%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA100^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n014.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 07:45:46 AM UTC 2026
% Result : Theorem 7.95s 3.42s
% Output : Refutation 8.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 45 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 246 ( 17 ~; 3 |; 0 &; 226 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 22 ^; 45 !; 0 ?; 70 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(sk1_decl,type,
sk1: skt1 > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/realax/real' ).
thf(sk3_decl,type,
sk3: skt1 > $o ).
thf(sk4_decl,type,
sk4: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: 'type/realax/real',C: skt1 > $o] :
( ( 'const/iterate/sum' @ skt1 @ C
@ ^ [D: skt1] : ( 'const/realax/real_mul' @ ( A @ D ) @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ C @ A ) @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
~ ! [B: skt1 > $o] :
( ( 'const/iterate/sum' @ skt1 @ B
@ ^ [C: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ A ) )
= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ B @ sk1 ) @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1 > $o] :
( ( 'const/iterate/sum' @ skt1 @ A
@ ^ [B: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ B ) @ sk2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) @ sk2 ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: 'type/realax/real',C: TA > $o] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ B @ ( A @ D ) ) )
= ( 'const/realax/real_mul' @ B @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_LMUL_') ).
thf(8,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: 'type/realax/real',C: TA > $o] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ B @ ( A @ D ) ) )
= ( 'const/realax/real_mul' @ B @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,C: TA > $o,B: 'type/realax/real',A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ B @ ( A @ D ) ) )
= ( 'const/realax/real_mul' @ B @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,C: TA > $o,B: 'type/realax/real',A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ B @ ( A @ D ) ) )
= ( 'const/realax/real_mul' @ B @ ( 'const/iterate/sum' @ TA @ C @ A ) ) ),
inference(lifteq,[status(thm)],[9]) ).
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/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_MUL_SYM_') ).
thf(11,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(12,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)],[11]) ).
thf(13,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)],[12]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > 'type/realax/real',B: 'type/realax/real',C: TA > $o] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ ( A @ D ) @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_RMUL_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: 'type/realax/real',C: TA > $o] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ ( A @ D ) @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: 'type/realax/real',C: TA > $o] :
( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ ( A @ D ) @ B ) )
= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ B @ A )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [C: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ C ) @ sk2 ) ) )
| ( ( 'const/realax/real_mul' @ A @ B )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(15,plain,
( ( 'const/realax/real_mul' @ sk2 @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(37,plain,
! [TA: $tType,C: TA > $o,B: 'type/realax/real',A: TA > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_mul' @ B @ ( A @ D ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [D: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ D ) @ sk2 ) ) )
| ( ( 'const/realax/real_mul' @ B @ ( 'const/iterate/sum' @ TA @ C @ A ) )
!= ( 'const/realax/real_mul' @ sk2 @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,15]) ).
thf(38,plain,
( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(50,plain,
( ( sk3 != sk3 )
| ( ( ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) )
!= ( ^ [A: skt1] : ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ A ) ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(52,plain,
( ( ^ [A: skt1] : ( 'const/realax/real_mul' @ ( sk1 @ A ) @ sk2 ) )
!= ( ^ [A: skt1] : ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(101,plain,
( ( 'const/realax/real_mul' @ ( sk1 @ sk4 ) @ sk2 )
!= ( 'const/realax/real_mul' @ sk2 @ ( sk1 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[52]) ).
thf(104,plain,
$false,
inference(simplifyReflect,[status(thm)],[101,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA100^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.11/0.25 % Computer : n014.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 17:41:14 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.26 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
% 0.95/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.03 % [INFO] Parsing done (245ms).
% 1.61/1.04 % [INFO] Running in sequential loop mode.
% 2.39/1.53 % [INFO] eprover registered as external prover.
% 2.39/1.54 % [INFO] Scanning for conjecture ...
% 2.55/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.71/1.73 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.71/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.75 % [INFO] Type checking passed.
% 2.71/1.75 % [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 ...
% 7.95/3.41 % [INFO] Killing All external provers ...
% 7.95/3.42 % Time passed: 2999ms (effective reasoning time: 2368ms)
% 7.95/3.42 % 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)>
% 7.95/3.42 % Axioms used in derivation (2): thm/iterate/SUM_LMUL_, thm/realax/REAL_MUL_SYM_
% 7.95/3.42 % No. of inferences in proof: 21
% 7.95/3.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2999 ms resp. 2368 ms w/o parsing
% 8.39/3.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.39/3.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------