%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n001.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 : Wed Sep 30 07:45:49 AM UTC 2026
% Result : Theorem 7.42s 3.29s
% Output : Refutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 57 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 209 ( 27 ~; 9 |; 1 &; 164 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 26 ^; 43 !; 0 ?; 71 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/iterate/polynomial_function_decl',type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/realax/real' ).
thf(sk9_decl,type,
sk9: 'type/realax/real' > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > 'type/realax/real'] :
~ ( ( 'const/iterate/polynomial_function' @ A )
=> ! [B: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
~ ( 'const/iterate/polynomial_function'
@ ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ A ) ) ) ) ).
thf(4,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ B )
= ( 'const/realax/real_mul' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_MUL_SYM_') ).
thf(13,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ B )
= ( 'const/realax/real_mul' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ B )
= ( 'const/realax/real_mul' @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ A @ B )
= ( 'const/realax/real_mul' @ B @ A ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(1,conjecture,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ! [B: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( A @ C ) @ B ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
( ( 'const/iterate/polynomial_function' @ sk1 )
& ~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
'const/iterate/polynomial_function' @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
thf(3,axiom,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(10,plain,
! [A: 'type/realax/real' > 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ A )
=> ! [B: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) ) ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(9,plain,
~ ( 'const/iterate/polynomial_function'
@ ^ [A: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(20,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ~ $true
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(21,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ( ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( 'const/iterate/polynomial_function'
@ ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(28,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ A )
| ( ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(36,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ~ $true
| ( ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) )
| ( ( 'const/iterate/polynomial_function' @ sk1 )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,28]) ).
thf(37,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > 'type/realax/real'] :
( ( ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ B @ ( A @ C ) ) )
!= ( ^ [C: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) )
| ( ( 'const/iterate/polynomial_function' @ sk1 )
!= ( 'const/iterate/polynomial_function' @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [A: 'type/realax/real'] :
( ( ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( sk1 @ B ) ) )
!= ( ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(40,plain,
! [A: 'type/realax/real'] :
( ( ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ A @ ( sk1 @ B ) ) )
!= ( ^ [B: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ sk2 ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(74,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( sk1 @ ( sk9 @ A ) ) @ sk2 )
!= ( 'const/realax/real_mul' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(func_ext,[status(esa)],[40]) ).
thf(218,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ B @ A )
!= ( 'const/realax/real_mul' @ C @ ( sk1 @ ( sk9 @ C ) ) ) )
| ( ( 'const/realax/real_mul' @ A @ B )
!= ( 'const/realax/real_mul' @ ( sk1 @ ( sk9 @ C ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,74]) ).
thf(219,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ ( sk9 @ A ) ) )
!= ( 'const/realax/real_mul' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( sk1 @ ( sk9 @ E ) )),bind(B,$thf( sk2 )),bind(C,$thf( E ))]]) ).
thf(222,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ ( sk9 @ A ) ) )
!= ( 'const/realax/real_mul' @ A @ ( sk1 @ ( sk9 @ A ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(227,plain,
$false,
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.16/0.27 % Computer : n001.cluster.edu
% 0.16/0.27 % Model : x86_64 x86_64
% 0.16/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.27 % Memory : 8046.5625MB
% 0.16/0.27 % OS : Linux 6.8.0-71-generic
% 0.16/0.27 % CPULimit : 300
% 0.16/0.27 % WCLimit : 300
% 0.16/0.27 % DateTime : Tue Sep 29 17:50:42 UTC 2026
% 0.16/0.27 % CPUTime :
% 0.16/0.27 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
% 0.91/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.05 % [INFO] Parsing done (179ms).
% 1.28/1.06 % [INFO] Running in sequential loop mode.
% 1.78/1.46 % [INFO] eprover registered as external prover.
% 1.78/1.47 % [INFO] Scanning for conjecture ...
% 1.96/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.96/1.59 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.11/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.61 % [INFO] Type checking passed.
% 2.11/1.61 % [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 ...
% 7.42/3.29 % [INFO] Killing All external provers ...
% 7.42/3.29 % Time passed: 2867ms (effective reasoning time: 2219ms)
% 7.42/3.29 % 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)>
% 7.42/3.29 % Axioms used in derivation (2): thm/realax/REAL_MUL_SYM_, thm/iterate/POLYNOMIAL_FUNCTION_LMUL_
% 7.42/3.29 % No. of inferences in proof: 27
% 7.42/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2867 ms resp. 2219 ms w/o parsing
% 7.98/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.98/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------