%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n010.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 06:46:51 AM UTC 2026
% Result : Unsatisfiable 21.01s 6.38s
% Output : Refutation 21.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 12 ~; 8 |; 0 &; 74 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(t_a_decl,type,
t_a: $i ).
thf(v_cs_____decl,type,
v_cs____: $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(4,negated_conjecture,
! [A: $i] :
( ( A
= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( A @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_cs____ @ c_Polynomial_Odegree ) ) )
| ( ( t_a @ ( A @ ( v_x @ hAPP ) @ ( v_cs____ @ c_Polynomial_Opoly ) ) )
!= ( t_a @ ( A @ ( v_x @ hAPP ) @ ( A @ c_Polynomial_Opoly ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1062,plain,
! [A: $i] :
( ( A
= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( A @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_cs____ @ c_Polynomial_Odegree ) ) )
| ( ( t_a @ ( A @ ( v_x @ hAPP ) @ ( v_cs____ @ c_Polynomial_Opoly ) ) )
!= ( t_a @ ( A @ ( v_x @ hAPP ) @ ( A @ c_Polynomial_Opoly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1067,plain,
! [A: $i] :
( ( A
= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( A @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_cs____ @ c_Polynomial_Odegree ) ) )
| ( ( t_a @ ( A @ ( v_x @ hAPP ) @ ( v_cs____ @ c_Polynomial_Opoly ) ) )
!= ( t_a @ ( A @ ( v_x @ hAPP ) @ ( A @ c_Polynomial_Opoly ) ) ) ) ),
inference(cnf,[status(esa)],[1062]) ).
thf(1068,plain,
! [A: $i] :
( ( A
= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( t_a @ ( A @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_cs____ @ c_Polynomial_Odegree ) ) )
| ( ( t_a @ ( A @ ( v_x @ hAPP ) @ ( v_cs____ @ c_Polynomial_Opoly ) ) )
!= ( t_a @ ( A @ ( v_x @ hAPP ) @ ( A @ c_Polynomial_Opoly ) ) ) ) ),
inference(lifteq,[status(thm)],[1067]) ).
thf(3616,plain,
( ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero )
= v_cs____ ),
inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( v_cs____ ))]]) ).
thf(2,negated_conjecture,
( v_cs____
!= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1060,plain,
( v_cs____
!= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1063,plain,
( v_cs____
!= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(polarity_switch,[status(thm)],[1060]) ).
thf(1064,plain,
( ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero )
!= v_cs____ ),
inference(lifteq,[status(thm)],[1063]) ).
thf(3622,plain,
$false,
inference(simplifyReflect,[status(thm)],[3616,1064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.15/0.41 % Computer : n010.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 : Sat Sep 26 21:57:31 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.37/1.44 % [INFO] Parsing done (453ms).
% 2.37/1.46 % [INFO] Running in sequential loop mode.
% 3.30/1.85 % [INFO] eprover registered as external prover.
% 3.30/1.86 % [INFO] Scanning for conjecture ...
% 3.82/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 1278 axioms. Running axiom selection ...
% 5.92/2.55 % [INFO] Axiom selection finished. Selected 1054 axioms (removed 224 axioms).
% 7.47/2.90 % [INFO] Problem is propositional (TPTP CNF).
% 7.47/2.93 % [INFO] Type checking passed.
% 7.47/2.94 % [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 ...
% 21.01/6.37 % [INFO] Killing All external provers ...
% 21.01/6.37 % Time passed: 5827ms (effective reasoning time: 4905ms)
% 21.01/6.38 % Axioms used in derivation (0):
% 21.01/6.38 % No. of inferences in proof: 10
% 21.01/6.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5827 ms resp. 4905 ms w/o parsing
% 21.79/6.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.79/6.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------