%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP124-9.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n004.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 07:20:05 AM UTC 2026
% Result : Unsatisfiable 6.82s 3.67s
% Output : Refutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 59 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 430 ( 68 ~; 68 |; 0 &; 294 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 5 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(e_4_decl,type,
e_4: $i ).
thf(e_2_decl,type,
e_2: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
thf(69,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)],[23]) ).
thf(14,axiom,
~ ( e_1 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(53,plain,
~ ( e_1 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( e_4 @ ( A @ product ) ) )
| ( B @ ( e_3 @ ( A @ product ) ) )
| ( B @ ( e_2 @ ( A @ product ) ) )
| ( B @ ( e_1 @ ( A @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( e_4 @ ( A @ product ) ) )
| ( 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)],[8]) ).
thf(25,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ ( A @ product2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
~ ( e_3 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(59,plain,
~ ( e_3 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
thf(66,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)],[21]) ).
thf(19,axiom,
e_2 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(63,plain,
e_2 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
~ ( e_4 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(43,plain,
~ ( e_4 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
~ ( e_1 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(55,plain,
~ ( e_1 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
~ ( e_2 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(57,plain,
~ ( e_2 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product2 ) ) )
| ( e_3 @ ( B @ ( A @ product2 ) ) )
| ( e_2 @ ( B @ ( A @ product2 ) ) )
| ( e_1 @ ( B @ ( A @ product2 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function1) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product2 ) ) )
| ( 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)],[28]) ).
thf(18,axiom,
~ ( e_2 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(61,plain,
~ ( e_2 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_left_cancellation) ).
thf(74,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)],[26]) ).
thf(6,axiom,
e_3 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(38,plain,
e_3 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
~ ( e_1 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(33,plain,
~ ( e_1 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
e_1 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(32,plain,
e_1 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
~ ( e_3 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(45,plain,
~ ( e_3 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function2) ).
thf(64,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)],[20]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product1 ) ) )
| ( e_3 @ ( B @ ( A @ product1 ) ) )
| ( e_2 @ ( B @ ( A @ product1 ) ) )
| ( e_1 @ ( B @ ( A @ product1 ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product1 ) ) )
| ( 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)],[24]) ).
thf(12,axiom,
~ ( e_3 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(49,plain,
~ ( e_3 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
thf(76,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)],[27]) ).
thf(7,axiom,
~ ( e_2 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(39,plain,
~ ( e_2 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product2 ) ) )
| ~ ( C @ ( B @ ( A @ product2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
thf(80,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)],[29]) ).
thf(4,axiom,
e_4 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
thf(35,plain,
e_4 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
~ ( e_4 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(36,plain,
~ ( e_4 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ product2 ) ) )
| ~ ( D @ ( A @ ( C @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ product2 ) ) )
| ~ ( D @ ( A @ ( C @ product1 ) ) )
| ~ ( C @ ( B @ ( A @ product1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
~ ( e_4 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(51,plain,
~ ( e_4 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( e_4 @ product ) ) )
| ( B @ ( A @ ( e_3 @ product ) ) )
| ( B @ ( A @ ( e_2 @ product ) ) )
| ( B @ ( A @ ( e_1 @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( e_4 @ product ) ) )
| ( 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)],[11]) ).
thf(22,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
thf(68,plain,
! [A: $i] : ( A @ ( A @ ( A @ product1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[69,53,41,73,59,66,63,43,55,57,78,61,74,38,33,32,45,64,71,49,76,39,80,35,36,30,51,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-9.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 14:25:36 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.33/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.56 % [INFO] Parsing done (299ms).
% 1.86/1.58 % [INFO] Running in sequential loop mode.
% 3.08/2.19 % [INFO] eprover registered as external prover.
% 3.19/2.21 % [INFO] Scanning for conjecture ...
% 3.19/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 3.39/2.36 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 3.39/2.40 % [INFO] Problem is propositional (TPTP CNF).
% 3.63/2.40 % [INFO] Type checking passed.
% 3.63/2.40 % [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 ...
% 6.82/3.66 % External prover 'e' found a proof!
% 6.82/3.66 % [INFO] Killing All external provers ...
% 6.82/3.67 % Time passed: 3058ms (effective reasoning time: 2073ms)
% 6.82/3.67 % Axioms used in derivation (28): e_3_is_not_e_2, product2_total_function1, element_4, product1_left_cancellation, element_2, e_4_is_not_e_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_1_is_not_e_4, 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, e_3_is_not_e_4, product1_right_cancellation, element_1, e_4_is_not_e_3, e_2_is_not_e_4, e_4_is_not_e_1
% 6.82/3.67 % No. of inferences in proof: 59
% 6.82/3.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3058 ms resp. 2073 ms w/o parsing
% 7.05/3.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.05/3.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------