( e_2 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(31,plain,
~ ( e_2 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
e_2 @ group_element,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(43,plain,
e_2 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( e_3 @ ( B @ ( A @ product2 ) ) )
| ( e_2 @ ( B @ ( A @ product2 ) ) )
| ( e_1 @ ( B @ ( A @ product2 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function1) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( e_3 @ ( B @ ( A @ product2 ) ) )
| ( e_2 @ ( B @ ( A @ product2 ) ) )
| ( e_1 @ ( B @ ( A @ product2 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
thf(51,plain,
! [A: $i] : ( A @ ( A @ ( A @ product2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
~ ( e_1 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(37,plain,
~ ( e_1 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,axiom,
e_1 @ group_element,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(25,plain,
e_1 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( e_3 @ ( A @ product ) ) )
| ( B @ ( e_2 @ ( A @ product ) ) )
| ( B @ ( e_1 @ ( A @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( e_3 @ ( A @ product ) ) )
| ( B @ ( e_2 @ ( A @ product ) ) )
| ( B @ ( e_1 @ ( A @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
e_3 @ group_element,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(28,plain,
e_3 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( e_3 @ product ) ) )
| ( B @ ( A @ ( e_2 @ product ) ) )
| ( B @ ( A @ ( e_1 @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( e_3 @ product ) ) )
| ( B @ ( A @ ( e_2 @ product ) ) )
| ( B @ ( A @ ( e_1 @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_left_cancellation) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
~ ( e_1 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(26,plain,
~ ( e_1 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ product2 ) ) )
| ~ ( D @ ( B @ ( C @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ product2 ) ) )
| ~ ( D @ ( B @ ( C @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(72,plain,
$false,
inference(e,[status(thm)],[56,52,60,41,44,39,35,48,31,43,58,51,37,25,46,29,28,33,54,49,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.12 % 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
% 0.22/0.50 % Computer : n007.cluster.edu
% 0.22/0.50 % Model : x86_64 x86_64
% 0.22/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.50 % Memory : 8046.5625MB
% 0.22/0.50 % OS : Linux 6.8.0-71-generic
% 0.22/0.50 % CPULimit : 300
% 0.22/0.50 % WCLimit : 300
% 0.22/0.50 % DateTime : Fri Sep 25 14:22:38 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 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
% 1.42/1.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.94/1.63 % [INFO] Parsing done (271ms).
% 1.94/1.66 % [INFO] Running in sequential loop mode.
% 2.92/2.27 % [INFO] eprover registered as external prover.
% 2.92/2.28 % [INFO] Scanning for conjecture ...
% 3.28/2.41 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 3.45/2.51 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.45/2.55 % [INFO] Problem is propositional (TPTP CNF).
% 3.45/2.56 % [INFO] Type checking passed.
% 3.45/2.57 % [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 ...
% 5.43/3.28 % External prover 'e' found a proof!
% 5.43/3.28 % [INFO] Killing All external provers ...
% 5.43/3.28 % Time passed: 2565ms (effective reasoning time: 1613ms)
% 5.43/3.28 % Axioms used in derivation (21): e_3_is_not_e_2, product2_total_function1, product1_left_cancellation, element_2, product1_total_function1, e_1_is_not_e_2, product1_total_function2, product2_idempotence, product2_total_function2, e_1_is_not_e_3, e_3_is_not_e_1, row_surjectivity, e_2_is_not_e_3, element_3, product1_idempotence, column_surjectivity, product2_left_cancellation, e_2_is_not_e_1, product2_right_cancellation, product1_right_cancellation, element_1
% 5.43/3.28 % No. of inferences in proof: 45
% 5.43/3.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2565 ms resp. 1613 ms w/o parsing
% 5.74/3.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.74/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------