TSTP Solution File: COL106-2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL106-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:29:37 EDT 2024
% Result : Unsatisfiable 3.29s 1.92s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 28
% Syntax : Number of formulae : 41 ( 9 unt; 16 typ; 0 def)
% Number of atoms : 55 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 454 ( 22 ~; 30 |; 0 &; 402 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 56 ( 0 ^ 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Comb_Ocomb_Oop_A_D_D_type,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(c_Comb_Ocomb_OK_type,type,
c_Comb_Ocomb_OK: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_ya_type,type,
v_ya: $i ).
thf(v_xb_type,type,
v_xb: $i ).
thf(tc_Comb_Ocomb_type,type,
tc_Comb_Ocomb: $i ).
thf(c_Comb_Oparcontract_type,type,
c_Comb_Oparcontract: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Comb_Ocomb_OS_type,type,
c_Comb_Ocomb_OS: $i ).
thf(v_sko__uTF_type,type,
v_sko__uTF: $i > $i > $i > $i ).
thf(v_sko__uTG_type,type,
v_sko__uTG: $i > $i > $i > $i ).
thf(v_sko__uTI_type,type,
v_sko__uTI: $i > $i > $i > $i ).
thf(v_sko__uTH_type,type,
v_sko__uTH: $i > $i > $i > $i ).
thf(v_sko__uTE_type,type,
v_sko__uTE: $i > $i > $i ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Comb_Ocomb_Oop_A_D_D @ A @ B )
!= ( c_Comb_Ocomb_Oop_A_D_D @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Comb_Ocomb_Oop_A_D_D @ A @ B )
!= ( c_Comb_Ocomb_Oop_A_D_D @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( c_in @ ( c_Pair @ v_xb @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ v_x @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Pair @ v_xb @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ v_x @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Comb_Ocomb_Oop_A_D_D @ A @ B )
!= ( c_Comb_Ocomb_Oop_A_D_D @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Comb_Ocomb_Oop_A_D_D @ A @ B )
!= ( c_Comb_Ocomb_Oop_A_D_D @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ v_x ) @ v_ya ) @ v_xb @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(13,plain,
c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ v_x ) @ v_ya ) @ v_xb @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( c_Comb_Ocomb_OK
!= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
thf(22,plain,
! [B: $i,A: $i] :
( c_Comb_Ocomb_OK
!= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B ) @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
thf(39,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B ) @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) @ C @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ C ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ ( v_sko__uTF @ A @ B @ C ) ) @ ( v_sko__uTG @ A @ B @ C ) ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ ( v_sko__uTI @ A @ B @ C ) @ ( v_sko__uTH @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_0) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) @ C @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ C ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ ( v_sko__uTF @ A @ B @ C ) ) @ ( v_sko__uTG @ A @ B @ C ) ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ ( v_sko__uTI @ A @ B @ C ) @ ( v_sko__uTH @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ C @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ C @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] : ( c_in @ ( c_Pair @ A @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
thf(38,plain,
! [A: $i] : ( c_in @ ( c_Pair @ A @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( B
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ ( v_sko__uTE @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_0) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( B
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ ( v_sko__uTE @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ A @ ( v_sko__uTE @ A @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_1) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ A ) @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ A @ ( v_sko__uTE @ A @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) @ C @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ A @ ( v_sko__uTI @ A @ B @ C ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ C ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ ( v_sko__uTF @ A @ B @ C ) ) @ ( v_sko__uTG @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_2) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) @ C @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ A @ ( v_sko__uTI @ A @ B @ C ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( C
= ( c_Comb_Ocomb_Oop_A_D_D @ A @ B ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ C ) )
| ( A
= ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ ( v_sko__uTF @ A @ B @ C ) ) @ ( v_sko__uTG @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[25,14,29,13,22,39,16,40,38,33,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL106-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 14:02:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (127ms).
% 1.21/0.99 % [INFO] Running in sequential loop mode.
% 1.67/1.22 % [INFO] eprover registered as external prover.
% 1.67/1.22 % [INFO] cvc4 registered as external prover.
% 1.67/1.22 % [INFO] Scanning for conjecture ...
% 1.81/1.29 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.81/1.32 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.81/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 1.81/1.37 % [INFO] Type checking passed.
% 1.81/1.38 % [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 ...
% 3.29/1.92 % External prover 'e' found a proof!
% 3.29/1.92 % [INFO] Killing All external provers ...
% 3.29/1.92 % Time passed: 1404ms (effective reasoning time: 931ms)
% 3.29/1.92 % 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)>
% 3.29/1.92 % Axioms used in derivation (10): cls_Comb_Oparcontract_Ointros__4_0, cls_Comb_OAp__parcontractE_0, cls_Comb_Ocomb_Oinject__iff1_0, cls_Comb_OK1__parcontractD__dest_1, cls_Comb_Oparcontract_Ointros__1_0, cls_Comb_Ocomb_Odistinct__3__iff1_0, cls_Comb_Oparcontract_Ointros__2_0, cls_Comb_OK1__parcontractD__dest_0, cls_Comb_OAp__parcontractE_2, cls_Comb_Ocomb_Oinject__iff1_1
% 3.29/1.92 % No. of inferences in proof: 25
% 3.29/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1404 ms resp. 931 ms w/o parsing
% 3.45/1.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------