%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP126-4.004 : 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 : n005.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 07:20:07 AM UTC 2026
% Result : Unsatisfiable 6.92s 3.83s
% Output : Refutation 7.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 53 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 362 ( 60 ~; 54 |; 0 &; 248 @)
% ( 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 : 8 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $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(17,axiom,
~ ( e_3 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(56,plain,
~ ( e_3 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
~ ( e_4 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(52,plain,
~ ( e_4 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ equalish ) )
| ~ ( C @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
e_2 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(60,plain,
e_2 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
~ ( e_1 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(34,plain,
~ ( e_1 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
~ ( e_2 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(54,plain,
~ ( e_2 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
e_3 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(39,plain,
e_3 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
~ ( e_1 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(50,plain,
~ ( e_1 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,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(72,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)],[26]) ).
thf(9,axiom,
~ ( e_2 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(40,plain,
~ ( e_2 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
~ ( e_2 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(58,plain,
~ ( e_2 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
e_4 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
thf(36,plain,
e_4 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ equalish ) )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
~ ( e_3 @ ( e_4 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(42,plain,
~ ( e_3 @ ( e_4 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
~ ( e_4 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(37,plain,
~ ( e_4 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
~ ( e_4 @ ( e_3 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(46,plain,
~ ( e_4 @ ( e_3 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( A @ ( C @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_2) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( A @ ( C @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product ) ) )
| ( e_3 @ ( B @ ( A @ product ) ) )
| ( e_2 @ ( B @ ( A @ product ) ) )
| ( e_1 @ ( B @ ( A @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( e_4 @ ( B @ ( A @ product ) ) )
| ( e_3 @ ( B @ ( A @ product ) ) )
| ( e_2 @ ( B @ ( A @ product ) ) )
| ( e_1 @ ( B @ ( A @ product ) ) )
| ~ ( B @ group_element )
| ~ ( A @ group_element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
e_1 @ group_element,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(33,plain,
e_1 @ group_element,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
~ ( e_3 @ ( e_1 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(44,plain,
~ ( e_3 @ ( e_1 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( B @ ( D @ ( C @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_1) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( B @ ( D @ ( C @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
~ ( e_1 @ ( e_2 @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(48,plain,
~ ( e_1 @ ( e_2 @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,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(63,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)],[21]) ).
thf(90,plain,
$false,
inference(e,[status(thm)],[56,52,61,60,65,34,54,39,66,50,72,40,58,36,68,42,37,46,29,28,70,33,44,27,48,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.11 % 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
% 0.23/0.48 % Computer : n005.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Fri Sep 25 14:26:47 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.45/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.64 % [INFO] Parsing done (288ms).
% 1.99/1.66 % [INFO] Running in sequential loop mode.
% 2.95/2.28 % [INFO] eprover registered as external prover.
% 2.95/2.29 % [INFO] Scanning for conjecture ...
% 3.34/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 3.51/2.56 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 3.73/2.60 % [INFO] Problem is propositional (TPTP CNF).
% 3.73/2.60 % [INFO] Type checking passed.
% 3.73/2.61 % [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 ...
% 6.92/3.82 % External prover 'e' found a proof!
% 6.92/3.82 % [INFO] Killing All external provers ...
% 6.92/3.82 % Time passed: 3126ms (effective reasoning time: 2148ms)
% 6.92/3.82 % Axioms used in derivation (23): e_3_is_not_e_2, element_4, element_2, product_right_cancellation, column_surjectivity, product_total_function1, e_1_is_not_e_2, e_2_is_not_e_1, e_1_is_not_e_3, e_1_is_not_e_4, e_3_is_not_e_1, product_left_cancellation, row_surjectivity, e_2_is_not_e_3, element_3, e_4_is_not_e_2, product_total_function2, product_idempotence, e_3_is_not_e_4, element_1, e_4_is_not_e_3, e_2_is_not_e_4, e_4_is_not_e_1
% 6.92/3.82 % No. of inferences in proof: 53
% 6.92/3.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3126 ms resp. 2148 ms w/o parsing
% 7.18/3.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.18/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------