%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 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 : n019.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 06:50:32 AM UTC 2026
% Result : Unsatisfiable 13.32s 4.24s
% Output : Refutation 13.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 164 ( 2 ~; 0 |; 0 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_decl,type,
d: $i > $i ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(cos_decl,type,
cos: $i > $i ).
thf('+_decl',type,
'+': $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(minus_decl,type,
minus: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(sin_decl,type,
sin: $i > $i ).
thf(6,axiom,
( ( one @ d )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_one) ).
thf(29,plain,
( ( one @ d )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ times ) )
= ( A @ ( B @ times ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_times) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ times ) )
= ( A @ ( B @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
( ( x @ d )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).
thf(45,plain,
( ( x @ d )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ '+' ) @ ( A @ '+' ) )
= ( C @ ( B @ ( A @ '+' ) @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ '+' ) @ ( A @ '+' ) )
= ( C @ ( B @ ( A @ '+' ) @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( zero @ times ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( zero @ times ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
( ( zero @ d )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_zero) ).
thf(39,plain,
( ( zero @ d )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ sin @ d )
= ( A @ d @ ( A @ cos @ times ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
thf(35,plain,
! [A: $i] :
( ( A @ sin @ d )
= ( A @ d @ ( A @ cos @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ d )
!= ( x @ cos @ ( x @ times ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(18,plain,
! [A: $i] :
( ( A @ d )
!= ( x @ cos @ ( x @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cos @ d )
= ( A @ d @ ( A @ sin @ times ) @ minus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
thf(31,plain,
! [A: $i] :
( ( A @ cos @ d )
= ( A @ d @ ( A @ sin @ times ) @ minus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( one @ times ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ times ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ minus @ ( A @ '+' ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).
thf(23,plain,
! [A: $i] :
( ( A @ minus @ ( A @ '+' ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ times ) @ d )
= ( A @ d @ ( B @ times ) @ ( B @ d @ ( A @ times ) @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ times ) @ d )
= ( A @ d @ ( B @ times ) @ ( B @ d @ ( A @ times ) @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) @ d )
= ( B @ d @ ( A @ d @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) @ d )
= ( B @ d @ ( A @ d @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ times ) @ ( A @ times ) )
= ( C @ ( B @ ( A @ times ) @ times ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_times) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ times ) @ ( A @ times ) )
= ( C @ ( B @ ( A @ times ) @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( zero @ '+' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( zero @ '+' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ '+' ) @ ( A @ times ) )
= ( C @ ( A @ times ) @ ( B @ ( A @ times ) @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ '+' ) @ ( A @ times ) )
= ( C @ ( A @ times ) @ ( B @ ( A @ times ) @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2667,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 22:14:18 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.16 % [INFO] Parsing done (188ms).
% 1.25/1.18 % [INFO] Running in sequential loop mode.
% 1.82/1.58 % [INFO] eprover registered as external prover.
% 1.82/1.59 % [INFO] Scanning for conjecture ...
% 2.02/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.19/1.75 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.19/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.19/1.78 % [INFO] Type checking passed.
% 2.19/1.78 % [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 ...
% 13.32/4.24 % External prover 'e' found a proof!
% 13.32/4.24 % [INFO] Killing All external provers ...
% 13.32/4.24 % Time passed: 3710ms (effective reasoning time: 3058ms)
% 13.32/4.24 % Axioms used in derivation (16): commutativity_of_plus, minus, derivative_of_times, derivative_of_zero, commutativity_of_times, derivative_of_cos, derivative_of_x, times_zero, derivative_of_sin, derivative_of_plus, associtivity_of_plus, distributivity, plus_zero, derivative_of_one, associativity_of_times, times_one
% 13.32/4.24 % No. of inferences in proof: 35
% 13.32/4.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3710 ms resp. 3058 ms w/o parsing
% 13.32/4.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.32/4.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------