%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n017.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 08:25:19 AM UTC 2026
% Result : Unsatisfiable 18.12s 10.47s
% Output : Refutation 18.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 55 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 512 ( 70 ~; 72 |; 0 &; 370 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 156 ( 0 ^; 156 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(l_decl,type,
l: $i ).
thf(n_decl,type,
n: $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(h_decl,type,
h: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(37,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(52,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(65,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ sum ) ) )
| ~ ( F @ ( E @ ( A @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(41,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ sum ) ) )
| ~ ( F @ ( E @ ( A @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(59,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(39,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(66,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(63,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [A: $i] :
( ( A = additive_identity )
| ( multiplicative_identity @ ( A @ h @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
thf(43,plain,
! [A: $i] :
( ( A = additive_identity )
| ( multiplicative_identity @ ( A @ h @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(58,plain,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(46,plain,
! [A: $i] : ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [A: $i] : ( A @ ( A @ ( multiplicative_identity @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_identity) ).
thf(57,plain,
! [A: $i] : ( A @ ( A @ ( multiplicative_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
d @ ( c @ ( b @ sum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
thf(29,plain,
d @ ( c @ ( b @ sum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,negated_conjecture,
~ ( additive_identity @ ( n @ ( l @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(28,plain,
~ ( additive_identity @ ( n @ ( l @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i] :
( ( A = additive_identity )
| ( multiplicative_identity @ ( A @ ( A @ h @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
thf(70,plain,
! [A: $i] :
( ( A = additive_identity )
| ( multiplicative_identity @ ( A @ ( A @ h @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,negated_conjecture,
n @ ( a @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
thf(32,plain,
n @ ( a @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_symmetry) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(50,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
l @ ( a @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
thf(31,plain,
l @ ( a @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] : ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(36,plain,
! [A: $i] : ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
additive_identity @ ( a @ ( d @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
thf(30,plain,
additive_identity @ ( a @ ( d @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_identity) ).
thf(51,plain,
! [A: $i] : ( A @ ( multiplicative_identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(68,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1847,plain,
$false,
inference(e,[status(thm)],[37,52,61,65,41,73,59,54,39,66,63,43,58,46,57,29,28,70,32,34,50,31,36,30,51,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % 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
% 0.16/5.42 % Computer : n017.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 05:46:54 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 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
% 1.32/6.24 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.84/6.55 % [INFO] Parsing done (306ms).
% 1.84/6.57 % [INFO] Running in sequential loop mode.
% 3.03/7.05 % [INFO] eprover registered as external prover.
% 3.03/7.06 % [INFO] Scanning for conjecture ...
% 3.34/7.20 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 3.34/7.25 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 3.34/7.29 % [INFO] Problem is propositional (TPTP CNF).
% 3.34/7.30 % [INFO] Type checking passed.
% 3.62/7.30 % [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 ...
% 18.12/10.46 % External prover 'e' found a proof!
% 18.12/10.46 % [INFO] Killing All external provers ...
% 18.12/10.46 % Time passed: 4828ms (effective reasoning time: 3878ms)
% 18.12/10.47 % Axioms used in derivation (22): addition_is_well_defined, clause31, commutativity_of_addition, additive_identity2, right_inverse, associativity_of_addition2, associativity_of_multiplication1, distributivity4, closure_of_addition, distributivity3, distributivity2, associativity_of_addition1, right_multiplicative_identity, additive_identity1, left_inverse, multiplication_is_well_defined, left_multiplicative_identity, associativity_of_multiplication2, distributivity1, product_symmetry, closure_of_multiplication, clause30
% 18.12/10.47 % No. of inferences in proof: 55
% 18.12/10.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4828 ms resp. 3878 ms w/o parsing
% 18.58/10.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.58/10.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------