%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP025-1 : 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 : n002.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 07:19:46 AM UTC 2026
% Result : Unsatisfiable 4.72s 12.53s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 65 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 378 ( 32 ~; 34 |; 0 &; 312 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $i > $o ).
thf(g2_decl,type,
g2: $i ).
thf(an_isomorphism_decl,type,
an_isomorphism: $i > $i ).
thf(d1_decl,type,
d1: $i ).
thf(d2_decl,type,
d2: $i ).
thf(d3_decl,type,
d3: $i ).
thf(group_member_decl,type,
group_member: $i > $i > $o ).
thf(inverse_decl,type,
inverse: $i > $i > $i ).
thf(identity_for_decl,type,
identity_for: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(g1_decl,type,
g1: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(d_decl,type,
d: $i ).
thf(c_decl,type,
c: $i ).
thf(24,axiom,
g2 @ ( d @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_member_of_group2) ).
thf(69,plain,
g2 @ ( d @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
a @ ( b @ ( b @ ( g1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_a) ).
thf(52,plain,
a @ ( b @ ( b @ ( g1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: $i] :
( ( A = d )
| ( A = c )
| ~ ( g2 @ ( A @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_and_d_only_members_of_group2) ).
thf(65,plain,
! [A: $i] :
( ( A = d )
| ( A = c )
| ~ ( g2 @ ( A @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
g1 @ ( d3 @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).
thf(53,plain,
g1 @ ( d3 @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
g1 @ ( d1 @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).
thf(77,plain,
g1 @ ( d1 @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
g1 @ ( a @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_member_of_group1) ).
thf(41,plain,
g1 @ ( a @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ inverse ) @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_in_group) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ inverse ) @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( D @ ( A @ product ) ) ) )
| ~ ( G @ ( F @ ( B @ ( A @ product ) ) ) )
| ~ ( F @ ( E @ ( C @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
thf(50,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( D @ ( A @ product ) ) ) )
| ~ ( G @ ( F @ ( B @ ( A @ product ) ) ) )
| ~ ( F @ ( E @ ( C @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ multiply ) ) @ ( C @ ( A @ ( B @ product ) ) ) )
| ~ ( B @ ( C @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_1) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ multiply ) ) @ ( C @ ( A @ ( B @ product ) ) ) )
| ~ ( B @ ( C @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
( ( a @ an_isomorphism )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).
thf(55,plain,
( ( a @ an_isomorphism )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i] :
( ( A = b )
| ( A = a )
| ~ ( g1 @ ( A @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
thf(42,plain,
! [A: $i] :
( ( A = b )
| ( A = a )
| ~ ( g1 @ ( A @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ identity_for @ group_member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_in_group) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ identity_for @ group_member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
g1 @ ( d2 @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).
thf(57,plain,
g1 @ ( d2 @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
c @ ( c @ ( c @ ( g2 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).
thf(78,plain,
c @ ( c @ ( c @ ( g2 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( B @ ( A @ identity_for @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(61,plain,
! [B: $i,A: $i] : ( B @ ( A @ identity_for @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [B: $i,A: $i] : ( A @ identity_for @ ( B @ ( A @ inverse ) @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(74,plain,
! [B: $i,A: $i] : ( A @ identity_for @ ( B @ ( A @ inverse ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
g1 @ ( b @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_member_of_group1) ).
thf(38,plain,
g1 @ ( b @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
d3 @ ( d2 @ ( d1 @ ( g1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
thf(70,plain,
d3 @ ( d2 @ ( d1 @ ( g1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,negated_conjecture,
~ ( d3 @ an_isomorphism @ ( d2 @ an_isomorphism @ ( d1 @ an_isomorphism @ ( g2 @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
thf(33,plain,
~ ( d3 @ an_isomorphism @ ( d2 @ an_isomorphism @ ( d1 @ an_isomorphism @ ( g2 @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( B @ ( A @ product ) ) ) )
| ~ ( G @ ( E @ ( D @ ( A @ product ) ) ) )
| ~ ( F @ ( E @ ( C @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(45,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( B @ ( A @ product ) ) ) )
| ~ ( G @ ( E @ ( D @ ( A @ product ) ) ) )
| ~ ( F @ ( E @ ( C @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
g2 @ ( c @ group_member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_member_of_group2) ).
thf(64,plain,
g2 @ ( c @ group_member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [B: $i,A: $i] : ( A @ identity_for @ ( B @ ( B @ ( A @ inverse ) @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(71,plain,
! [B: $i,A: $i] : ( A @ identity_for @ ( B @ ( B @ ( A @ inverse ) @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
d @ ( c @ ( d @ ( g2 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).
thf(54,plain,
d @ ( c @ ( d @ ( g2 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
d @ ( d @ ( c @ ( g2 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).
thf(76,plain,
d @ ( d @ ( c @ ( g2 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ multiply ) ) @ group_member ) )
| ~ ( B @ ( C @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_2) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ multiply ) ) @ group_member ) )
| ~ ( B @ ( C @ group_member ) )
| ~ ( B @ ( A @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ( b @ an_isomorphism )
= d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).
thf(48,plain,
( ( b @ an_isomorphism )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
b @ ( a @ ( b @ ( g1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).
thf(63,plain,
b @ ( a @ ( b @ ( g1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
b @ ( b @ ( a @ ( g1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
thf(75,plain,
b @ ( b @ ( a @ ( g1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( E @ ( C @ ( B @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
thf(58,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( E @ ( C @ ( B @ ( A @ product ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ product ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
c @ ( d @ ( d @ ( g2 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).
thf(47,plain,
c @ ( d @ ( d @ ( g2 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
a @ ( a @ ( a @ ( g1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
thf(68,plain,
a @ ( a @ ( a @ ( g1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ identity_for @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(62,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ identity_for @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(85,plain,
$false,
inference(e,[status(thm)],[69,52,65,53,77,41,35,50,72,55,42,37,57,78,61,74,38,70,33,45,64,71,54,76,39,48,63,75,58,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % 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
% 0.16/10.42 % Computer : n002.cluster.edu
% 0.16/10.42 % Model : x86_64 x86_64
% 0.16/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.42 % Memory : 8046.5625MB
% 0.16/10.42 % OS : Linux 6.8.0-71-generic
% 0.16/10.42 % CPULimit : 300
% 0.16/10.42 % WCLimit : 300
% 0.16/10.42 % DateTime : Fri Sep 25 14:20:03 UTC 2026
% 0.16/10.43 % CPUTime :
% 0.16/10.43 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
% 0.19/10.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/11.11 % [INFO] Parsing done (212ms).
% 1.20/11.13 % [INFO] Running in sequential loop mode.
% 2.01/11.56 % [INFO] eprover registered as external prover.
% 2.01/11.57 % [INFO] Scanning for conjecture ...
% 2.24/11.68 % [INFO] Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ...
% 2.43/11.74 % [INFO] Axiom selection finished. Selected 31 axioms (removed 0 axioms).
% 2.43/11.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.43/11.79 % [INFO] Type checking passed.
% 2.43/11.79 % [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 ...
% 4.72/12.52 % External prover 'e' found a proof!
% 4.72/12.52 % [INFO] Killing All external provers ...
% 4.72/12.52 % Time passed: 1929ms (effective reasoning time: 1387ms)
% 4.72/12.53 % Axioms used in derivation (31): b_times_a_is_b, d1_times_d2_is_d3, left_identity, a_and_b_only_members_of_group1, d_times_d_is_c, right_identity, total_function1_1, associativity1, a_times_b_is_b, d_member_of_group2, a_member_of_group1, total_function2, b_member_of_group1, b_maps_to_d, c_and_d_only_members_of_group2, c_times_c_is_c, identity_in_group, d1_member_of_group1, c_member_of_group2, c_times_d_is_d, a_maps_to_c, left_inverse, a_times_a_is_a, right_inverse, b_times_b_is_a, total_function1_2, d_times_c_is_d, d3_member_of_group1, inverse_in_group, d2_member_of_group1, associativity2
% 4.72/12.53 % No. of inferences in proof: 65
% 4.72/12.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1929 ms resp. 1387 ms w/o parsing
% 4.72/12.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.72/12.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------