%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n016.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 07:20:26 AM UTC 2026
% Result : Theorem 3.90s 2.44s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 172 ( 2 ~; 0 |; 14 &; 140 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 0 ^; 29 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(left_zero_decl,type,
left_zero: $i > $i > $o ).
thf(h_decl,type,
h: $i ).
thf(phi_decl,type,
phi: $i > $i ).
thf(f_left_zero_decl,type,
f_left_zero: $i ).
thf(group_member_decl,type,
group_member: $i > $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i > $i ).
thf(f_decl,type,
f: $i ).
thf(1,conjecture,
f_left_zero @ phi @ ( h @ left_zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_zero_h) ).
thf(2,negated_conjecture,
~ ( f_left_zero @ phi @ ( h @ left_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( f_left_zero @ phi @ ( h @ left_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
f_left_zero @ ( f @ left_zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_zero_for_f) ).
thf(37,plain,
f_left_zero @ ( f @ left_zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( h @ ( A @ group_member ) )
=> ? [B: $i] :
( ( ( B @ phi )
= A )
& ( f @ ( B @ group_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
thf(21,plain,
! [A: $i] :
( ( h @ ( A @ group_member ) )
=> ? [B: $i] :
( ( ( B @ phi )
= A )
& ( f @ ( B @ group_member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ group_member ) )
& ( A @ ( C @ group_member ) )
& ( A @ ( B @ group_member ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ multiply ) ) @ ( A @ multiply ) ) )
= ( D @ ( C @ ( A @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(13,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ group_member ) )
& ( A @ ( C @ group_member ) )
& ( A @ ( B @ group_member ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ multiply ) ) @ ( A @ multiply ) ) )
= ( D @ ( C @ ( A @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( f @ ( B @ group_member ) )
& ( f @ ( A @ group_member ) ) )
=> ( ( B @ phi @ ( A @ phi @ ( h @ multiply ) ) )
= ( B @ ( A @ ( f @ multiply ) ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( f @ ( B @ group_member ) )
& ( f @ ( A @ group_member ) ) )
=> ( ( B @ phi @ ( A @ phi @ ( h @ multiply ) ) )
= ( B @ ( A @ ( f @ multiply ) ) @ phi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( f @ ( A @ group_member ) )
=> ( h @ ( A @ phi @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(16,plain,
! [A: $i] :
( ( f @ ( A @ group_member ) )
=> ( h @ ( A @ phi @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ group_member ) )
& ( A @ ( B @ group_member ) ) )
=> ( A @ ( C @ ( B @ ( A @ multiply ) ) @ group_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function) ).
thf(11,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ group_member ) )
& ( A @ ( B @ group_member ) ) )
=> ( A @ ( C @ ( B @ ( A @ multiply ) ) @ group_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ left_zero ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ group_member ) )
=> ( ( C @ ( B @ ( A @ multiply ) ) )
= B ) )
& ( A @ ( B @ group_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_zero) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( A @ ( C @ group_member ) )
=> ( ( C @ ( B @ ( A @ multiply ) ) )
= B ) )
& ( A @ ( B @ group_member ) ) )
=> ( B @ ( A @ left_zero ) ) )
& ( ( B @ ( A @ left_zero ) )
=> ( ! [C: $i] :
( ( A @ ( C @ group_member ) )
=> ( ( C @ ( B @ ( A @ multiply ) ) )
= B ) )
& ( A @ ( B @ group_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[10,37,21,13,18,16,11,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 14:42:14 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (201ms).
% 1.43/1.20 % [INFO] Running in sequential loop mode.
% 2.11/1.62 % [INFO] eprover registered as external prover.
% 2.11/1.63 % [INFO] Scanning for conjecture ...
% 2.30/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.30/1.75 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.30/1.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.79 % [INFO] Type checking passed.
% 2.49/1.80 % [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 ...
% 3.90/2.44 % External prover 'e' found a proof!
% 3.90/2.44 % [INFO] Killing All external provers ...
% 3.90/2.44 % Time passed: 1889ms (effective reasoning time: 1229ms)
% 3.90/2.44 % Solved by 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)>
% 3.90/2.44 % Axioms used in derivation (7): associativity, homomorphism1, surjective, left_zero_for_f, total_function, homomorphism2, left_zero
% 3.90/2.44 % No. of inferences in proof: 18
% 3.90/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1889 ms resp. 1229 ms w/o parsing
% 3.90/2.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.90/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------